3
Geometry, compatibility and structure preservation in computational differential equations
http://sms.cam.ac.uk/collection/3028099
Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive allpurpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purposebuilt algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a largescale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of spacetime discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics.
1440
2019
Mon, 16 Dec 2019 16:06:02 +0000
Wed, 17 Jul 2019 14:42:03 +0100
en
smssupport@ucs.cam.ac.uk
Geometry, compatibility and structure preservation in computational differential equations
http://sms.cam.ac.uk/collection/3028099
http://rss.sms.cam.ac.uk/itunesimage/3103513.jpg
http://video.search.yahoo.com/mrss
Geometry, compatibility and structure preservation in computational differential equations
Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive allpurpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purposebuilt algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a largescale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of spacetime discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics.
Geometry, compatibility and structure preservation in computational differential equations
Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive allpurpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purposebuilt algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a largescale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of spacetime discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics.
Cambridge University
K. Kher
http://sms.cam.ac.uk/collection/3028099
Geometry, compatibility and structure preservation in computational differential equations
20190717T14:42:03+01:00
INIMS
002281
no

Computational Challenges in Numerical Relativity
ucs_sms_3028099_3071216
http://sms.cam.ac.uk/media/3071216
Computational Challenges in Numerical Relativity
Pretorius, F
Monday 30th September 2019  16:00 to 17:00
Mon, 30 Sep 2019 17:27:46 +0100
Isaac Newton Institute
Pretorius, F
cd2a54f778099decb614302c2e7a2db2
979bc9c3b936f6e90f9f1d3bdc806104
de29727e12e3378a157efb5ecea058bc
545608e63f66795b0fde8351466994c3
Pretorius, F
Monday 30th September 2019  16:00 to 17:00
Pretorius, F
Monday 30th September 2019  16:00 to 17:00
Cambridge University
3840
http://sms.cam.ac.uk/media/3071216
Computational Challenges in Numerical Relativity
Pretorius, F
Monday 30th September 2019  16:00 to 17:00
I will give a brief overview of the some of the challenges in computational solution of the Einstein field equations.I will then describe the background error subtraction technique, designed to allow for more computationally efficient solution of scenarios where a significant portion of the domain is close to a know, exact solution. To demonstrate, I will discuss application to tidal disruption of a star by a supermassive black hole, and studies of black hole superradiance.
20190930T17:27:46+01:00
3840
3071216
true
16x9
false
no

Equivariance and structure preservation in numerical methods; some cases and viewpoints
ucs_sms_3028099_3124317
http://sms.cam.ac.uk/media/3124317
Equivariance and structure preservation in numerical methods; some cases and viewpoints
Owren, B
Wednesday 11th December 2019  15:05 to 15:50
Mon, 16 Dec 2019 16:06:02 +0000
Isaac Newton Institute
Owren, B
c564e0df6f840a57617334f3473e4ab5
908282ec48dd5793ea9f18cb7867f7c8
dc77af6dc36fc473f1ec77e7c6e55636
6e536cec195204157e95c30f0bf0261f
Owren, B
Wednesday 11th December 2019  15:05 to 15:50
Owren, B
Wednesday 11th December 2019  15:05 to 15:50
Cambridge University
3178
http://sms.cam.ac.uk/media/3124317
Equivariance and structure preservation in numerical methods; some cases and viewpoints
Owren, B
Wednesday 11th December 2019  15:05 to 15:50
Our point of departure is the situation when there is a group of transformations acting both on our problem space and on the space in which our computations are produced. Equivariance happens when the map from the problem space to the computation space, i.e. our numerical method, commutes with the group action. This is a rather general and vague definition, but we shall make it precise and consider a few concrete examples in the talk. In some cases, the equivariance property is natural, in other cases it is something that we want to impose in the numerical method in order to obtain computational schemes with certain desired structure preserving qualities. Many of the examples we present will be related to the numerical solution of differential equations and we may also present some recent examples from artificial neural networks and discrete integrable systems. This is work in progress and it summarises some of the ideas the speaker has been discussing with other participants this autumn.
20191216T16:06:02+00:00
3178
3124317
true
16x9
false
no

General Relativity: One Block at a Time
ucs_sms_3028099_3073190
http://sms.cam.ac.uk/media/3073190
General Relativity: One Block at a Time
Miller, W
Thursday 3rd October 2019  13:30 to 14:30
Thu, 03 Oct 2019 14:40:52 +0100
Isaac Newton Institute
Miller, W
82bbf81867c55a798692c99cb0b6a1eb
1f9cffde38e1ff5bb95a6c036693070d
a448dfc180e6a4f94b3ae6978e89c9d3
0e219d16f43dd05d131b86645eb5ff78
Miller, W
Thursday 3rd October 2019  13:30 to 14:30
Miller, W
Thursday 3rd October 2019  13:30 to 14:30
Cambridge University
3900
http://sms.cam.ac.uk/media/3073190
General Relativity: One Block at a Time
Miller, W
Thursday 3rd October 2019  13:30 to 14:30
This talk will provide an overview and motivation for Regge calculus (RC). We will highlight our insights into unique features of building GR on a discrete geometry in regards to structure preservation, and highlight some relative strengths and weaknesses of RC. We will review some numerical applications of RC, including our more recent work on discrete Ricci flow.
20191003T14:40:52+01:00
3900
3073190
true
16x9
false
no

Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.
ucs_sms_3028099_3105521
http://sms.cam.ac.uk/media/3105521
Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.
Barp, A
Thursday 21st November 2019  13:05 to 13:45
Fri, 22 Nov 2019 12:21:00 +0000
Isaac Newton Institute
Barp, A
2427f78e4c3bd735bedd84f9ea730592
d65c62a645befb00095f4c54e9e63a77
b3d526c160596fa1914328e67c07d7ef
922a0280c96c27192604fdc3960eb54a
Barp, A
Thursday 21st November 2019  13:05 to 13:45
Barp, A
Thursday 21st November 2019  13:05 to 13:45
Cambridge University
2334
http://sms.cam.ac.uk/media/3105521
Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.
Barp, A
Thursday 21st November 2019  13:05 to 13:45
20191122T12:21:00+00:00
2334
3105521
true
16x9
false
no

Hyperbolicity and boundary conditions.
ucs_sms_3028099_3071760
http://sms.cam.ac.uk/media/3071760
Hyperbolicity and boundary conditions.
Reula, O
Tuesday 1st October 2019  13:30 to 14:30
Tue, 01 Oct 2019 14:35:48 +0100
Isaac Newton Institute
Reula, O
c4cd1b3721458facfede318812d366e8
1532b90e3170a038e83a3fe1776e820f
13497efa5592fbbcb69f4d84e7dfa7b6
e2164f99e42b94c7a7981de582090707
Reula, O
Tuesday 1st October 2019  13:30 to 14:30
Reula, O
Tuesday 1st October 2019  13:30 to 14:30
Cambridge University
3600
http://sms.cam.ac.uk/media/3071760
Hyperbolicity and boundary conditions.
Reula, O
Tuesday 1st October 2019  13:30 to 14:30
Abstract: (In collaboration with Fernando Abalos.) Very often in physics, the evolution systems we have to deal with are not purely hyperbolic, but contain also constraints and gauge freedoms. After fixing these gauge freedoms we obtain a new system with constraints which we want to solve subject to initial and boundary values. In particular, these values have to imply the correct propagation of constraints. In general, after fixing some reduction to a purely evolutionary system, this is asserting by computing by hand what is called the constraint subsidiary system, namely a system which is satisfied by the constraints quantities when the fields satisfy the reduced evolution system. If the subsidiary system is also hyperbolic then for the initial data case the situation is clear: we need to impose the constraints on the initial data and then they will correctly propagate along evolution. For the boundary data, we need to impose the constraint for all incoming constraint modes. These must be done by fixing some of the otherwise free boundary data, that is the incoming modes. Thus, there must be a relation between some of the incoming modes of the evolution system and all the incoming modes of the constraint subsidiary system. Under certain conditions on the constraints, this relation is known and understood, but those conditions are very restrictive. In this talk, we shall review the known results and discuss what is known so far for the general case and what are the open questions that still remain.
20191001T14:35:48+01:00
3600
3071760
true
16x9
false
no

New prospects in numerical relativity
ucs_sms_3028099_3072353
http://sms.cam.ac.uk/media/3072353
New prospects in numerical relativity
Witek, H
Wednesday 2nd October 2019  13:30 to 14:30
Wed, 02 Oct 2019 14:35:05 +0100
Isaac Newton Institute
Witek, H
259b563b4b00b7123e1ea1bc8f233d54
cd93b8d5e2220252399d2cff8b9c3a24
c2ac406cb4369831ed8520c65ab56e5a
78f0fe5474011e326f9c10bc1f36570d
Witek, H
Wednesday 2nd October 2019  13:30 to 14:30
Witek, H
Wednesday 2nd October 2019  13:30 to 14:30
Cambridge University
3536
http://sms.cam.ac.uk/media/3072353
New prospects in numerical relativity
Witek, H
Wednesday 2nd October 2019  13:30 to 14:30
Both observations and deeply theoretical considerations indicate that general relativity, our elegant standard model of gravity, requires modifications at high curvatures scales. Candidate theories of quantum gravity, in their lowenergy limit, typically predict couplings to additional fields or extensions that involve higher curvature terms. At the same time, the breakthrough discovery of gravitational waves has provided a new channel to probe gravity in its most extreme, strongfield regime. Modelling the expected gravitational radiation in these extensions of general relativity enables us to search for  or place novel observational bounds on  deviations from our standard model. In this talk I will give an overview of the recent progress on simulating binary collisions in these situations and address renewed mathematical challenges such as wellposedness of the underlying initial value formulation.
20191002T14:35:05+01:00
3536
3072353
true
16x9
false
no

Numerical relativity beyond astrophysics: new challenges and new dynamics
ucs_sms_3028099_3071106
http://sms.cam.ac.uk/media/3071106
Numerical relativity beyond astrophysics: new challenges and new dynamics
Figueras, P
Monday 30th September 2019  13:30 to 14:30
Mon, 30 Sep 2019 14:39:07 +0100
Isaac Newton Institute
Figueras, P
2243225c6ab1bf9d6d12d3b2a3024746
605bc11461d32b1ad446d946d943a77c
fcadec79f2bbc859275b610dae1486ee
37b5467ac3f5c41dc13ae85c9a689624
Figueras, P
Monday 30th September 2019  13:30 to 14:30
Figueras, P
Monday 30th September 2019  13:30 to 14:30
Cambridge University
3600
http://sms.cam.ac.uk/media/3071106
Numerical relativity beyond astrophysics: new challenges and new dynamics
Figueras, P
Monday 30th September 2019  13:30 to 14:30
Motivated by more fundamental theories of gravity such as string theory, in recent years there has been a growing interesting in solving the Einstein equations numerically beyond the traditional astrophysical set up. For instance in spacetime dimensions higher than the four that we have observed, or in exotic spaces such as antide Sitter spaces. In this talk I will give an overview of the challenges that are often encountered when solving the Einstein equations in these new settings. In the second part of the talk I will provide some examples, such as the dynamics of unstable black holes in higher dimensions and gravitational collapse in antide Sitter spaces.
20190930T14:39:07+01:00
3600
3071106
true
16x9
false
no

Optimal control and the geometry of integrable systems
ucs_sms_3028099_3036842
http://sms.cam.ac.uk/media/3036842
Optimal control and the geometry of integrable systems
Bloch, A
Wednesday 31st July 2019  15:00 to 16:00
Thu, 01 Aug 2019 14:36:30 +0100
Isaac Newton Institute
Bloch, A
3fe8298338e4ee54eda4d46363c643aa
2b65bf42805791cca3868fffefcf29b4
9c44a9975d9faaec381d792bed2e655f
6cdf188607f61e49212afeaacee2516d
Bloch, A
Wednesday 31st July 2019  15:00 to 16:00
Bloch, A
Wednesday 31st July 2019  15:00 to 16:00
Cambridge University
3525
http://sms.cam.ac.uk/media/3036842
Optimal control and the geometry of integrable systems
Bloch, A
Wednesday 31st July 2019  15:00 to 16:00
In this talk we discuss a geometric approach to certain optimal control
problems and discuss the relationship of the solutions of these problem
to some classical integrable dynamical systems and their generalizations.
We consider the
socalled Clebsch optimal control problem and its relationship
to Lie group actions on manifolds. The integrable systems discussed include
the rigid body equations, geodesic flows on the ellipsoid, flows
on Stiefel manifolds, and the Toda lattice
flows. We discuss the Hamiltonian structure of these systems and relate
our work to some work of Moser. We also discuss the link to discrete dynamics
and symplectic integration.
20190801T14:36:30+01:00
3525
3036842
true
16x9
false
no

Putting Infinity on the Grid
ucs_sms_3028099_3072957
http://sms.cam.ac.uk/media/3072957
Putting Infinity on the Grid
Hilditch, D
Thursday 3rd October 2019  11:00 to 12:00
Thu, 03 Oct 2019 12:06:01 +0100
Isaac Newton Institute
Hilditch, D
bd352b6a06024d5faca207ed84b95ba3
3d841fde98dbec0ecec123bd13ff812d
da6c0cd130375e423a2989fdd1ecf8aa
4df7308ea2ca75f1d133d8ca12974843
Hilditch, D
Thursday 3rd October 2019  11:00 to 12:00
Hilditch, D
Thursday 3rd October 2019  11:00 to 12:00
Cambridge University
3600
http://sms.cam.ac.uk/media/3072957
Putting Infinity on the Grid
Hilditch, D
Thursday 3rd October 2019  11:00 to 12:00
I will talk about an ongoing research program relying on a dual frame approach to treat numerically the field equations of GR (in generalized harmonic gauge) on compactified hyperboloidal slices. These slices terminate at futurenull infinity, and the hope is to eventually extract gravitational waves from simulations there. The main obstacle to their use is the presence of 'infinities' coming from the compactified coordinates, which have to somehow interact well with the assumption of asymptotic flatness so that we may arrive at regular equations for regular unknowns. I will present a new 'subtract the logs' regularization strategy for a toy nonlinear wave equation that achieves this goal.
20191003T12:06:01+01:00
3600
3072957
true
16x9
false
no

