Scalable solvers for complex electromagnetics problems

01/25/2019
by   Santiago Badia, et al.
0

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce the continuity across subdomains of the method, we use a partition of the interface objects (edges and faces) into sub-objects determined by the variation of the physical coefficients of the problem. For multi-material problems, a constant coefficient condition is enough to define this sub-partition of the objects. For arbitrarily heterogeneous problems, a relaxed version of the method is defined, where we only require that the maximal contrast of the physical coefficient in each object is smaller than a predefined threshold. Besides, the addition of perturbation terms to the preconditioner is empirically shown to be effective in order to deal with the case where the two coefficients of the model problem jump simultaneously across the interface. The new method, in contrast to existing approaches for problems in curl-conforming spaces, preserves the simplicity of the original preconditioner, i.e., no spectral information is required, whilst providing robustness with regard to coefficient jumps and heterogeneous materials. A detailed set of numerical experiments, which includes the application of the preconditioner to 3D realistic cases, shows excellent weak scalability properties of the implementation of the proposed algorithms.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 14

page 17

page 19

page 24

06/19/2020

Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems

This work introduces a novel, fully robust and highly-scalable, h-adapti...
06/11/2021

Multilevel Spectral Domain Decomposition

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation o...
04/19/2021

Learning adaptive coarse spaces of BDDC algorithms for stochastic elliptic problems with oscillatory and high contrast coefficients

In this paper, we consider the balancing domain decomposition by constra...
12/13/2021

A Weak Galerkin Method for Elasticity Interface Problems

This article introduces a weak Galerkin (WG) finite element method for l...
06/23/2020

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the n...
04/08/2020

Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation

We consider one-level additive Schwarz domain decomposition precondition...
08/08/2021

Scalable adaptive PDE solvers in arbitrary domains

Efficiently and accurately simulating partial differential equations (PD...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.