Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

S. C. Brenner; Jintao Cui; Z. Nan; L. Y. Sung

doi:10.1090/S0025-5718-2011-02540-8

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

S. C. Brenner, Jintao Cui, Z. Nan, L. Y. Sung

Research output: Journal article publication › Journal article › Academic research › peer-review

24 Citations (Scopus)

Abstract

We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergencefree vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.

Original language	English
Pages (from-to)	643-659
Number of pages	17
Journal	Mathematics of Computation
Volume	81
Issue number	278
DOIs	https://doi.org/10.1090/S0025-5718-2011-02540-8
Publication status	Published - 30 Mar 2012
Externally published	Yes

Keywords

Finite element
Hodge decomposition
Maxwell's equations

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

More information

10.1090/S0025-5718-2011-02540-8

Cite this

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title = "Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations",

abstract = "We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergencefree vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.",

keywords = "Finite element, Hodge decomposition, Maxwell's equations",

author = "Brenner, {S. C.} and Jintao Cui and Z. Nan and Sung, {L. Y.}",

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T1 - Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

AU - Brenner, S. C.

AU - Cui, Jintao

AU - Nan, Z.

AU - Sung, L. Y.

PY - 2012/3/30

Y1 - 2012/3/30

N2 - We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergencefree vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.

AB - We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergencefree vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.

KW - Finite element

KW - Hodge decomposition

KW - Maxwell's equations

UR - http://www.scopus.com/inward/record.url?scp=84858962673&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-2011-02540-8

DO - 10.1090/S0025-5718-2011-02540-8

M3 - Journal article

SN - 0025-5718

VL - 81

SP - 643

EP - 659

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 278

ER -

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

Abstract

Keywords

ASJC Scopus subject areas

More information

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