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Dienstag, 09.03.2021, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
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Online Event

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Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Dienstag, 16.03.2021, 13:30 Uhr (Online Event)
Seminar Numerische Mathematik
Dr. Jürgen Fuhrmann, WIAS Berlin:
PDELib.jl: Towards software components for the numerical solution of partial differential equations in Julia
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Online Event

Abstrakt
In recent years, in particular since the release of version 1.0, the Julia programming language gained significant momentum in fields related to scientific computing and data science. Taking advantage of accumulated experience and know-how in language design, designed around the just-in-time compilation paradigm, and featuring first class multidimensional array handling, it allows for the implementation of complex numerical algorithms without sacrificing efficiency. In recent years, in particular since the release of version 1..0, the Julia programming language gained significant momentum in fields related to scientific computing and data science.
In the talk, we will give a short overview on features of the Julia language which renders it well suited for the implementation of solvers for complex systems of partial differential equations, including multiple dispatch allowing for the implementation of automatic differentiation, interface oriented API design and its package manager supporting reusability and reproducibility.
We will report on the successful steps towards the implementation of software components for the numerical solution of PDEs.. Focus will be on the package VoronoiFVM.jl and supporting packages.

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For zoom login details please contact Alexander Linke linke@wias-berlin.de

Veranstalter
WIAS Berlin
Dienstag, 16.03.2021, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Kostas Papafitsoros, WIAS Berlin:
Optimization with learning-informed differential equation constraints and its applications (online talk)
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Online Event

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Donnerstag, 18.03.2021, 14:00 Uhr (Online Event)
Seminar Numerische Mathematik
Prof. Leo Rebholz, Clemson University, USA:
Anderson acceleration and how it speeds up convergence in fixed point iterations
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Online Event

Abstrakt
Anderson acceleration (AA) is an extrapolation technique originally proposed in 1965 that recombines the most recent iterates and update steps in a fixed point iteration to improve the convergence properties of the sequence. Despite being successfully used for many years to improve nonlinear solver behavior on a wide variety of problems, a theory that explains the often-observed accelerated convergence was lacking. In this talk, we give an introduction to AA, then present a proof of AA convergence which shows that it improves the linear convergence rate based on a gain factor of an underlying optimization problem, but also introduces higher order terms in the residual error bound. We then discuss improvements to AA based on our convergence theory, and show numerical results for the algorithms applied to several application problems including Navier--Stokes, Boussinesq, and nonlinear Helmholtz systems.

Weitere Informationen
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Veranstalter
WIAS Berlin
Donnerstag, 25.03.2021, 14:00 Uhr (Online Event)
Seminar Numerische Mathematik
Benoît Gaudeul, Université de Lille, France:
Two entropic finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints
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Online Event

Abstrakt
In this talk, I consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation.
I present two finite volume schemes based on different formulations of the fluxes. I will also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence result is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.
This is a joint work with Jürgen Fuhrmann.

Weitere Informationen
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Veranstalter
WIAS Berlin
Donnerstag, 15.04.2021, 14:00 Uhr (Online Event)
Seminar Numerische Mathematik
Prof. Julia Novo, Universidad Autónoma de Madrid, Spanien:
Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows
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Online Event

Abstrakt
Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are presented. We consider two cases: the case in which the snapshots are based on a non inf-sup stable method and the case in which the snapshots are based on an inf-sup stable method. For both cases we construct approximations to the velocity and the pressure. For the first case, we analyze a method in which the snapshots are based on a stabilized scheme with equal order polynomials for the velocity and the pressure with local projection stabilization (LPS) for the gradient of the velocity and the pressure. For the POD method we add the same kind of LPS stabilization for the gradient of the velocity and the pressure as the direct method, together with grad-div stabilization. In the second case, the snapshots are based on an inf-sup stable Galerkin method with grad-div stabilization and for the POD model we also apply grad-div stabilization. In this case, since the snapshots are discretely divergence-free, the pressure can be removed from the formulation of the POD approximation to the velocity. To approximate the pressure, needed in many engineering applications, we use a supremizer pressure recovery method. Error bounds with constants independent of inverse powers of the viscosity parameter are proved for both methods. Numerical experiments show the accuracy and performance of the schemes.

Weitere Informationen
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Veranstalter
WIAS Berlin
29. April 2021 (Online Event)
Workshop/Konferenz: FUHRI2021: Finite volUme metHods for Real-world applIcations
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Online Event

Veranstalter
WIAS Berlin