Compatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere law
Martin Campos Pinto, Eric Sonnendrücker
Abstract
This article is the first of a series where we develop and analyze structure-preserving finite element discretizations for the time-dependent 2D Maxwell system with long-time stability properties, and propose a charge-conserving deposition scheme to extend the stability properties in the case where the current source is provided by a particle method. The schemes proposed here derive from a previous study where a generalized commuting diagram was identified as an abstract compatibility criterion in the design of stable schemes for the Maxwell system alone, and applied to build a series of conforming and non-conforming schemes in the 3D case. Here the theory is extended to account for approximate sources, and specific charge-conserving schemes are provided for the 2D case. In this article we study two schemes which include a strong discretization of the Ampere law. The first one is based on a standard conforming mixed finite element discretization and the long-time stability is ensured by a Raviart-Thomas finite element interpolation for the current source, thanks to its commuting diagram properties. The second one is a new non-conforming variant where the numerical fields are sought in fully discontinuous spaces. Numerical experiments involving Maxwell and Maxwell-Vlasov problems are then provided to validate the stability of the proposed methods.
BibTeX
@article{Campos_Pinto_2017,
title={Compatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere law},
volume={3},
ISSN={2426-8399},
url={http://dx.doi.org/10.5802/smai-jcm.20},
DOI={10.5802/smai-jcm.20},
journal={The SMAI Journal of computational mathematics},
publisher={MathDoc/Centre Mersenne},
author={Campos Pinto, Martin and Sonnendrücker, Eric},
year={2017},
month=sep,
pages={53–89} }