Some Research Problems in Mathematical and Numerical General Relativity
ucs_sms_3028099_3071547
http://sms.cam.ac.uk/media/3071547
Some Research Problems in Mathematical and Numerical General Relativity
Holst, M
Monday 30th September 2019  11:00 to 12:00
Tue, 01 Oct 2019 09:29:14 +0100
Isaac Newton Institute
Holst, M
3323e902a275492ee67a983338f3b980
aee04f18f7d334b98c1e2505b2f34274
491b8f42b48aee6ff3f05b799d66e711
f7c8525ecc45f7fcaa52e82584ecd6e2
Holst, M
Monday 30th September 2019  11:00 to 12:00
Holst, M
Monday 30th September 2019  11:00 to 12:00
Cambridge University
3780
http://sms.cam.ac.uk/media/3071547
Some Research Problems in Mathematical and Numerical General Relativity
Holst, M
Monday 30th September 2019  11:00 to 12:00
The 2017 Nobel Prize in Physics was awarded to three of the key scientists involved in the development of LIGO and its eventual successful first detections of gravitational waves. How do LIGO (and other gravitational wave detector) scientists know what they are detecting? The answer is that the signals detected by the devices are shown, after extensive data analysis and numerical simulations of the Einstein equations, to be a very close match to computer simulations of wave emission from very particular types of binary collisions. In this lecture, we begin with a brief overview of the mathematical formulation of Einstein (evolution and constraint) equations, and then focus on some fundamental mathematics research questions involving the Einstein constraint equations. We begin with a look at the most useful mathematical formulation of the constraint equations, and then summarize the known existence, uniqueness, and multiplicity results through 2009. We then present a number of new existence and multiplicity results developed since 2009 that substantially change the solution theory for the constraint equations. In the second part of the talk, we consider approaches for developing "provably good" numerical methods for solving these types of geometric PDE systems on 2 and 3manifolds. We examine how one proves rigorous error estimates for particular classes of numerical methods, including both classical finite element methods and newer methods from the finite element exterior calculus. This lecture will touch on several joint projects that span more than a decade, involving a number of collaborators. The lecture is intended both for mathematicians interested in potential research problems in mathematical and numerical general relativity, as well as physicists interested in relevant new developments in mathematical and numerical methods for nonlinear geometric PDE.
20191001T09:29:14+01:00
3780
3071547
true
16x9
false
no

Structurepreserving time discretization: lessons for numerical relativity?
ucs_sms_3028099_3071157
http://sms.cam.ac.uk/media/3071157
Structurepreserving time discretization: lessons for numerical relativity?
Stern, A
Monday 30th September 2019  14:30 to 15:30
Mon, 30 Sep 2019 15:45:51 +0100
Isaac Newton Institute
Stern, A
dcc5b4ed737fe671529cbdbe2274a2fd
79e6ff817524c3590bccfe0274c637cd
912505a93dc0335a89788990c65aae8a
9acd3e4f2acf05bf36d77e32dbcd59c0
Stern, A
Monday 30th September 2019  14:30 to 15:30
Stern, A
Monday 30th September 2019  14:30 to 15:30
Cambridge University
3570
http://sms.cam.ac.uk/media/3071157
Structurepreserving time discretization: lessons for numerical relativity?
Stern, A
Monday 30th September 2019  14:30 to 15:30
In numerical ODEs, there is a rich literature on methods that preserve certain geometric structures arising in physical systems, such as Hamiltonian/symplectic structure, symmetries, and conservation laws. I will give an introduction to these methods and discuss recent work extending some of these ideas to numerical PDEs in classical field theory.
20190930T15:45:51+01:00
3570
3071157
true
16x9
false
no

Tetrad methods in numerical relativity
ucs_sms_3028099_3074059
http://sms.cam.ac.uk/media/3074059
Tetrad methods in numerical relativity
Garfinkle, D
Friday 4th October 2019  16:00 to 17:00
Fri, 04 Oct 2019 17:15:40 +0100
Isaac Newton Institute
Garfinkle, D
d39abe52cd1e6b823c475209925a1829
ce714d4b87448f973866e4d9a0e98d96
361ce4c96fb6faea611ca12e545ebfde
114cad30d1dab0399bffe1e2a4df2725
Garfinkle, D
Friday 4th October 2019  16:00 to 17:00
Garfinkle, D
Friday 4th October 2019  16:00 to 17:00
Cambridge University
4080
http://sms.cam.ac.uk/media/3074059
Tetrad methods in numerical relativity
Garfinkle, D
Friday 4th October 2019  16:00 to 17:00
Most numerical relativity simulations use the usual coordinate methods to put the Einstein field equations in the form of partial differential equations (PDE), which are then handled using more or less standard numerical PDE methods, such as finite differences. However, there are some advantages to instead using a tetrad (orthonormal) basis rather than the usual coordinate basis. I will present the tetrad method and its numerical uses, particularly for simulating the approach to a spacetime singularity. I will end with open questions about which tetrad systems are suitable for numerical simulations.
20191004T17:15:40+01:00
4080
3074059
true
16x9
false
no

Variational discretizations of gauge field theories using groupequivariant interpolation spaces
ucs_sms_3028099_3071682
http://sms.cam.ac.uk/media/3071682
Variational discretizations of gauge field theories using groupequivariant interpolation spaces
Leok, M
Tuesday 1st October 2019  11:00 to 12:00
Tue, 01 Oct 2019 12:03:02 +0100
Isaac Newton Institute
Leok, M
ef8fd2368c3a1477b969519161e5c026
f4cb8d07063f135d67cfb4b51ff1c0ab
a5145c56938dd0b7b3cc990ff2d1199e
bd0770b95f7fc4dfb647eda7c908aef5
Leok, M
Tuesday 1st October 2019  11:00 to 12:00
Leok, M
Tuesday 1st October 2019  11:00 to 12:00
Cambridge University
3600
http://sms.cam.ac.uk/media/3071682
Variational discretizations of gauge field theories using groupequivariant interpolation spaces
Leok, M
Tuesday 1st October 2019  11:00 to 12:00
Variational integrators are geometric structurepreserving numerical methods that preserve the symplectic structure, satisfy a discrete Noether's theorem, and exhibit exhibit excellent longtime energy stability properties. An exact discrete Lagrangian arises from Jacobi's solution of the HamiltonJacobi equation, and it generates the exact flow of a Lagrangian system. By approximating the exact discrete Lagrangian using an appropriate choice of interpolation space and quadrature rule, we obtain a systematic approach for constructing variational integrators. The convergence rates of such variational integrators are related to the best approximation properties of the interpolation space. Many gauge field theories can be formulated variationally using a multisymplectic Lagrangian formulation, and we will present a characterization of the exact generating functionals that generate the multisymplectic relation. By discretizing these using groupequivariant spacetime finite element spaces, we obtain methods that exhibit a discrete multimomentum conservation law. We will then briefly describe an approach for constructing groupequivariant interpolation spaces that take values in the space of Lorentzian metrics that can be efficiently computed using a generalized polar decomposition. The goal is to eventually apply this to the construction of variational discretizations of general relativity, which is a secondorder gauge field theory whose configuration manifold is the space of Lorentzian metrics.
20191001T12:03:02+01:00
3600
3071682
true
16x9
false
no

A Monte Carlo method to sample a Stratification
ucs_sms_3028099_3104885
http://sms.cam.ac.uk/media/3104885
A Monte Carlo method to sample a Stratification
HolmesCefron, M
Wednesday 20th November 2019  15:40 to 16:10
Thu, 21 Nov 2019 15:42:10 +0000
Isaac Newton Institute
HolmesCefron, M
5c49386fc424ca210145ab467f914066
04c760a1c7edaabf97db615eecc15735
7876b4bbc4f8abb7067299243a6a5655
30808c51f9d176ab00761fcb59758407
HolmesCefron, M
Wednesday 20th November 2019  15:40 to 16:10
HolmesCefron, M
Wednesday 20th November 2019  15:40 to 16:10
Cambridge University
2688
http://sms.cam.ac.uk/media/3104885
A Monte Carlo method to sample a Stratification
HolmesCefron, M
Wednesday 20th November 2019  15:40 to 16:10
Many problems in materials science and biology involve particles interacting with strong, shortranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. Abstractly, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lowerdimensional manifolds lie on the boundaries of the higherdimensional manifolds. We show several applications in polymer physics, selfassembly of colloids, and volume calculation.
20191121T15:42:11+00:00
2688
3104885
true
16x9
false
no

A new wavetowire waveenergy model: from variational principle to compatible spacetime discretisation
ucs_sms_3028099_3032279
http://sms.cam.ac.uk/media/3032279
A new wavetowire waveenergy model: from variational principle to compatible spacetime discretisation
Bokhove, O
Wednesday 24th July 2019  15:00 to 16:00
Wed, 24 Jul 2019 16:29:47 +0100
Isaac Newton Institute
Bokhove, O
0c6dc45bb6a746ae30e6d477d8fb8926
17fa03ccf8c443a2a22b82f4baf864b1
7495549b2939c41eaf28837592ca32e8
9ed60979134720ddc9496e538fe5d133
Bokhove, O
Wednesday 24th July 2019  15:00 to 16:00
Bokhove, O
Wednesday 24th July 2019  15:00 to 16:00
Cambridge University
3128
http://sms.cam.ac.uk/media/3032279
A new wavetowire waveenergy model: from variational principle to compatible spacetime discretisation
Bokhove, O
Wednesday 24th July 2019  15:00 to 16:00
Amplification phenomena in a socalled boresolitonsplash have led us to develop a novel waveenergy device with wave amplification in a contraction used to enhance waveactivated buoy motion and magneticallyinduced energy generation. An experimental proofofprinciple shows that our waveenergy device works. Most importantly, we develop a novel wavetowire mathematical model of the combined wave hydrodynamics, waveactivated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is subtly solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LEDloads, are added a posteriori. New is also the intricate and compatible (finiteelement) spacetime discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised waveenergy model are encouraging, yet suboptimal, and involve a first study of the resonant behaviour and parameter dependence of the device.
20190724T16:29:47+01:00
3128
3032279
true
16x9
false
no

A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
ucs_sms_3028099_3093861
http://sms.cam.ac.uk/media/3093861
A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Mon, 04 Nov 2019 11:29:59 +0000
Isaac Newton Institute
Farrell, P
a1e3e266523966c912cec73befaaf554
0cd8590c6ceac0beae5dec0390fb8f90
1039cf25c9ccbc255da39b550c1c3fc0
2b96caab40164244c8ab806a49734311
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Cambridge University
2960
http://sms.cam.ac.uk/media/3093861
A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. Achieving this for the stationary NavierStokes has proven challenging: LU factorisation is Reynoldsrobust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased. Building on ideas of Schöberl, Xu, Zikatanov, Benzi & Olshanskii, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier–Stokes equations in three dimensions that achieves both optimal complexity and Reynoldsrobustness. The scheme combines augmented Lagrangian stabilisation to control the Schur complement, the convection stabilisation proposed by Douglas & Dupont, a divergencecapturing additive Schwarz relaxation method on each level, and a specialised prolongation operator involving nonoverlapping local Stokes solves. The properties of the preconditioner are tailored to the divergencefree CG(k)DG(k1) discretisation and the appropriate relaxation is derived from considerations of finite element exterior calculus. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds numbers 10 to 5000.
20191104T11:29:59+00:00
2960
3093861
true
16x9
false
no

A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
ucs_sms_3028099_3095934
http://sms.cam.ac.uk/media/3095934
A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Thu, 07 Nov 2019 09:35:35 +0000
Isaac Newton Institute
Farrell, P
868be37b494bf964e9f98e921719c82a
2d1c68b4a67463ddefbc52150db700a3
adcf28ea1fe9a903eb0412d77f2ee3ca
2b96caab40164244c8ab806a49734311
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
Cambridge University
2960
http://sms.cam.ac.uk/media/3095934
A Reynoldsrobust preconditioner for the 3D stationary NavierStokes equations
Farrell, P
Thursday 31st October 2019  16:00 to 17:00
When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. Achieving this for the stationary NavierStokes has proven challenging: LU factorisation is Reynoldsrobust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased. Building on ideas of Schöberl, Xu, Zikatanov, Benzi & Olshanskii, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier–Stokes equations in three dimensions that achieves both optimal complexity and Reynoldsrobustness. The scheme combines augmented Lagrangian stabilisation to control the Schur complement, the convection stabilisation proposed by Douglas & Dupont, a divergencecapturing additive Schwarz relaxation method on each level, and a specialised prolongation operator involving nonoverlapping local Stokes solves. The properties of the preconditioner are tailored to the divergencefree CG(k)DG(k1) discretisation and the appropriate relaxation is derived from considerations of finite element exterior calculus. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds numbers 10 to 5000.
20191107T09:35:35+00:00
2960
3095934
true
16x9
false
no

