Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

Conference paper (2022)

Authors

A. Heinlein Numerical Analysis - EEMCS
A. Klawonn University of Cologne
Martin Lanser University of Cologne
Janine Weber University of Cologne
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2022 A. Heinlein, Axel Klawonn, Martin Lanser, Janine Weber
DOI: https://doi.org/10.1007/978-3-030-95025-5_32
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.

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