14:00 - 15:00
- Lehel Banjai, Heriot-Watt Univerity
- Emmanuil Georgoulis, University of Leicester/NTU Athens
- María López Fernández, University of Malaga
- Charalambos Makridakis, IACM/University of Sussex/Crete
- Daniel Peterseim, University of Augsburg
This is a One World Seminar Series.
The seminars occur every two weeks, on a Monday (14:00-15:00 BST).
Zoom links will be sent on the Friday prior to each seminar, with a reminder on Monday morning.
Recordings of talks given as part of this series can be found here.
- Slender structures that undergo large deformations with minor (thermal, electrical or chemical) actuation are ubiquitous in the construction of micro and macro devices in engineering and medicine. Their reduced 2d models consist of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate surface and the latter is a restriction on its first fundamental form. We discuss a formal derivation of reduced models for single layer, bilayer, and prestrained plates along with equivalent formulations that make them amenable to computation. We propose a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian, and discuss its properties including Gamma-convergence. We design discrete gradient flows to minimize the ensuing nonconvex problems and to find suitable initial configurations. We present several insightful simulations, some of practical interest, and assess a number of computational challenges of the approximation process.
- The Hamiltonian Monte Carlo (aka Hybrid Monte Carlo) method is an extremely popular Markov chain algorithm to obtain samples from a target probability distribution. The computational cost of the algorithm mostly originates from the need to numerically integrate, at each step of the chain, a Hamiltonian system of ordinary differential equations. It is therefore important to carry out those integrations as efficiently as possible. While at present the Stormer/Verlet integrator is the integrator of choice, it is possible to construct special integrators tailored to this task. These alternative integrators, while being as easy to implement as Stormer/Verlet, allow for very substantial reductions of the work required to obtain the samples. The talk will focus on the numerical analysis principles used to construct the new integrators.
Endre Süli (University of Oxford) - Discrete De Giorgi--Nash--Moser theory and the finite element approximation of chemically reacting fluids
3 May 2021
Victorita Dolean (University of Strathclyde, Glasgow) - Robust solvers for time-harmonic wave propagation problems
19 April 2021
Andreas Veeser (Università degli Studi di Milano) - Accurate error bounds and equivalence of seminorms
22 March 2021
Maria Lopez Fernandez - Pseudospectral Roaming Contour Integral Methods for Convection-Diffusion Equations
8 March 2021
Carola-Bibiane Schönlie, University of Cambridge - Structure-Preserving Deep Learning
22 February 2021
Wolfgang Dahmen, University of South Carolina - Nonlinear Model Reduction: Recent Developments and Perspectives
8 February 2021
Michael Feischl, TU Vienna - Black box Algorithms for Adaptive FEM
11 January 2021
Ivan Oseledets, Skolkovo Institute of Science and Technology
14 December 2020
Nick Trefethen, University of Oxford - Exactness of Quadrature Formulas
30 November 2020
Max Jensen, University of Sussex - Monotone Finite Element Solution of Fully Nonlinear Differential Equations
16 November 2020
Desmond Higham, University of Edinburgh - Should We Be Perturbed About Deep Learning?
2 November 2020
Houman Owhadi, Caltech - On Learning Adapted Kernels for Numerical Approximation
19 October 2020
Virginie Ehrlacher, ENPC - Finite Volume Scheme for the Stefan-Maxwell System
- Joint work with Clément Cancès and Laurent Monasse
- Reference: Clément Cancès, Virginie Ehrlacher, Laurent Monasse, Finite volumes for the Stefan-Maxwell cross-diffusion system (2020)
5 October 2020
Christian Lubich, University of Tubingen - Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations
21 September 2020
Ilaria Perugia, University of Vienna - Space-Time Discontinuous Galerkin Methods for Wave Propagation
7 September 2020
Christoph Schwab, ETH Zurich - Exponential Convergence of hp-FEM for Spectral Fractional Diffusion in Polygons
20 July 2020
Alfio Quarteroni, Politecnico di Milano/Ecole Polytechnique Fédérale de Lausanne - The Mathematical Heart: a Computational Model for the Simulation of the Heart Function
This seminar is supported as part of the ICMS Online Mathematical Sciences Seminars.