Application of the WienerHopf approach to incorrectly posed BVP of plane elasticity
ucs_sms_3028099_3047363
http://sms.cam.ac.uk/media/3047363
Application of the WienerHopf approach to incorrectly posed BVP of plane elasticity
Galybin, A
Friday 16th August 2019  13:30 to 14:00
Mon, 19 Aug 2019 10:34:30 +0100
Isaac Newton Institute
Galybin, A
b617ad208a954dee98b663b7e5c5c31e
55ee5f9c83b394cee5a7edee6a649320
b63ed9e19d3d8ede069c0f0bf891ffb6
56380dc6cc75a3cba220fa8a4dc2f25a
Galybin, A
Friday 16th August 2019  13:30 to 14:00
Galybin, A
Friday 16th August 2019  13:30 to 14:00
Cambridge University
1825
http://sms.cam.ac.uk/media/3047363
Application of the WienerHopf approach to incorrectly posed BVP of plane elasticity
Galybin, A
Friday 16th August 2019  13:30 to 14:00
20190819T10:34:30+01:00
1825
3047363
true
16x9
false
no

Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamples
ucs_sms_3028099_3078387
http://sms.cam.ac.uk/media/3078387
Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamples
Boffi, D
Wednesday 9th October 2019  15:05 to 15:50
Thu, 10 Oct 2019 11:11:30 +0100
Isaac Newton Institute
Boffi, D
4bfde39ecddfd9ce478d1de68df17f55
201c53a24e18bb60a8fdb7a4b7edb4c8
73973b89a0cf99668f5809fd33c3db4a
da4de47717baa908ec127a2b924a0741
Boffi, D
Wednesday 9th October 2019  15:05 to 15:50
Boffi, D
Wednesday 9th October 2019  15:05 to 15:50
Cambridge University
3238
http://sms.cam.ac.uk/media/3078387
Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamples
Boffi, D
Wednesday 9th October 2019  15:05 to 15:50
We discuss the finite element approximation of eigenvalue problems arising from elliptic partial differential equations. We present various examples of nonstandard schemes, including mixed finite elements, approximation of operators related to the leastsquares finite element method, parameter dependent formulations such as those produced by the virtual element method. Each example is studied theoretically; advantages and disadvantages of
each approach are pointed out.
20191010T11:11:30+01:00
3238
3078387
true
16x9
false
no

Compatible finite element spaces for metrics with curvature
ucs_sms_3028099_3071796
http://sms.cam.ac.uk/media/3071796
Compatible finite element spaces for metrics with curvature
Christiansen, S
Tuesday 1st October 2019  14:30 to 15:30
Tue, 01 Oct 2019 15:38:26 +0100
Isaac Newton Institute
Christiansen, S
404955b0b3f19b9a61a4d56c081eb52b
f0b5c47a6c546908139e6cdbaef91932
2b9872c1b946c5b8604c7ff92e334151
8d6744bbac417ea21c1f0a3523eb5b7a
Christiansen, S
Tuesday 1st October 2019  14:30 to 15:30
Christiansen, S
Tuesday 1st October 2019  14:30 to 15:30
Cambridge University
3550
http://sms.cam.ac.uk/media/3071796
Compatible finite element spaces for metrics with curvature
Christiansen, S
Tuesday 1st October 2019  14:30 to 15:30
I will present some new finite element spaces for metrics with integrable curvature. These were obtained in the framework of finite element systems, developed for constructing differential complexes with adequate gluing conditions between the cells of a mesh. The new spaces have a higher regularity than those of Regge calculus, for which the scalar curvature contains measures supported on lower dimensional simplices (Dirac deltas). This is joint work with Kaibo Hu.
20191001T15:38:26+01:00
3550
3071796
true
16x9
false
no

Computational geometric optics: MongeAmpere
ucs_sms_3028099_3053007
http://sms.cam.ac.uk/media/3053007
Computational geometric optics: MongeAmpere
Awanou, G
Wednesday 28th August 2019  14:00 to 15:00
Thu, 29 Aug 2019 12:34:31 +0100
Isaac Newton Institute
Awanou, G
844b1b735812162c55ac90c06c38f686
600fc38d60ea8df93856662648f2a7b6
0b74b39597375609537592fe5f5d2f82
da7d47b0a8f06200e48174e5ce0c81d8
Awanou, G
Wednesday 28th August 2019  14:00 to 15:00
Awanou, G
Wednesday 28th August 2019  14:00 to 15:00
Cambridge University
2753
http://sms.cam.ac.uk/media/3053007
Computational geometric optics: MongeAmpere
Awanou, G
Wednesday 28th August 2019  14:00 to 15:00
I will review recent developments in the numerical resolution of the second boundary value problem for MongeAmpere type equations and their applications to the design of reflectors and refractors.
20190829T12:34:31+01:00
2753
3053007
true
16x9
false
no

Computational methods for simulating inertial particles in discrete incompressible flows
ucs_sms_3028099_3035549
http://sms.cam.ac.uk/media/3035549
Computational methods for simulating inertial particles in discrete incompressible flows
Tapley, B
Tuesday 30th July 2019  15:00 to 16:00
Wed, 31 Jul 2019 10:40:58 +0100
Isaac Newton Institute
Tapley, B
a5a9ec7465c2f5b70fb5c792a2a94887
6ddaeec338f4d6f969b80c3e9d2d5557
e3f982dae1da6e76a6caa8651ccff010
edf257b7ec8bc07201ee2d74227452b2
Tapley, B
Tuesday 30th July 2019  15:00 to 16:00
Tapley, B
Tuesday 30th July 2019  15:00 to 16:00
Cambridge University
2795
http://sms.cam.ac.uk/media/3035549
Computational methods for simulating inertial particles in discrete incompressible flows
Tapley, B
Tuesday 30th July 2019  15:00 to 16:00
20190731T10:40:58+01:00
2795
3035549
true
16x9
false
no

Conformally mapping water waves: top, bottom or sides
ucs_sms_3028099_3059113
http://sms.cam.ac.uk/media/3059113
Conformally mapping water waves: top, bottom or sides
Nachbin, A
Monday 9th September 2019  15:00 to 15:30
Mon, 09 Sep 2019 16:16:32 +0100
Isaac Newton Institute
Nachbin, A
b875586561e7aa339b65ac657b1d96fe
93404091dab2ab5be0068d9bb8fb1097
205c4dac34db6ec8ec250a9a5bef0b44
f2bd69d1a0c3839855f0a79d2f505039
Nachbin, A
Monday 9th September 2019  15:00 to 15:30
Nachbin, A
Monday 9th September 2019  15:00 to 15:30
Cambridge University
2065
http://sms.cam.ac.uk/media/3059113
Conformally mapping water waves: top, bottom or sides
Nachbin, A
Monday 9th September 2019  15:00 to 15:30
I will present a brief overview of recent work showcasing conformal mapping's important role on surface waterwave dynamics. Conformal mapping can be used to flatten the free surface or a highly irregular bottom topography. It has also been used along the sides of forked channel regions, leading to a Boussinesq system with solitary waves on a graph. Mapping a highly variable bottom topography, among other features, allows the construction of a DirichlettoNeumann operator over a polygonal bottom profile. One very recent example applies to a hydrodynamic pilotwave model, capturing two bouncing droplets confined in cavities, where they can synchronize as nonlinearly coupled oscillators. Finally, on another topic, I will briefly present a very recent result displaying a spectrally accurate finite difference operator. This difference operator is constructed by unconventional means, having in mind complex analytic functions.
20190909T16:16:33+01:00
2065
3059113
true
16x9
false
no

Conservation laws and Euler operators
ucs_sms_3028099_3060816
http://sms.cam.ac.uk/media/3060816
Conservation laws and Euler operators
Hydon, P
Wednesday 11th September 2019  14:00 to 15:00
Thu, 12 Sep 2019 13:09:50 +0100
Isaac Newton Institute
Hydon, P
ad870f08bd85ac23ad2250167a3f2bef
d89374d61cf338fda4cf981e247209f8
bdbd0f09646eec45e18cd8635b0416b5
c343e07076e44e0089f93db30b5c7611
Hydon, P
Wednesday 11th September 2019  14:00 to 15:00
Hydon, P
Wednesday 11th September 2019  14:00 to 15:00
Cambridge University
2911
http://sms.cam.ac.uk/media/3060816
Conservation laws and Euler operators
Hydon, P
Wednesday 11th September 2019  14:00 to 15:00
A (local) conservation law of a given system of differential or difference equations is a divergence expression that is zero on all solutions. The Euler operator is a powerful tool in the formal theory of conservation laws that enables key results to be proved simply, including several generalizations of Noether's theorems. This talk begins with a short survey of the main ideas and results. The current method for inverting the divergence operator generates many unnecessary terms by integrating in all directions simultaneously. As a result, symbolic algebra packages create overcomplicated representations of conservation laws, making it difficult to obtain efficient conservative finite difference approximations symbolically. A new approach resolves this problem by using partial Euler operators to construct nearoptimal representations. The talk explains this approach, which was developed during the GCS programme.
20190912T13:09:51+01:00
2911
3060816
true
16x9
false
no

Deep learning as optimal control problems and Riemannian discrete gradient descent.
ucs_sms_3028099_3105528
http://sms.cam.ac.uk/media/3105528
Deep learning as optimal control problems and Riemannian discrete gradient descent.
Celledoni, E
Thursday 21st November 2019  15:05 to 15:45
Fri, 22 Nov 2019 12:24:08 +0000
Isaac Newton Institute
Celledoni, E
5224cd68137d3e6d3d48beda943474ba
e503cdf77d810edbcfd52f34249f0f47
35945df8462be417f85df2b1c2883c6c
3b719ec0da9990c4dd31b16fa787d5dc
Celledoni, E
Thursday 21st November 2019  15:05 to 15:45
Celledoni, E
Thursday 21st November 2019  15:05 to 15:45
Cambridge University
2893
http://sms.cam.ac.uk/media/3105528
Deep learning as optimal control problems and Riemannian discrete gradient descent.
Celledoni, E
Thursday 21st November 2019  15:05 to 15:45
We consider recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. The differential equation setting lends itself to learning additional parameters such as the time discretisation. We explore this extension alongside natural constraints (e.g. time steps lie in a simplex). We compare these deep learning algorithms numerically in terms of induced flow and generalisation ability. References  M Benning, E Celledoni, MJ Ehrhardt, B Owren, CB Schönlieb, Deep learning as optimal control problems: models and numerical methods, JCD.
20191122T12:24:08+00:00
2893
3105528
true
16x9
false
no

Deep Neural Networks and Multigrid Methods
ucs_sms_3028099_3093854
http://sms.cam.ac.uk/media/3093854
Deep Neural Networks and Multigrid Methods
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Mon, 04 Nov 2019 11:29:33 +0000
Isaac Newton Institute
Xu, J
d4535e6b3dcd6a01126e23238e2f013f
b80239fa0cb0d1a0d9145bf8ed30d401
f203509b046bb7fb3d520ff358644fc5
012abd412c3425ec18184626a822279a
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Cambridge University
3600
http://sms.cam.ac.uk/media/3093854
Deep Neural Networks and Multigrid Methods
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
In this talk, I will first give an introduction to several models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. I will then explore mathematical relationships between these models and algorithms and demonstrate how such relationships can be used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular, I will demonstrate how a new convolutional neural network known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then explore the theoretical and practical potentials of MgNet.
20191104T11:29:33+00:00
3600
3093854
true
16x9
false
no

Deep Neural Networks and Multigrid Methods
ucs_sms_3028099_3095927
http://sms.cam.ac.uk/media/3095927
Deep Neural Networks and Multigrid Methods
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Thu, 07 Nov 2019 09:34:58 +0000
Isaac Newton Institute
Xu, J
d0f70e847e381130accee410448b711f
4310847d59b10ffa1dcd6b3caf60bf80
83469b51357a97c1ddd142b529d70701
012abd412c3425ec18184626a822279a
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
Cambridge University
3600
http://sms.cam.ac.uk/media/3095927
Deep Neural Networks and Multigrid Methods
Xu, J
Wednesday 30th October 2019  14:05 to 15:05
In this talk, I will first give an introduction to several models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. I will then explore mathematical relationships between these models and algorithms and demonstrate how such relationships can be used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular, I will demonstrate how a new convolutional neural network known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then explore the theoretical and practical potentials of MgNet.
20191107T09:34:58+00:00
3600
3095927
true
16x9
false
no

Detection of high codimensional bifurcations in variational PDEs
ucs_sms_3028099_3028106
http://sms.cam.ac.uk/media/3028106
Detection of high codimensional bifurcations in variational PDEs
Offen, C
Wednesday 17th July 2019  11:00 to 12:00
Wed, 17 Jul 2019 14:49:35 +0100
Isaac Newton Institute
Offen, C
8ecc3ff8a67deee0e7acdeab0896ade7
57c06b8dc851b4c4876d48cf7897ffe2
47f4c108f4a24d0ed795413c2dd61bb7
59d3f24cba988646a8029cae3a31f651
Offen, C
Wednesday 17th July 2019  11:00 to 12:00
Offen, C
Wednesday 17th July 2019  11:00 to 12:00
Cambridge University
2300
http://sms.cam.ac.uk/media/3028106
Detection of high codimensional bifurcations in variational PDEs
Offen, C
Wednesday 17th July 2019  11:00 to 12:00
We derive bifurcation test equations for Aseries singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimensional bifurcations in parameterdependent PDEs such as parameterdependent semilinear Poisson equations. As an example, we consider a Bratutype problem and show how high codimensional bifurcations such as the swallowtail bifurcation can be found numerically.
Lisa Maria Kreusser, Robert I McLachlan, Christian Offen
20190717T14:49:35+01:00
2300
3028106
true
16x9
false
no

