Numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids

Niel K. Madsen; Richard W. Ziolkowski

doi:10.1016/0165-2125(88)90013-3

Numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids

Niel K. Madsen, Richard W. Ziolkowski

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

62 Scopus citations

Abstract

Several different methods for solving Maxwell's equations in the time-domain through the use of irregular nonorthogonal grids are presented. Employing quadrilateral and/or triangular elements, these methods allow more accurate modeling of nonrectangular structures. The traditional "stair-stepping" boundary approximations associated with standard orthogonal-grid finite-difference methods are avoided. Numerical results comparing all of the methods are given. A modified finite-volume method, which is a direct generalization of the standard finite-difference method to arbitrary polygonal grids, is shown to be the most accurate.

Original language	English (US)
Pages (from-to)	583-596
Number of pages	14
Journal	Wave Motion
Volume	10
Issue number	6
DOIs	https://doi.org/10.1016/0165-2125(88)90013-3
State	Published - Dec 1988

ASJC Scopus subject areas

Modeling and Simulation
Physics and Astronomy(all)
Computational Mathematics
Applied Mathematics

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title = "Numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids",

abstract = "Several different methods for solving Maxwell's equations in the time-domain through the use of irregular nonorthogonal grids are presented. Employing quadrilateral and/or triangular elements, these methods allow more accurate modeling of nonrectangular structures. The traditional {"}stair-stepping{"} boundary approximations associated with standard orthogonal-grid finite-difference methods are avoided. Numerical results comparing all of the methods are given. A modified finite-volume method, which is a direct generalization of the standard finite-difference method to arbitrary polygonal grids, is shown to be the most accurate.",

author = "Madsen, {Niel K.} and Ziolkowski, {Richard W.}",

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year = "1988",

month = dec,

doi = "10.1016/0165-2125(88)90013-3",

language = "English (US)",

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journal = "Wave Motion",

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AU - Madsen, Niel K.

AU - Ziolkowski, Richard W.

N1 - Funding Information: The authorsw ouldlike to thanka ndacknowl-edget hef ollowingin dividualfso r theira ssistance and involvemenint the work presenteidn this paper:O liverE dwardsJ,. Brian Grant,R obertL . Lee, John Peterson, Scott Ray, and Ron Schmucker. This work wasp erformeudn dert hea uspiceos f the U.S. Departmenotf Energyb y the Lawrence LivermoreN ationalL aboratoryu ndercontract W-7405-ENG-48.

PY - 1988/12

Y1 - 1988/12

N2 - Several different methods for solving Maxwell's equations in the time-domain through the use of irregular nonorthogonal grids are presented. Employing quadrilateral and/or triangular elements, these methods allow more accurate modeling of nonrectangular structures. The traditional "stair-stepping" boundary approximations associated with standard orthogonal-grid finite-difference methods are avoided. Numerical results comparing all of the methods are given. A modified finite-volume method, which is a direct generalization of the standard finite-difference method to arbitrary polygonal grids, is shown to be the most accurate.

AB - Several different methods for solving Maxwell's equations in the time-domain through the use of irregular nonorthogonal grids are presented. Employing quadrilateral and/or triangular elements, these methods allow more accurate modeling of nonrectangular structures. The traditional "stair-stepping" boundary approximations associated with standard orthogonal-grid finite-difference methods are avoided. Numerical results comparing all of the methods are given. A modified finite-volume method, which is a direct generalization of the standard finite-difference method to arbitrary polygonal grids, is shown to be the most accurate.

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