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Current Problems in Numerical Analysis

usually takes place each Friday, at 10:00 in IM, rear building, ground floor
Chair: Michal Křížek, Pavel Kůs, Jan Papež, Jakub Šístek, Tomáš Vejchodský
Old web page with the seminar history: https://workshop.math.cas.cz/okmma/

A parallel domain decomposition solver for immersed boundary finite element method

Pavel Kůs
Institute of Mathematics of the Czech Academy of Sciences
Friday, 2. December 2022 - 10:00 to 11:00
A conforming mesh generation for large-scale finite element method calculations is often a computational bottleneck, especially in the case of complex geometries. Not only is it compute time demanding, but transforming a CAD model to a volumetric mesh with required properties might be a hard problem. Immersed boundary approaches are gaining popularity as they can circumvent the need for the creation of conforming mesh. In this presentation, we discuss the challenges of the use of immersed boundary FEM solver with adaptivity of the underlying mesh and parallel implementation of domain decomposition. We show the algorithmic treatment, the influence of this setting on load balancing, and show performance of our implementation using challenging engineering geometries. Seminar exceptionally takes place in the lecture hall in the 3rd floor of the front building.

A-posteriori-steered h- and p-robust multigrid solvers and adaptivity

Ani Miraçi
TU Wien
Friday, 9. December 2022 - 10:00 to 11:00
We study a symmetric second-order linear elliptic PDE discretized by piecewise polynomials of arbitrary degree p ≥ 1. To treat the arising linear system, we propose a geometric multigrid method with zero pre- and one post-smoothing step by an overlapping Schwarz (block-Jacobi) method [1]. Introducing optimal step sizes which minimize the algebraic error in the level-wise error correction step of multigrid, one obtains an explicit Pythagorean formula for the algebraic error. Importantly, this inherently induces a fully computable a posteriori estimator for the energy norm of the algebraic error. We show the two following results and their equivalence: 1) the solver contracts the algebraic error independently of the polynomial degree p; 2) the estimator represents a two-sided p-robust bound on the algebraic error. The p-robustness results are obtained by carefully applying the results of [2] for one mesh, combined with a multilevel stable decomposition for piecewise affine polynomials... more

Christmas lecture: Continuous Dispersion Problems and Farthest-First Traversals in a Simplex

Jan Brandts
University of Amsterdam
Friday, 16. December 2022 - 10:00 to 11:00

t.b.a.

Hana Horníková
University of West Bohemia, Pilsen
Friday, 20. January 2023 - 10:00 to 11:00

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