Discrete Vector Bundles with Connection and the First Chern Class
ucs_sms_3028099_3072210
http://sms.cam.ac.uk/media/3072210
Discrete Vector Bundles with Connection and the First Chern Class
Hirani, A
Wednesday 2nd October 2019  09:30 to 10:30
Wed, 02 Oct 2019 10:46:27 +0100
Isaac Newton Institute
Hirani, A
94b4cc624f640dc6582de5e37bffdd1a
35d0f07fc86f19b6fce852382b05831e
e0b30a329652c22f0810d0cebb23ca0f
3435901bcb1df6b924987a56007124d5
Hirani, A
Wednesday 2nd October 2019  09:30 to 10:30
Hirani, A
Wednesday 2nd October 2019  09:30 to 10:30
Cambridge University
3780
http://sms.cam.ac.uk/media/3072210
Discrete Vector Bundles with Connection and the First Chern Class
Hirani, A
Wednesday 2nd October 2019  09:30 to 10:30
The use of differential forms in general relativity requires ingredients like the covariant exterior derivative and curvature. One potential approach to numerical relativity would require discretizations of these ingredients. I will describe a discrete combinatorial theory of vector bundles with connections. The main operator we develop is a discrete covariant exterior derivative that generalizes the coboundary operator and yields a discrete curvature and a discrete Bianchi identity. We test this theory by defining a discrete first Chern class, a topological invariant of vector bundles. This discrete theory is built by generalizing discrete exterior calculus (DEC) which is a discretization of exterior calculus on manifolds for realvalued differential forms. In the first part of the talk I will describe DEC and its applications to the HodgeLaplace problem and NavierStokes equations on surfaces, and then I will develop the discrete covariant exterior derivative and its implications. This is joint work with Daniel BerwickEvans and Mark Schubel.
20191002T10:46:27+01:00
3780
3072210
true
16x9
false
no

Energy estimates: proving stability for evolving surface PDEs and geometric flows
ucs_sms_3028099_3118234
http://sms.cam.ac.uk/media/3118234
Energy estimates: proving stability for evolving surface PDEs and geometric flows
Kovács, B
Wednesday 4th December 2019  14:05 to 14:50
Fri, 06 Dec 2019 11:18:26 +0000
Isaac Newton Institute
Kovács, B
da7ef39820a604f555164160f9dc588f
0310583aa534535c81c7f689d539f321
8671d61f364afd124f06c65e378e2055
47fd21a213760f1d30f6f6ec16750f31
Kovács, B
Wednesday 4th December 2019  14:05 to 14:50
Kovács, B
Wednesday 4th December 2019  14:05 to 14:50
Cambridge University
2727
http://sms.cam.ac.uk/media/3118234
Energy estimates: proving stability for evolving surface PDEs and geometric flows
Kovács, B
Wednesday 4th December 2019  14:05 to 14:50
In this talk we will give some details on the main steps and ideas behind energy estimates used to prove stability of backward difference semi and full discretisations of parabolic evolving surface problems, or geometric flows (e.g. mean curvature flow). We will give details on how the Gstability result of Dahlquist and the multiplier techniques of Nevanlinna and Odeh will be used.
20191206T11:18:26+00:00
2727
3118234
true
16x9
false
no

Exterior Shape Calculus
ucs_sms_3028099_3032070
http://sms.cam.ac.uk/media/3032070
Exterior Shape Calculus
Hiptmair, R
Monday 22nd July 2019  14:00 to 15:00
Wed, 24 Jul 2019 09:07:17 +0100
Isaac Newton Institute
Hiptmair, R
7822ccfea8098c6bca94a2e70e704819
4ce30aacd24985fd54a48700b3bbb551
dc788b51e18c7da61edcfa271c0d0abd
27c7623d9c3c21e1e72e4f9a2e1dc08a
Hiptmair, R
Monday 22nd July 2019  14:00 to 15:00
Hiptmair, R
Monday 22nd July 2019  14:00 to 15:00
Cambridge University
4020
http://sms.cam.ac.uk/media/3032070
Exterior Shape Calculus
Hiptmair, R
Monday 22nd July 2019  14:00 to 15:00
20190724T09:07:17+01:00
4020
3032070
true
16x9
false
no

Fast approximation on the real line
ucs_sms_3028099_3041986
http://sms.cam.ac.uk/media/3041986
Fast approximation on the real line
Iserles, A
Wednesday 7th August 2019  14:00 to 15:00
Fri, 09 Aug 2019 15:56:14 +0100
Isaac Newton Institute
Iserles, A
839359290bde620844d11cc8919f30ad
f6c8fc8c27665a8fe286dfbfc8cf9390
c926379bdb56779e2b4d3d7e97e4d164
9f973cc7a8f089f43ec593131ebd605f
Iserles, A
Wednesday 7th August 2019  14:00 to 15:00
Iserles, A
Wednesday 7th August 2019  14:00 to 15:00
Cambridge University
3287
http://sms.cam.ac.uk/media/3041986
Fast approximation on the real line
Iserles, A
Wednesday 7th August 2019  14:00 to 15:00
While approximation theory in an interval is thoroughly understood, the real line represents something of a mystery. In this talk we review the state of the art in this area, commencing from the familiar Hermite functions and moving to recent results characterising all orthonormal sets on L2(−∞,∞) that have a skewsymmetric (or skewHermitian) tridiagonal differentiation matrix and such that their first n expansion coefficients can be calculated in O(nlogn) operations. In particular, we describe the generalised Malmquist–Takenaka system. The talk concludes with a (too!) long list of open problems and challenges.
20190809T15:56:14+01:00
3287
3041986
true
16x9
false
no

FEEC 4 GR?
ucs_sms_3028099_3073395
http://sms.cam.ac.uk/media/3073395
FEEC 4 GR?
Arnold, D
Thursday 3rd October 2019  16:00 to 17:00
Thu, 03 Oct 2019 17:18:28 +0100
Isaac Newton Institute
Arnold, D
b8f0bdbdaace475e2c98a2c39ea52f2e
49b0aa4a4cf016bd2da627252ad6c668
0035eab77a5312d7eef153bcfb8adc95
22f0b84b25e709b687869912b32f1634
Arnold, D
Thursday 3rd October 2019  16:00 to 17:00
Arnold, D
Thursday 3rd October 2019  16:00 to 17:00
Cambridge University
4440
http://sms.cam.ac.uk/media/3073395
FEEC 4 GR?
Arnold, D
Thursday 3rd October 2019  16:00 to 17:00
The finite element exterior calculus (FEEC) has proven to be a powerful tool for the design and understanding of numerical methods for solving PDEs from many branches of physics: solid mechanics, fluid flow, electromagnetics, etc. Based on preserving crucial geometric and topological structures underlying the equations, it is a prime example of a structurepreserving numerical method. It has organized many known finite element methods resulting in the periodic table of finite elements. For elasticity, which is not covered by the table, it led to new methods with long soughtafter properties. Might the FEEC approach lead to better numerical solutions of the Einstein equations as well? This talk will explore this question through two examples: the EinsteinBianchi formulation of the Einstein equations based on Bel decomposition of the Weyl tensor, and the Regge elements, a family of finite elements inspired by Regge calculus. Our goal in the talk is to raise questions and inspire future work; we do not purport to provide anything near definitive answers.
20191003T17:18:28+01:00
4440
3073395
true
16x9
false
no

Finite element exterior calculus as a tool for compatible discretizations
ucs_sms_3028099_3073298
http://sms.cam.ac.uk/media/3073298
Finite element exterior calculus as a tool for compatible discretizations
Winther, R
Thursday 3rd October 2019  14:30 to 15:30
Thu, 03 Oct 2019 16:08:10 +0100
Isaac Newton Institute
Winther, R
fc795403f1e4b094b349094efecd91ac
9181d4b8ef3470675bcaba730da25c23
63788f7a45b1838cc9420d2b4cb914a8
ac8c974680164bb3c7a2a241f8ba4129
Winther, R
Thursday 3rd October 2019  14:30 to 15:30
Winther, R
Thursday 3rd October 2019  14:30 to 15:30
Cambridge University
3420
http://sms.cam.ac.uk/media/3073298
Finite element exterior calculus as a tool for compatible discretizations
Winther, R
Thursday 3rd October 2019  14:30 to 15:30
The purpose of this talk is to review the basic results of finite element exterior calculus (FEEC) and to illustrate how the set up gives rise to
to compatible discretizations of various problems. In particular, we will recall how FEEC, combined with the BernsteinGelfandGelfand framework,
gave new insight into the construction of stable schemes for elasticity methods based on the HellingerReissner variational principle.
20191003T16:08:10+01:00
3420
3073298
true
16x9
false
no

Finite element methods for Hamiltonian PDEs
ucs_sms_3028099_3045975
http://sms.cam.ac.uk/media/3045975
Finite element methods for Hamiltonian PDEs
Stern, A
Wednesday 14th August 2019  15:00 to 16:00
Fri, 16 Aug 2019 15:17:29 +0100
Isaac Newton Institute
Stern, A
5db4018ab4c8b4b25c74fc8340c0cf11
a6157911898954141aeb2d24f881d71e
e923e26be0abbf3c59f1b1cf6e922fb5
19c7fcad9a6da0a3f70ff544fa5b4414
Stern, A
Wednesday 14th August 2019  15:00 to 16:00
Stern, A
Wednesday 14th August 2019  15:00 to 16:00
Cambridge University
3340
http://sms.cam.ac.uk/media/3045975
Finite element methods for Hamiltonian PDEs
Stern, A
Wednesday 14th August 2019  15:00 to 16:00
Hamiltonian ODEs satisfy a symplectic conservation law, and there are many advantages to using numerical integrators that preserves this structure. This talk will discuss how the canonical Hamiltonian structure, and its preservation by a numerical method, can be generalized to PDEs. I will also provide a basic introduction to the finite element method and, time permitting, discuss how some classic symplectic integrators can be understood from this point of view.
20190816T15:17:29+01:00
3340
3045975
true
16x9
false
no

Highorder splitting for the VlasovPoisson equation
ucs_sms_3028099_3093759
http://sms.cam.ac.uk/media/3093759
Highorder splitting for the VlasovPoisson equation
Faou, E
Monday 28th October 2019  10:00 to 10:45
Mon, 04 Nov 2019 10:14:41 +0000
Isaac Newton Institute
Faou, E
2a293b439124dffc8c4182f72f0155a7
a328be5e093f28bdd18f05d9ed5dc70b
64e45e1fc57872e7bd3e96ea519baaec
9eba1aa9aab449f2118a8a3b3c1fcb12
Faou, E
Monday 28th October 2019  10:00 to 10:45
Faou, E
Monday 28th October 2019  10:00 to 10:45
Cambridge University
2828
http://sms.cam.ac.uk/media/3093759
Highorder splitting for the VlasovPoisson equation
Faou, E
Monday 28th October 2019  10:00 to 10:45
We consider the Vlasov{Poisson equation in a Hamiltonian framework and
derive time splitting methods based on the decomposition of the Hamiltonian functional
between the kinetic and electric energy. We also apply a similar strategy to the Vlasov{
Maxwell system. These are joint works with N. Crouseilles, F. Casas, M. Mehrenberger
and L. Einkemmer.
20191104T10:14:41+00:00
2828
3093759
true
16x9
false
no

Hybrid Monte Carlo methods for sampling probability measures on submanifolds
ucs_sms_3028099_3104609
http://sms.cam.ac.uk/media/3104609
Hybrid Monte Carlo methods for sampling probability measures on submanifolds
Lelievre, T
Wednesday 20th November 2019  13:50 to 14:30
Thu, 21 Nov 2019 10:36:03 +0000
Isaac Newton Institute
Lelievre, T
faf565e15194972193fc21d50198f8d0
b0e0b849cc2b4299dae08a1e2dbd3327
12df95efda6214fc2485244ea85eb413
3d353ad940fd277ee87445064f43646d
Lelievre, T
Wednesday 20th November 2019  13:50 to 14:30
Lelievre, T
Wednesday 20th November 2019  13:50 to 14:30
Cambridge University
2721
http://sms.cam.ac.uk/media/3104609
Hybrid Monte Carlo methods for sampling probability measures on submanifolds
Lelievre, T
Wednesday 20th November 2019  13:50 to 14:30
Various applications require the sampling of probability measures restricted to submanifolds defined as the level set of some functions, in particular in computational statistical physics. We will present recent results on socalled Hybrid Monte Carlo methods, which consists in adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In order to avoid biases in the invariant probability measures sampled by discretizations of these stochastically perturbed Hamiltonian dynamics, a Metropolis rejection procedure can be considered. The soobtained scheme belongs to the class of generalized Hybrid Monte Carlo (GHMC) algorithms, and we will discuss how to ensure that the sampling method is unbiased in practice.
References:
 T. Lelièvre, M. Rousset and G. Stoltz, Langevin dynamics with constraints and computation of free energy differences, Mathematics of Computation, 81(280), 2012.
 T. Lelièvre, M. Rousset and G. Stoltz, Hybrid Monte Carlo methods for sampling probability measures on submanifolds, to appear in Numerische Mathematik, 2019.
 E. Zappa, M. HolmesCerfon, and J. Goodman. Monte Carlo on manifolds: sampling densities and integrating functions. Communications in Pure and Applied Mathematics, 71(12), 2018.
20191121T10:36:03+00:00
2721
3104609
true
16x9
false
no

