Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

Marcella Bonazzoli 1 Victorita Dolean 2, 3 Ivan G. Graham 4 Euan A. Spence 4 Pierre-Henri Tournier 5, 6
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
6 ALPINES - Algorithms and parallel tools for integrated numerical simulations
Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL - Laboratoire Jacques-Louis Lions
Abstract : This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is constructed using Additive Schwarz domain decomposition methods. The theory developed here shows that if the absorption is large enough, and if the subdomain and coarse mesh diameters and overlap are chosen appropriately, then the classical two-level overlapping Additive Schwarz preconditioner (with PEC boundary conditions on the subdomains) performs optimally -- in the sense that GMRES converges in a wavenumber-independent number of iterations -- for the problem with absorption. An important feature of the theory is that it allows the coarse space to be built from low-order elements even if the PDE is discretised using high-order elements. It also shows that additive methods with minimal overlap can be robust. Numerical experiments are given that illustrate the theory and its dependence on various parameters. These experiments motivate some extensions of the preconditioners which have better robustness for problems with less absorption, including the propagative case. At the end of the paper we illustrate the performance of these on two substantial applications; the first (a problem with absorption arising from medical imaging) shows the empirical robustness of the preconditioner against heterogeneity, and the second (scattering by a COBRA cavity) shows good scalability of the preconditioner with up to 3,000 processors.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01644011
Contributor : Marcella Bonazzoli <>
Submitted on : Tuesday, November 21, 2017 - 7:32:16 PM
Last modification on : Sunday, June 23, 2019 - 1:25:24 AM

Links full text

Identifiers

Citation

Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham, Euan A. Spence, Pierre-Henri Tournier. Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption. Mathematics of Computation, American Mathematical Society, In press, ⟨10.1090/mcom/3447⟩. ⟨hal-01644011⟩

Share

Metrics

Record views

322