Hyponormal quantization of planar domains
ucs_sms_3028099_3060915
http://sms.cam.ac.uk/media/3060915
Hyponormal quantization of planar domains
Putinar, M
Thursday 12th September 2019  14:00 to 15:00
Thu, 12 Sep 2019 15:07:21 +0100
Isaac Newton Institute
Putinar, M
3724468cafd6291feac0ebd6e82201ee
440a0e51de9c55d40902a62cf32c3ab4
8b7ee513f226479f62fad4874bb7b720
f5ed33fd0aab5a1fea04f1589668f34e
6e57bdc903a38f457b3e108d91c2cb12
Putinar, M
Thursday 12th September 2019  14:00 to 15:00
Putinar, M
Thursday 12th September 2019  14:00 to 15:00
Cambridge University
3780
http://sms.cam.ac.uk/media/3060915
Hyponormal quantization of planar domains
Putinar, M
Thursday 12th September 2019  14:00 to 15:00
By replacing the identity operator in Heisenberg commutation relation [T*,T]=I by a rankone projection one unveils an accessible spectral analysis classification with singular integrals of Cauchy type as generic examples. An inverse spectral problem for this class of (hyponormal) operators can be invoked for encoding and decoding (partial) data of 2D pictures carrying a grey shade function. An exponential transform, the two dimensional analog of a similar operation on Cauchy integrals introduced by A, Markov in his pioneering work on 1D moment problems, provides an effective dictionary between "pictures" in the frequency domain and "matrices" in the state space interpretation. A natural RiemannHilbert problem lies at the origin of this kernel with potential theoretic flavor. Quadrature domains for analytic functions are singled out by a rationality property of the exponential transform, and hence an exact reconstruction algorithm for this class of black and white shapes emerges. A two variable diagonal Pade approximation scheme and some related complex orthogonal polynomials enter into the picture, with their elusive zero asymptotics. Most of the results streaming from two decades of joint work with Bjorn Gustafsson.
20190912T15:07:21+01:00
3780
3060915
true
16x9
false
no

Inside the Final Black Hole from Black Hole Collisions
ucs_sms_3028099_3073887
http://sms.cam.ac.uk/media/3073887
Inside the Final Black Hole from Black Hole Collisions
Laguna, P
Friday 4th October 2019  11:00 to 12:00
Fri, 04 Oct 2019 12:13:44 +0100
Isaac Newton Institute
Laguna, P
fc0ee138c7b71d3b2f1e50a24830d9d4
ade187c34f8ce81ae94f9d83eb02379c
3dcf4b53848ec41e578c83a75717f59c
3ec9d4da217d3f0845d90704965c2a2b
Laguna, P
Friday 4th October 2019  11:00 to 12:00
Laguna, P
Friday 4th October 2019  11:00 to 12:00
Cambridge University
3960
http://sms.cam.ac.uk/media/3073887
Inside the Final Black Hole from Black Hole Collisions
Laguna, P
Friday 4th October 2019  11:00 to 12:00
Modeling black hole singularities as punctures in spacetime is common in binary black hole simulations. As the punctures approach each other, a common apparent horizon forms, signaling the coalescence of the black holes and the formation of the final black hole. I will present results from a study that investigates the fate of the punctures and in particular the dynamics of the trapped surfaces on each puncture.
Coauthors: Christopher Evans, Deborah Ferguson, Bhavesh Khamesra and Deirdre Shoemaker
20191004T12:13:44+01:00
3960
3073887
true
16x9
false
no

Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element Method
ucs_sms_3028099_3084641
http://sms.cam.ac.uk/media/3084641
Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element Method
Marini, D
Monday 21st October 2019  16:00 to 17:00
Mon, 21 Oct 2019 16:58:56 +0100
Isaac Newton Institute
Marini, D
4816b7c2016b1532d0b99b544d91c902
cbd3a9a341a519ddd55c3805a4257c34
607153aa922abcba615a05168d456366
7d214f3d22510436982cc0ad98d56e80
Marini, D
Monday 21st October 2019  16:00 to 17:00
Marini, D
Monday 21st October 2019  16:00 to 17:00
Cambridge University
3260
http://sms.cam.ac.uk/media/3084641
Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element Method
Marini, D
Monday 21st October 2019  16:00 to 17:00
The Virtual Element Method (VEM) is a recent technology for the numerical solution of boundary value problems for Partial Differential Equations. It could be seen as a generalization of the Finite Element Method (FEM). With FEM the computational domain is typically split in triangles/quads (tetrahedra/hexahedra). VEM responds to the recent interest in using decompositions into polygons/polyhedra of very general shape, whenever more convenient for the approximation of problems of practical interest. Indeed,the possibility of using general polytopal meshes opens up a new range of opportunities in terms of accuracy, efficiency and flexibility. This is for instance reflected by the fact that various (commercial and free) codes recently included and keep developing polytopal meshes, showing in selected applications an improved computational efficiency with respect to tetrahedral or hexahedral grids. In this talk, after a general description of the use and potential of Scientific Computing, basic ideas of conforming VEM will be described on a simple model problem. Numerical results on more general problems in two and three dimension will be shown. Hints on Serendipity versions will be given at the end. These procedures allow to decrease significantly the number of degrees of freedom, that is, to reduce the dimension of the final linear system.
20191021T16:58:56+01:00
3260
3084641
true
16x9
false
no

Lowregularity time integrators
ucs_sms_3028099_3102884
http://sms.cam.ac.uk/media/3102884
Lowregularity time integrators
Ostermann, A
Wednesday 13th November 2019  16:00 to 17:00
Mon, 18 Nov 2019 11:20:26 +0000
Isaac Newton Institute
Ostermann, A
1fb3389300929a8e53cc83cbe6551a2c
c3f9aafe5cd6a645db1c400985154fcd
ab666e7ef8dfa8f35d9b55da1e144c27
7a5406ae1b3382b23b0070d5af2ecc3b
Ostermann, A
Wednesday 13th November 2019  16:00 to 17:00
Ostermann, A
Wednesday 13th November 2019  16:00 to 17:00
Cambridge University
3720
http://sms.cam.ac.uk/media/3102884
Lowregularity time integrators
Ostermann, A
Wednesday 13th November 2019  16:00 to 17:00
Nonlinear Schrödinger equations are usually solved by pseudospectral methods, where the time integration is performed by splitting schemes or exponential integrators. Notwithstanding the benefits of this approach, its successful application requires additional regularity of the solution. For instance, secondorder Strang splitting requires four additional derivatives for the solution of the cubic nonlinear Schrödinger equation. Similar statements can be made about other dispersive equations like the Kortewegde Vries or the Boussinesq equation. In this talk, we introduce lowregularity Fourier integrators as an alternative. They are obtained from Duhamel's formula in the following way: first, a Lawsontype transformation eliminates the leading linear term and second, the dominant nonlinear terms are integrated exactly in Fourier space. For cubic nonlinear Schrödinger equations, firstorder convergence of such methods only requires the boundedness of one additional derivative of the solution, and secondorder convergence the boundedness of two derivatives. Similar improvements can also be obtained for other dispersive problems. This is joint work with Frédéric Rousset (Université ParisSud), Katharina Schratz (HariotWatt, UK), and Chunmei Su (Technical University of Munich).
20191118T11:20:26+00:00
3720
3102884
true
16x9
false
no

Magnus, splitting and composition techniques for solving nonlinear Schrödinger equations
ucs_sms_3028099_3100184
http://sms.cam.ac.uk/media/3100184
Magnus, splitting and composition techniques for solving nonlinear Schrödinger equations
Blanes, S
Monday 11th November 2019  16:00 to 17:00
Wed, 13 Nov 2019 08:43:21 +0000
Isaac Newton Institute
Blanes, S
4e7389abf5cc213a8fa8f38017b30542
f7d9747d7eb41acc31fb420180a42843
5ee8ec5ac926b053dde890c14fd03bd8
9d16020426f37f2e763274e9f9d97bcb
Blanes, S
Monday 11th November 2019  16:00 to 17:00
Blanes, S
Monday 11th November 2019  16:00 to 17:00
Cambridge University
2888
http://sms.cam.ac.uk/media/3100184
Magnus, splitting and composition techniques for solving nonlinear Schrödinger equations
Blanes, S
Monday 11th November 2019  16:00 to 17:00
In this talk I will consider several nonautonomous nonlinear Schrödinger equations
(the GrossPitaevskii equation, the KohnSham equation and an Quantum Optimal Control equation)
and some of the numerical methods that have been used to solve them.
With a proper linearization of these equations we end up with nonautonomous linear systems
where many of the algebraic techniques from Magnus, splitting and composition algorithms can be used.
This will be an introductory talk to stimulate some collaboration between participants of the program
at the INI.
20191113T08:43:21+00:00
2888
3100184
true
16x9
false
no

Mixed order and multirate variational integrators for the simulation of dynamics on different time scales
ucs_sms_3028099_3056801
http://sms.cam.ac.uk/media/3056801
Mixed order and multirate variational integrators for the simulation of dynamics on different time scales
Leyendecker, S
Wednesday 4th September 2019  15:00 to 16:00
Thu, 05 Sep 2019 12:21:58 +0100
Isaac Newton Institute
Leyendecker, S
49ba145e7f69a56041ab6be070f8ab47
2452f410bd54e24c5f31ca82b7bba8eb
c0c6a24a9288cc74aa873c0a56986492
aa748bd3f2cc7e568e907fc4ead786db
Leyendecker, S
Wednesday 4th September 2019  15:00 to 16:00
Leyendecker, S
Wednesday 4th September 2019  15:00 to 16:00
Cambridge University
3384
http://sms.cam.ac.uk/media/3056801
Mixed order and multirate variational integrators for the simulation of dynamics on different time scales
Leyendecker, S
Wednesday 4th September 2019  15:00 to 16:00
Mechanical systems with dynamics on varying time scales, e.g. including highly oscillatory motion, impose challenging questions for numerical integration schemes. High resolution is required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a lower resolution is accurate enough  and computationally cheaper, especially for costly function evaluations. Two approaches are presented, a mixed order Galerkin variational integrator and a multirate variational integrator, and analysed with respect to the preservation of invariants, computational costs, accuracy and linear stability.
20190905T12:21:58+01:00
3384
3056801
true
16x9
false
no

Modelling processes in landscapes  Van Oijen, M
ucs_sms_3028099_3036130
http://sms.cam.ac.uk/media/3036130
Modelling processes in landscapes  Van Oijen, M
Van Oijen, M
Wednesday 31st July 2019  15:30 to 16:00
Wed, 31 Jul 2019 16:51:20 +0100
Isaac Newton Institute
Van Oijen, M
d21bd392e6465c4601d3058ff0b739d7
4f4aa6ec49763bbb69ecfcc598f610f2
c118c01affbbbbc22198afbceee33ae1
1aef264ba6b0a0c7a60a5e18e499d13c
Van Oijen, M
Wednesday 31st July 2019  15:30 to 16:00
Van Oijen, M
Wednesday 31st July 2019  15:30 to 16:00
Cambridge University
1812
http://sms.cam.ac.uk/media/3036130
Modelling processes in landscapes  Van Oijen, M
Van Oijen, M
Wednesday 31st July 2019  15:30 to 16:00
20190731T16:51:21+01:00
1812
3036130
true
16x9
false
no

More on composition methods: error estimation and pseudosymmetry
ucs_sms_3028099_3049612
http://sms.cam.ac.uk/media/3049612
More on composition methods: error estimation and pseudosymmetry
Casas, F
Wednesday 21st August 2019  14:00 to 15:00
Thu, 22 Aug 2019 14:03:05 +0100
Isaac Newton Institute
Casas, F
fad5a6bf06622b7d8aa1446c3d4910bc
26d4ab4e9c391b4ccf1226f4f572a6b1
39ac43a2676b3b194271a1e5ff7ec6fa
c6602f8b1da81f2fd4c4127da91f5d3f
Casas, F
Wednesday 21st August 2019  14:00 to 15:00
Casas, F
Wednesday 21st August 2019  14:00 to 15:00
Cambridge University
3011
http://sms.cam.ac.uk/media/3049612
More on composition methods: error estimation and pseudosymmetry
Casas, F
Wednesday 21st August 2019  14:00 to 15:00
In this talk I will review composition methods for the time integration of differential equations,
paying special attention to two recent contributions in this area. The first one is the construction
of a new local error estimator so that the additional computational effort required is almost insignificant.
The second one is related to a new family of highorder methods obtained from a basic symmetric
(symplectic) scheme in such a way that they are timesymmetric (symplectic) only up to a certain order.
20190822T14:03:06+01:00
3011
3049612
true
16x9
false
no

Newest Results in Newest Vertex Bisection
ucs_sms_3028099_3093726
http://sms.cam.ac.uk/media/3093726
Newest Results in Newest Vertex Bisection
Licht, M
Wednesday 25th September 2019  14:05 to 14:50
Mon, 04 Nov 2019 09:03:21 +0000
Isaac Newton Institute
Licht, M
4171eb961a3f3c7f9474078e51f5818b
218bc4a7112711d244418b2a34eea68c
1cffe59a73860829c4bc51ed84778dbf
6abc56e5233fa5c68301cab55e2472fd
Licht, M
Wednesday 25th September 2019  14:05 to 14:50
Licht, M
Wednesday 25th September 2019  14:05 to 14:50
Cambridge University
3229
http://sms.cam.ac.uk/media/3093726
Newest Results in Newest Vertex Bisection
Licht, M
Wednesday 25th September 2019  14:05 to 14:50
The algorithmic refinement of triangular meshes is an important component in numerical simulation codes. Newest vertex bisection is one of the most popular methods for geometrically stable local refinement. Its complexity analysis, however, is a fairly intricate recent result and many combinatorial aspects of this method are not yet fully understood. In this talk, we access newest vertex bisection from the perspective of theoretical computer science. We outline the amortized complexity analysis over generalized triangulations. An immediate application is the convergence and complexity analysis of adaptive finite element methods over embedded surfaces and singular surfaces. Moreover, we "combinatorialize" the complexity estimate and remove any geometrydependent constants, which is only natural for this purely combinatorial algorithm and improves upon prior results. This is joint work with Michael Holst and Zhao Lyu.
20191104T09:03:21+00:00
3229
3093726
true
16x9
false
no

Numerical approximations of a tractable mathematical model for tissue growth
ucs_sms_3028099_3118241
http://sms.cam.ac.uk/media/3118241
Numerical approximations of a tractable mathematical model for tissue growth
Styles, V
Thursday 5th December 2019  13:30 to 14:15
Fri, 06 Dec 2019 11:20:18 +0000
Isaac Newton Institute
Styles, V
8d745258be995f1c33e98e33a89dcdf3
b4655806403a9cb0f650d019f1d0fe6d
4d96152d99bac9ec0f39b65154f651bc
3ab595d4df5e5f643e3aa48e81d37278
Styles, V
Thursday 5th December 2019  13:30 to 14:15
Styles, V
Thursday 5th December 2019  13:30 to 14:15
Cambridge University
2549
http://sms.cam.ac.uk/media/3118241
Numerical approximations of a tractable mathematical model for tissue growth
Styles, V
Thursday 5th December 2019  13:30 to 14:15
We consider a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We derive sharp interface and diffuse interface finite element approximations of this model and present some numerical results
20191206T11:20:18+00:00
2549
3118241
true
16x9
false
no

Numerical Computation of Hausdorff Dimension
ucs_sms_3028099_3078374
http://sms.cam.ac.uk/media/3078374
Numerical Computation of Hausdorff Dimension
Falk, R
Wednesday 9th October 2019  14:05 to 14:50
Thu, 10 Oct 2019 11:10:29 +0100
Isaac Newton Institute
Falk, R
27de4252501e331635ee5a6f5199dad4
d4ce3a48a494391893f3963bdc1a78fe
153aded63846c0ec9bbc06221ab93ad0
9170cf0187f0e7524a7568a4f77f027d
Falk, R
Wednesday 9th October 2019  14:05 to 14:50
Falk, R
Wednesday 9th October 2019  14:05 to 14:50
Cambridge University
2543
http://sms.cam.ac.uk/media/3078374
Numerical Computation of Hausdorff Dimension
Falk, R
Wednesday 9th October 2019  14:05 to 14:50
We show how finite element approximation theory can be combined with theoretical results about the properties of the eigenvectors of a class of linear PerronFrobenius operators to obtain accurate approximations of the Hausdorff dimension of some invariant sets arising from iterated function systems.
The theory produces rigorous upper and lower bounds on the Hausdorff dimension. Applications to the computation of the Hausdorff dimension of some Cantor sets arising from real and complex continued fraction expansions are described.
20191010T11:10:29+01:00
2543
3078374
true
16x9
false
no

Numerical General Relativity
ucs_sms_3028099_3045967
http://sms.cam.ac.uk/media/3045967
Numerical General Relativity
Garfinkle, D
Wednesday 14th August 2019  14:00 to 15:00
Fri, 16 Aug 2019 15:15:43 +0100
Isaac Newton Institute
Garfinkle, D
76fe40b633e06fd8f57409d04ebc35bb
6eea979c786e254c85d17f5181e1525d
e346084f8cc0f3b5ffc110fb51a92424
98f51c0ac9424fcd6a8f242fa7cfddf3
Garfinkle, D
Wednesday 14th August 2019  14:00 to 15:00
Garfinkle, D
Wednesday 14th August 2019  14:00 to 15:00
Cambridge University
3311
http://sms.cam.ac.uk/media/3045967
Numerical General Relativity
Garfinkle, D
Wednesday 14th August 2019  14:00 to 15:00
This talk will cover the basic properties of the equations of General Relativity, and issues involved in performing numerical simulations of those equations. Particular emphasis will be placed on three issues: (1) hyperbolicity of the equations. (2) preserving constraints. (3) dealing with black holes and spacetime singularities.
20190816T15:15:43+01:00
3311
3045967
true
16x9
false
no

Numerical Integrators for the Hamiltonian Monte Carlo Method
ucs_sms_3028099_3057336
http://sms.cam.ac.uk/media/3057336
Numerical Integrators for the Hamiltonian Monte Carlo Method
SanzSerna, C
Thursday 5th September 2019  14:15 to 15:15
Fri, 06 Sep 2019 12:50:26 +0100
Isaac Newton Institute
SanzSerna, C
4e04ca087e3a5de4e402ea42e19e1ea8
21c41986dcc16bf08ff0bc7e3e1cd5a8
80ed426d126928974e3e218e1a2d3fcd
69804033601eb3c4672842a0cc5de3a4
SanzSerna, C
Thursday 5th September 2019  14:15 to 15:15
SanzSerna, C
Thursday 5th September 2019  14:15 to 15:15
Cambridge University
3578
http://sms.cam.ac.uk/media/3057336
Numerical Integrators for the Hamiltonian Monte Carlo Method
SanzSerna, C
Thursday 5th September 2019  14:15 to 15:15
20190906T12:50:26+01:00
3578
3057336
true
16x9
false
no

Numerical preservation of local conservation laws
ucs_sms_3028099_3060823
http://sms.cam.ac.uk/media/3060823
Numerical preservation of local conservation laws
FrascaCaccia, G
Wednesday 11th September 2019  15:00 to 16:00
Thu, 12 Sep 2019 13:10:26 +0100
Isaac Newton Institute
FrascaCaccia, G
949844513583d6c53fceea503cb88baa
c7a9e38e4d712685390a5656289224d1
55ea4dcc947f2a095bb6e94bd68a4465
e8d707d54ac76a67489cb798bcccbc69
FrascaCaccia, G
Wednesday 11th September 2019  15:00 to 16:00
FrascaCaccia, G
Wednesday 11th September 2019  15:00 to 16:00
Cambridge University
2903
http://sms.cam.ac.uk/media/3060823
Numerical preservation of local conservation laws
FrascaCaccia, G
Wednesday 11th September 2019  15:00 to 16:00
In the numerical treatment of partial differential equations (PDEs), the benefits of preserving global integral invariants are wellknown. Preserving the underlying local conservation law gives, in general, a stricter constraint than conserving the global invariant obtained by integrating it in space. Conservation laws, in fact, hold throughout the domain and are satisfied by all solutions, independently of initial and boundary conditions. A new approach that uses symbolic algebra to develop bespoke finite difference schemes that preserve multiple local conservation laws has been recently applied to PDEs with polynomial nonlinearity. The talk illustrates this new strategy using some wellknown equations as benchmark examples and shows comparisons between the obtained schemes and other integrators known in literature.
20190912T13:10:26+01:00
2903
3060823
true
16x9
false
no

Numerical Relativity in the Era of Gravitational Wave Observations
ucs_sms_3028099_3070921
http://sms.cam.ac.uk/media/3070921
Numerical Relativity in the Era of Gravitational Wave Observations
Shoemaker, D
Monday 30th September 2019  09:30 to 10:30
Mon, 30 Sep 2019 10:40:24 +0100
Isaac Newton Institute
Shoemaker, D
6c5fb9fe2d35cd8440479992fa35dcd3
52a3eeac696d56a8891a4b00da3ee7ef
7bc13a31553b446bcda52327bb5d970c
1b757948bca412e50fb809f70c13a8b6
Shoemaker, D
Monday 30th September 2019  09:30 to 10:30
Shoemaker, D
Monday 30th September 2019  09:30 to 10:30
Cambridge University
3780
http://sms.cam.ac.uk/media/3070921
Numerical Relativity in the Era of Gravitational Wave Observations
Shoemaker, D
Monday 30th September 2019  09:30 to 10:30
The birth and future of gravitational wave astronomy offers new opportunities and challenges for numerical methods in general relativity. Numerical relativity in particular provides critical support to detect and interpret gravitational wave measurements. In this talk, I’ll discuss the role numerical relativity is playing in the observed black hole binaries by LIGO and Virgo and its future potential for unveiling strongfield gravity in future detections with an emphasis on the computational challenges. I'll frame a discussion about what demands will be placed on this field to maximize the science output of the new era.
20190930T10:40:24+01:00
3780
3070921
true
16x9
false
no

On numerical conservation of the PoincaréCartan integral invariant in relativistic fluid dynamics
ucs_sms_3028099_3073946
http://sms.cam.ac.uk/media/3073946
On numerical conservation of the PoincaréCartan integral invariant in relativistic fluid dynamics
Markakis, C
Friday 4th October 2019  13:30 to 14:30
Fri, 04 Oct 2019 14:21:17 +0100
Isaac Newton Institute
Markakis, C
55eaa57f8569676f90d2200a604d8738
b15eecdb731943d94e42adcfe29ae4e3
b13e13e31ca9adcff90ad2dff8dea6d9
91d2622f289e8801d18d16e62aaa0c85
Markakis, C
Friday 4th October 2019  13:30 to 14:30
Markakis, C
Friday 4th October 2019  13:30 to 14:30
Cambridge University
2383
http://sms.cam.ac.uk/media/3073946
On numerical conservation of the PoincaréCartan integral invariant in relativistic fluid dynamics
Markakis, C
Friday 4th October 2019  13:30 to 14:30
The motion of strongly gravitating fluid bodies is described by the EulerEinstein system of partial differential equations. We report progress on formulating wellposed, acoustical and canonical hydrodynamic schemes, suitable for binary inspiral simulations and gravitationalwave source modelling. The schemes use a variational principle by CarterLichnerowicz stating that barotropic fluid motions are conformally geodesic, a corollary to Kelvin's theorem stating that initially irrotational flows remain irrotational, and Christodoulou's acoustic metric approach adopted to numerical relativity, in order to evolve the canonical momentum of a fluid element via Hamilton or HamiltonJacobi equations. These mathematical theorems leave their imprints on inspiral waveforms from binary neutron stars observed by the LIGOVirgo detectors. We describe a constraint damping scheme for preserving circulation in numerical general relativity, in accordance with Helmholtz's third theorem.
20191004T14:21:17+01:00
2383
3073946
true
16x9
false
no

On structurepreserving particleincell methods for the VlasovMaxwell equations
ucs_sms_3028099_3093766
http://sms.cam.ac.uk/media/3093766
On structurepreserving particleincell methods for the VlasovMaxwell equations
Kormann, K
Monday 28th October 2019  10:45 to 11:30
Mon, 04 Nov 2019 10:16:28 +0000
Isaac Newton Institute
Kormann, K
b2874c0ffde3e15ffae80e390fc88242
d7931abf9c753d1cb11b223137023691
27092215bf83a2e6ce0e23ff83af70ba
b8f19234246421b6bcf0fc2902666bbe
Kormann, K
Monday 28th October 2019  10:45 to 11:30
Kormann, K
Monday 28th October 2019  10:45 to 11:30
Cambridge University
2991
http://sms.cam.ac.uk/media/3093766
On structurepreserving particleincell methods for the VlasovMaxwell equations
Kormann, K
Monday 28th October 2019  10:45 to 11:30
Numerical schemes that preserve the structure of the kinetic equations can
provide new insight into the long time behavior of fusion plasmas. An electromagnetic
particleincell solver for the Vlasov{Maxwell equations that preserves at the discrete
level the noncanonical Hamiltonian structure of the Vlasov{Maxwell equations has
been presented in [1]. In this talk, the framework of this geometric particleincell
method will be presented and extension to curvilinear coordinates will be discussed.
Moreover, various options for the temporal discretizations will be proposed and compared.
[1] M. Kraus, K. Kormann, P. J. Morrison, and E. Sonnendrucker. GEMPIC: geometric electromag
netic particleincell methods. Journal of Plasma Physics, 83(4), 2017.
20191104T10:16:28+00:00
2991
3093766
true
16x9
false
no

On the construction of some symplectic Pstable additive Runge—Kutta methods
ucs_sms_3028099_3124310
http://sms.cam.ac.uk/media/3124310
On the construction of some symplectic Pstable additive Runge—Kutta methods
Zanna, A
Wednesday 11th December 2019  14:05 to 14:50
Mon, 16 Dec 2019 16:03:51 +0000
Isaac Newton Institute
Zanna, A
a32362359b2425775f2d9339d7ede16e
e972f21a93276dd7a8c00994ee38efc0
2dc7cb2c34edd224bcf7e731e3154df9
4df70fb10b2302cbb0f2f87c9e31abfa
Zanna, A
Wednesday 11th December 2019  14:05 to 14:50
Zanna, A
Wednesday 11th December 2019  14:05 to 14:50
Cambridge University
2938
http://sms.cam.ac.uk/media/3124310
On the construction of some symplectic Pstable additive Runge—Kutta methods
Zanna, A
Wednesday 11th December 2019  14:05 to 14:50
Symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation treating all the terms in the Lagrangian with the same quadrature formula. We construct a family of symplectic methods allowing the use of different quadrature formula for different parts of the Lagrangian. In particular, we study a family of methods using Lobatto quadrature (with corresponding Lobatto IIIAIIIB symplectic method) and Gauss–Legendre quadrature combined in an appropriate way. The resulting methods are similar to additive RungeKutta methods. The IMEX method, using the Verlet and IMR combination is a particular case of this family. The methods have the same favourable implicitness as the underlying Lobatto IIIAIIIB pair. Differently from the Lobatto IIIAIIIB, which are known not to be Pstable, we show that the new methods satisfy the requirements for Pstability.
20191216T16:03:51+00:00
2938
3124310
true
4x3
false
no

On the nature of mathematical joy
ucs_sms_3028099_3111717
http://sms.cam.ac.uk/media/3111717
On the nature of mathematical joy
Mansfield, E
Thursday 28th November 2019  16:00 to 17:00
Thu, 28 Nov 2019 16:49:07 +0000
Isaac Newton Institute
Mansfield, E
f0e17561188158a2d103fcafd65a628d
db8be4630b32ef38d6ab04844f09e5b4
0f278abcb94b1bc648dad19aab174edd
1c7d4cebd9d59bd750455de577bfec8c
Mansfield, E
Thursday 28th November 2019  16:00 to 17:00
Mansfield, E
Thursday 28th November 2019  16:00 to 17:00
Cambridge University
2541
http://sms.cam.ac.uk/media/3111717
On the nature of mathematical joy
Mansfield, E
Thursday 28th November 2019  16:00 to 17:00
Elizabeth Mansfield will discuss seven levels of mathematical joy based on her mathematical travels. This is a talk for a general audience.
20191128T16:49:07+00:00
2541
3111717
true
16x9
false
no

On the Solvability Complexity Index (SCI) hierarchy  Establishing the foundations of computational mathematics
ucs_sms_3028099_3110069
http://sms.cam.ac.uk/media/3110069
On the Solvability Complexity Index (SCI) hierarchy  Establishing the foundations of computational mathematics
Hansen, A
Tuesday 26th November 2019  15:05 to 16:05
Tue, 26 Nov 2019 16:04:30 +0000
Isaac Newton Institute
Hansen, A
79c3a52ae7f5a9b6fff8249600002f17
18040bc03546e0b4a76bb9ef3b2b1698
c8a00555d652db3aa84dbb347de8a947
5191028bcd92504b6e0e9d59b5bf27f8
Hansen, A
Tuesday 26th November 2019  15:05 to 16:05
Hansen, A
Tuesday 26th November 2019  15:05 to 16:05
Cambridge University
3334
http://sms.cam.ac.uk/media/3110069
On the Solvability Complexity Index (SCI) hierarchy  Establishing the foundations of computational mathematics
Hansen, A
Tuesday 26th November 2019  15:05 to 16:05
There are four areas in computational mathematics that have been intensely investigated over more than half a century: Spectral problems, PDEs, optimisation and inverse problems. However, despite the matureness of these fields, the foundations are far from known. Indeed, despite almost 90 years of quantum mechanics, it is still unknown whether it is possible to compute the spectrum of a selfadjoint Schrodinger operator with a bounded smooth potential. Similarly, it is not known which time dependent Schrodinger equations can be computed (despite well posedness of the equation). Linear programs (LP) can be solved with rational inputs in polynomial time, but can LPs be solved with irrational inputs? Problems in signal and image processing tend to use irrational numbers, so what happens if one plugs in the discrete cosine transform in one's favourite LP solver? Moreover, can one always compute the solutions to wellconditioned infinitedimensional inverse problems, and if not, which inverse problems can then be solved? In this talk we will discuss solutions to many of the questions above, and some of the results may seem paradoxical. Indeed, despite being an open problem for more than half a century, computing spectra of Schrodinger operators with a bounded potential is not harder than computing spectra of infinite diagonal matrices, the simplest of all infinitedimensional spectral problems. Moreover, computing spectra of compact operators, for which the method has been known for decades, is strictly harder than computing spectra of such Schrodinger operators. Regarding linear programs (and basis pursuit, semidefinite programs and LASSO) we have the following. For any integer K > 2 and any norm, there exists a family of well conditioned inputs containing irrational numbers so that no algorithm can compute K correct digits of a minimiser, however, there exists an algorithm that can compute K1 correct digits. But any algorithm producing K1 correct digits will need arbitrarily long time. Finally, computing K2 correct digits can be done in polynomial time in the number of variables. As we will see, all of these problems can be solved via the the Solvability Complexity Index (SCI) hierarchy, which is a theoretical program for establishing the boundaries of what computers can achieve in the sciences.
20191126T16:04:30+00:00
3334
3110069
true
16x9
false
no

Phase field modelling of free boundary problems
ucs_sms_3028099_3118248
http://sms.cam.ac.uk/media/3118248
Phase field modelling of free boundary problems
Stinner, B
Thursday 5th December 2019  14:15 to 15:00
Fri, 06 Dec 2019 11:23:59 +0000
Isaac Newton Institute
Stinner, B
a3d708203863b2d5de61423e7bfe701e
b901051c7f1b2b7a98ad7efa9c11b0af
d894a19e4ba176a8e33fa2e799df82c2
eb7bac25e572404ef98bccc254a890d0
Stinner, B
Thursday 5th December 2019  14:15 to 15:00
Stinner, B
Thursday 5th December 2019  14:15 to 15:00
Cambridge University
2801
http://sms.cam.ac.uk/media/3118248
Phase field modelling of free boundary problems
Stinner, B
Thursday 5th December 2019  14:15 to 15:00
Diffuse interface models based on the phase field methodology have been developed and investigated in various applications such as solidification processes, tumour growth, or multiphase flow. The interfaces are represented by thin layers, across which quantities rapidly but smoothly change their values. These interfacial layers are described in terms of order parameters, the equations for which can be solved using relatively straightforward methods, such as finite elements with adaptive mesh refinement, as no tracking of any interface is required. The interface motion is usually coupled to other fields and equations adjacent or on the interface, for instance, diffusion equations in alloys or the momentum equation in fluid flow. We discuss how such systems can be incorporated into phase field models in a generic way. Furthermore, we present a computational framework where specific models can be implemented and later on conveniently amended, if desired, in a highlevel language, and which then bind to efficient software backends. A couple of code listings and numerical simulations serve to illustrate the approach
20191206T11:23:59+00:00
2801
3118248
true
16x9
false
no

Random Batch Methods for Interacting Particle Systems and Consensusbased Global Nonconvex Optimization in Highdimensional Machine Learning (copy)
ucs_sms_3028099_3100177
http://sms.cam.ac.uk/media/3100177
Random Batch Methods for Interacting Particle Systems and Consensusbased Global Nonconvex Optimization in Highdimensional Machine Learning (copy)
Jin, S
Monday 11th November 2019  14:00 to 15:00
Wed, 13 Nov 2019 08:43:26 +0000
Isaac Newton Institute
Jin, S
1c7f7316b2002464d5bfc5e1e08ce1ed
c46f6cc34a42b56fda2c0aea4f853f9e
58fe89cf6cb9f3ec255ac97232dd54fe
63be86cce1e9f62cc753d32bcaa1614a
Jin, S
Monday 11th November 2019  14:00 to 15:00
Jin, S
Monday 11th November 2019  14:00 to 15:00
Cambridge University
3263
http://sms.cam.ac.uk/media/3100177
Random Batch Methods for Interacting Particle Systems and Consensusbased Global Nonconvex Optimization in Highdimensional Machine Learning (copy)
Jin, S
Monday 11th November 2019  14:00 to 15:00
We develop random batch methods for interacting particle systems with large number of particles. These methods
use small but random batches for particle interactions,
thus the computational cost is reduced from O(N^2) per time step to O(N), for a
system with N particles with binary interactions.
For one of the methods, we give a particle number independent error estimate under some special interactions.
Then, we apply these methods
to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian
motion from random matrix theory, Thomson's problem,
distribution of wealth, opinion dynamics and clustering. Numerical results show that
the methods can capture both the transient solutions and the global equilibrium in
these problems.
We also apply this method and improve the consensusbased global optimization algorithm for high
dimensional machine learning problems. This method does not require taking gradient in finding global
minima for nonconvex functions in high dimensions.
20191113T08:43:26+00:00
3263
3100177
true
16x9
false
no

Rothschild Lecture: Hamiltonian Monte Carlo and geometric integration
ucs_sms_3028099_3118443
http://sms.cam.ac.uk/media/3118443
Rothschild Lecture: Hamiltonian Monte Carlo and geometric integration
SanzSerna, C
Friday 6th December 2019  16:00 to 17:00
Fri, 06 Dec 2019 17:03:15 +0000
Isaac Newton Institute
SanzSerna, C
a8baed80fdc92b3e913d7cff16a31a16
4d6ed431e2d9d84da1a22b6de3b04ad4
6f4f884c3afcf7cdd54ae461c4d87a59
7f628db186aa32fa6cfc0c153e3c5af1
SanzSerna, C
Friday 6th December 2019  16:00 to 17:00
SanzSerna, C
Friday 6th December 2019  16:00 to 17:00
Cambridge University
3324
http://sms.cam.ac.uk/media/3118443
Rothschild Lecture: Hamiltonian Monte Carlo and geometric integration
SanzSerna, C
Friday 6th December 2019  16:00 to 17:00
Many application fields require samples from an arbitrary probability distribution. Hamiltonian Monte Carlo is a sampling algorithm that originated in the physics literature and has later gained much popularity among statisticians. This is a talk addressed to a general audience, where I will describe the algorithm and some of its applications. The exposition requires basic ideas from different fields, from statistical physics to geometric integration of differential equations and from Bayesian statistics to Hamiltonian dynamics and I will provide the necessary background, albeit superficially.
20191206T17:03:15+00:00
3324
3118443
true
16x9
false
no

Serendipity Virtual Elements
ucs_sms_3028099_3085016
http://sms.cam.ac.uk/media/3085016
Serendipity Virtual Elements
Brezzi, F
Tuesday 22nd October 2019  09:05 to 09:50
Tue, 22 Oct 2019 09:59:01 +0100
Isaac Newton Institute
Brezzi, F
e009285b33e49b39ff9641cf96ff6a0e
fad6b381a19a1e6c71230376fb743d33
bd3826ddd860632a9d764ab7ec0aaab4
981c8fa9e6162d19eb1bbf9b80be8b42
Brezzi, F
Tuesday 22nd October 2019  09:05 to 09:50
Brezzi, F
Tuesday 22nd October 2019  09:05 to 09:50
Cambridge University
2982
http://sms.cam.ac.uk/media/3085016
Serendipity Virtual Elements
Brezzi, F
Tuesday 22nd October 2019  09:05 to 09:50
After a brief reminder of classical ("plain vanilla") Virtual Elements we will see the general philosophy of "enhanced Virtual Elements" and the various types of Serendipity spaces as particular cases. The construction will always be conceptually simple (and extremely powerful, in particular for polygons with many edges), but a code exploiting the full advantage of having many edges might become difficult in the presence of non convex polygons, and in particular for complicated shapes. We shall also discuss different choices ensuring various advantages for different amounts of work.
20191022T09:59:01+01:00
2982
3085016
true
16x9
false
no

Solving PDEs Numerically on Manifolds with Arbitrary Spatial Topologies
ucs_sms_3028099_3071587
http://sms.cam.ac.uk/media/3071587
Solving PDEs Numerically on Manifolds with Arbitrary Spatial Topologies
Lindblom, L
Tuesday 1st October 2019  09:30 to 10:30
Tue, 01 Oct 2019 10:36:05 +0100
Isaac Newton Institute
Lindblom, L
da71cfbd5596e4770be9ef7059e1e95e
539fb4d4bcc8f4315b302ee75430f7f1
8f2dac5caf179bc33497b604a433da66
c3513b92c047087abf6dd830817fbd1e
Lindblom, L
Tuesday 1st October 2019  09:30 to 10:30
Lindblom, L
Tuesday 1st October 2019  09:30 to 10:30
Cambridge University
3600
http://sms.cam.ac.uk/media/3071587
Solving PDEs Numerically on Manifolds with Arbitrary Spatial Topologies
Lindblom, L
Tuesday 1st October 2019  09:30 to 10:30
20191001T10:36:05+01:00
3600
3071587
true
16x9
false
no

Some results in the long time analysis of Hamiltonian PDEs and their numerical approximations
ucs_sms_3028099_3100255
http://sms.cam.ac.uk/media/3100255
Some results in the long time analysis of Hamiltonian PDEs and their numerical approximations
Faou, E
Tuesday 12th November 2019  16:00 to 17:00
Wed, 13 Nov 2019 09:37:45 +0000
Isaac Newton Institute
Faou, E
665afd63e3a94ca1c1de0be5a48b1e26
871aebeb2cf6b53efc3032c8f777c2d6
dee8f20cadb64c3036729c81f3568925
7f78749a3d2d4abc2c3c7c2755d4f666
Faou, E
Tuesday 12th November 2019  16:00 to 17:00
Faou, E
Tuesday 12th November 2019  16:00 to 17:00
Cambridge University
3451
http://sms.cam.ac.uk/media/3100255
Some results in the long time analysis of Hamiltonian PDEs and their numerical approximations
Faou, E
Tuesday 12th November 2019  16:00 to 17:00
I will review some results concerning the long time behavior of Hamiltonian PDEs, and address
similar questions for their numerical approximation. I will show numerical resonances can appear
both in space and time. I will also discuss the long time stability of solitary waves evolving
on a discret set of lattice points.
20191113T09:37:45+00:00
3451
3100255
true
16x9
false
no

Some thoughts about constrained sampling algorithms
ucs_sms_3028099_3105604
http://sms.cam.ac.uk/media/3105604
Some thoughts about constrained sampling algorithms
Leimkuhler, B
Thursday 21st November 2019  13:50 to 14:30
Fri, 22 Nov 2019 12:41:53 +0000
Isaac Newton Institute
Leimkuhler, B
47fccca4fbd6948c5b4d60b7b537a06c
d0a3d153ced7331cb03ac0dce8363fb0
270a263f691dcf4ec0921e39a322ebc1
66fae10168106187522c8da9a9dd0eb3
Leimkuhler, B
Thursday 21st November 2019  13:50 to 14:30
Leimkuhler, B
Thursday 21st November 2019  13:50 to 14:30
Cambridge University
2838
http://sms.cam.ac.uk/media/3105604
Some thoughts about constrained sampling algorithms
Leimkuhler, B
Thursday 21st November 2019  13:50 to 14:30
I will survey our work on algorithms for sampling diffusions on manifolds, including isokinetic methods and constrained Langevin dynamics methods. These have mostly been introduced and tested in the setting of molecular dynamics. It is interesting to consider possible uses of these ideas in other types of sampling computations, like neural network parameterization and training of generative models.
20191122T12:41:53+00:00
2838
3105604
true
16x9
false
no

Spatial/temporal scaling  Comber. A
ucs_sms_3028099_3036116
http://sms.cam.ac.uk/media/3036116
Spatial/temporal scaling  Comber. A
Comber. A
Wednesday 31st July 2019  12:30 to 13:00
Wed, 31 Jul 2019 16:51:18 +0100
Isaac Newton Institute
Comber. A
b721d2d5fd0fe6bb37223a595d4600cb
392a878a7c52c310ed2b8dedeecf34fb
f276f6cdf4437725d6b22d2ac4168266
08b109bc3fb48385db59c74a44164ea4
Comber. A
Wednesday 31st July 2019  12:30 to 13:00
Comber. A
Wednesday 31st July 2019  12:30 to 13:00
Cambridge University
1928
http://sms.cam.ac.uk/media/3036116
Spatial/temporal scaling  Comber. A
Comber. A
Wednesday 31st July 2019  12:30 to 13:00
20190731T16:51:18+01:00
1928
3036116
true
16x9
false
no

Spectral deferred correction in particleincell methods
ucs_sms_3028099_3093773
http://sms.cam.ac.uk/media/3093773
Spectral deferred correction in particleincell methods
Niesen, J
Monday 28th October 2019  15:15 to 16:00
Mon, 04 Nov 2019 10:16:03 +0000
Isaac Newton Institute
Niesen, J
6ff3f0e456650e59e19900ad75f08273
e46fc998772f10ac7af5c9d79d72bd8c
533ef969039eaeb00af64b6e4e6e1b6d
d93dfbe0ca08b55f6c3d671f73675306
Niesen, J
Monday 28th October 2019  15:15 to 16:00
Niesen, J
Monday 28th October 2019  15:15 to 16:00
Cambridge University
2326
http://sms.cam.ac.uk/media/3093773
Spectral deferred correction in particleincell methods
Niesen, J
Monday 28th October 2019  15:15 to 16:00
Particleincell methods solve the Maxwell equations for the electromagnetic
eld in combination with the equation of motion for the charged particles in a
plasma. The motion of charegd particles is usually computed using the Boris algorithm,
a variant of Stormer{Verlet for Lorentz force omputations, which has impressive
performance and order two (like Stormer{Verlet). Spectral deferred correction is an
iterative time stepping method based on collocation, which in each time step performs
multiple sweeps of a loworder method (here, the Boris method) in order to obtain a
highorder approximation. This talk describes the ongoing eorts of Kristoer Smedt,
Daniel Ruprecht, Steve Tobias and the speaker to embed a spectral deferred correction
time stepper based on the Boris method in a particleincell method.
20191104T10:16:03+00:00
2326
3093773
true
16x9
false
no

Step size control for Newton type MCMC samplers Jonathan Goodman
ucs_sms_3028099_3105414
http://sms.cam.ac.uk/media/3105414
Step size control for Newton type MCMC samplers Jonathan Goodman
Goodman, J
Wednesday 20th November 2019  15:05 to 15:35
Fri, 22 Nov 2019 08:43:44 +0000
Isaac Newton Institute
Goodman, J
edd49735d590519f60dbb4a0f60e1f4e
5905c60256154cfdf0e6c29b48bf3d84
a6d611d2d923a49e2aa959a881338736
756773249c93335ac36431ca379ff7d7
Goodman, J
Wednesday 20th November 2019  15:05 to 15:35
Goodman, J
Wednesday 20th November 2019  15:05 to 15:35
Cambridge University
1347
http://sms.cam.ac.uk/media/3105414
Step size control for Newton type MCMC samplers Jonathan Goodman
Goodman, J
Wednesday 20th November 2019  15:05 to 15:35
ABSTRACT: MCMC sampling can use ideas from the optimization community. Optimization via Newton’s method can fail without line search, even for smooth strictly convex problems. Affine invariant Newton based MCMC sampling uses a Gaussian proposal based on a quadratic model of the potential using the local gradient and Hessian. This can fail (conjecture: give a transient Markov chain) even for smooth strictly convex potentials. We describe a criterion that allows a sequence of proposal distributions from X_n with decreasing “step sizes” until (with probability 1) a proposal is accepted. “Very detailed balance” allows the whole process to preserve the target distribution. The method works in experiments but the theory is missing.
20191122T08:43:44+00:00
1347
3105414
true
16x9
false
no

Symmetry Preserving Interpolation
ucs_sms_3028099_3110053
http://sms.cam.ac.uk/media/3110053
Symmetry Preserving Interpolation
Hubert, E
Tuesday 26th November 2019  14:05 to 14:50
Tue, 26 Nov 2019 15:29:30 +0000
Isaac Newton Institute
Hubert, E
fea8517f0b5d787adfcbc275ffa732b4
8203c45a3b3082dc59ec71b664e7fac2
754701b8dcf97c89f4928a30b72378a3
4885fc008e50be1bc35ba218b095a172
Hubert, E
Tuesday 26th November 2019  14:05 to 14:50
Hubert, E
Tuesday 26th November 2019  14:05 to 14:50
Cambridge University
3150
http://sms.cam.ac.uk/media/3110053
Symmetry Preserving Interpolation
Hubert, E
Tuesday 26th November 2019  14:05 to 14:50
In this talk I choose to present the PhD work of Erick Rodriguez Bazan. We address multivariate interpolation in the presence of symmetry as given by a finite group. Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature
that can be more relevant to a mathematical model than the numerical accuracy of the parameters. Beside its preservation, symmetry shall also be exploited to alleviate the computational cost.
We revisit minimal degree and least interpolation spaces [de Boor & Ron 1990] with symmetry adapted bases (rather than the usual monomial bases). In these bases, the multivariate Vandermonde matrix (a.k.a colocation matrix) is block diagonal as soon as the set of nodes is invariant. These blocks capture the inherent redundancy in the computations. Furthermore any equivariance an interpolation problem might have will be automatically preserved : the output interpolant will have the same equivariance property.
The special case of multivariate Hermite interpolation leads us to question the representation of polynomial ideals. Gröbner bases, the preferred tool for algebraic computations, breaks any kind of symmetry. The prior notion of HBases, introduced by Macaulay, appears as more suitable.
Reference:
https://dl.acm.org/citation.cfm?doid=3326229.3326247
https://hal.inria.fr/hal01994016 Joint work with Erick Rodriguez Bazan
20191126T15:29:30+00:00
3150
3110053
true
16x9
false
no

tba
ucs_sms_3028099_3074002
http://sms.cam.ac.uk/media/3074002
tba
Lehner, L
Friday 4th October 2019  14:30 to 15:30
Fri, 04 Oct 2019 15:56:29 +0100
Isaac Newton Institute
Lehner, L
453c372e5c73774e4c1301fb3aebcec8
6df84cf35824fbe6565892dd706416f2
2269dbab36764a7a4417b72eddaf9e97
356c0b4b8e7c91d0b884774a92977e86
Lehner, L
Friday 4th October 2019  14:30 to 15:30
Lehner, L
Friday 4th October 2019  14:30 to 15:30
Cambridge University
3720
http://sms.cam.ac.uk/media/3074002
tba
Lehner, L
Friday 4th October 2019  14:30 to 15:30
20191004T15:56:29+01:00
3720
3074002
true
16x9
false
no

The Connections Between Discrete Geometric Mechanics, Information Geometry and Machine Learning
ucs_sms_3028099_3035542
http://sms.cam.ac.uk/media/3035542
The Connections Between Discrete Geometric Mechanics, Information Geometry and Machine Learning
Leok, M
Tuesday 30th July 2019  14:00 to 15:00
Wed, 31 Jul 2019 12:11:43 +0100
Isaac Newton Institute
Leok, M
92a7e3fde732dcb159e0fa04eece4721
67ce64178ae87c7b46e7413ef3931c62
be1ce33fc5d56f168dce1c8dc7194ba9
3d6b939aabc076dac4676c7b7b6826ee
Leok, M
Tuesday 30th July 2019  14:00 to 15:00
Leok, M
Tuesday 30th July 2019  14:00 to 15:00
Cambridge University
3335
http://sms.cam.ac.uk/media/3035542
The Connections Between Discrete Geometric Mechanics, Information Geometry and Machine Learning
Leok, M
Tuesday 30th July 2019  14:00 to 15:00
20190731T12:11:44+01:00
3335
3035542
true
16x9
false
no

UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTIONDIFFUSION PROBLEMS
ucs_sms_3028099_3085214
http://sms.cam.ac.uk/media/3085214
UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTIONDIFFUSION PROBLEMS
Xu, J
Tuesday 22nd October 2019  13:55 to 14:40
Tue, 22 Oct 2019 14:56:16 +0100
Isaac Newton Institute
Xu, J
57b0cfee898b940f3b2197f9a6382f8d
1d0e793d5d9f7aff9f3d8f6d610597be
a94af433d1713537fae8a0ba72c62982
25a55c4d5e0f633c7a903283d8ab1431
Xu, J
Tuesday 22nd October 2019  13:55 to 14:40
Xu, J
Tuesday 22nd October 2019  13:55 to 14:40
Cambridge University
3009
http://sms.cam.ac.uk/media/3085214
UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTIONDIFFUSION PROBLEMS
Xu, J
Tuesday 22nd October 2019  13:55 to 14:40
This talk is devoted to the construction and analysis of the finite element approximations for the H(grad), H(curl) and H(div) convectiondiffusion problems. An essential feature of these constructions is to properly average the PDE coefficients on subsimplexes from the underlying simplicial finite element meshes. The schemes are of the class of exponential fitting methods that result in special upwind schemes when the diffusion coefficient approaches to zero. Their wellposedness are established for sufficiently small mesh size assuming that the convectiondiffusion problems are uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate the robustness and effectiveness for general convectiondiffusion problems. This is a joint work with Shounan Wu.
20191022T14:56:17+01:00
3009
3085214
true
16x9
false
no

Variational formulations for dissipative systems
ucs_sms_3028099_3056794
http://sms.cam.ac.uk/media/3056794
Variational formulations for dissipative systems
OberBlöbaum, S
Wednesday 4th September 2019  14:00 to 15:00
Thu, 05 Sep 2019 12:21:22 +0100
Isaac Newton Institute
OberBlöbaum, S
bcfd5fd5508a536b92b08de4327b3ee1
71c81f7c8493ea660814f55bc0d1779c
8ed0ce8d970a8fdcf46ed7fea6b29630
230b8c232812c6888146e962a79dcfc1
OberBlöbaum, S
Wednesday 4th September 2019  14:00 to 15:00
OberBlöbaum, S
Wednesday 4th September 2019  14:00 to 15:00
Cambridge University
3056
http://sms.cam.ac.uk/media/3056794
Variational formulations for dissipative systems
OberBlöbaum, S
Wednesday 4th September 2019  14:00 to 15:00
Variational principles are powerful tools for the modelling and simulation of conservative mechanical and electrical systems. As it is wellknown, the fulfilment of a variational principle leads to the EulerLagrange equations of motion describing the dynamics of such systems. Furthermore, a variational discretisation directly yields unified numerical schemes with powerful structurepreserving properties. Since many years there have been several attempts to provide a variational description also for dissipative mechanical systems, a task that is addressed in the talk in order to construct both Lagrangian and Hamiltonian pictures of their dynamics. One way doing this is to use fractional terms in the Lagrangian or Hamiltonian function which allows for a purely variational derivation of dissipative systems. Another approach followed in this talk is to embed the nonconservative systems in larger conservative systems. These concepts are used to develop variational integrators for which superior qualitative numerical properties such as the correct energy dissipation rate are demonstrated.
20190905T12:21:22+01:00
3056
3056794
true
16x9
false
no

What it takes to catch a wave packet
ucs_sms_3028099_3102867
http://sms.cam.ac.uk/media/3102867
What it takes to catch a wave packet
Lasser, C
Wednesday 13th November 2019  14:00 to 15:00
Mon, 18 Nov 2019 11:18:21 +0000
Isaac Newton Institute
Lasser, C
9100c7d65aed9639893fcc848ef818a5
9e9d0adbd91853e55359cbcac516cd95
b0e6113ffb124020f747a37a37ff648d
b6a76fe0f08e1b6ed4f56b4f659d8bed
Lasser, C
Wednesday 13th November 2019  14:00 to 15:00
Lasser, C
Wednesday 13th November 2019  14:00 to 15:00
Cambridge University
3900
http://sms.cam.ac.uk/media/3102867
What it takes to catch a wave packet
Lasser, C
Wednesday 13th November 2019  14:00 to 15:00
Wave packets describe the quantum vibrations of a molecule. They are highly oscillatory,
highly localized and move in high dimensional configuration spaces. The talk addresses
three meshless numerical methods for catching them: single Gaussian beams,
superpositions of them, and the socalled linearized initial value representation.
20191118T11:18:22+00:00
3900
3102867
true
16x9
false
no
3028099