Bounded error schemes for the wave equation on complex domains

Saul Abarbanel; Adi Ditkowski; Amir Yefet

doi:10.1007/s10915-004-4800-x

Bounded error schemes for the wave equation on complex domains

Saul Abarbanel, Adi Ditkowski, Amir Yefet

Tel Aviv University

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

10 Scopus citations

Abstract

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)-we achieve a decrease of two orders of magnitude in the level of the L ₂-error.

Original language	English
Pages (from-to)	67-81
Number of pages	15
Journal	Journal of Scientific Computing
Volume	26
Issue number	1
DOIs	https://doi.org/10.1007/s10915-004-4800-x
State	Published - Jan 2006
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-2199. S. Abarbanel was also supported in part by the Air Force Office of Scientific research Grant No. AFOSR-F49620-95-1-0074, and by the Department of Energy under grant DOE-DE-FG02-95ER25239.

Funding

This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-2199. S. Abarbanel was also supported in part by the Air Force Office of Scientific research Grant No. AFOSR-F49620-95-1-0074, and by the Department of Energy under grant DOE-DE-FG02-95ER25239.

Funders	Funder number
U.S. Department of Energy	DOE-DE-FG02-95ER25239
National Aeronautics and Space Administration
Air Force Office of Scientific Research	AFOSR-F49620-95-1-0074

Keywords

Embedded methods
FDTD
Finite difference
Wave equation

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10.1007/s10915-004-4800-x

Cite this

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title = "Bounded error schemes for the wave equation on complex domains",

abstract = "This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)-we achieve a decrease of two orders of magnitude in the level of the L 2-error.",

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author = "Saul Abarbanel and Adi Ditkowski and Amir Yefet",

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N2 - This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)-we achieve a decrease of two orders of magnitude in the level of the L 2-error.

AB - This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)-we achieve a decrease of two orders of magnitude in the level of the L 2-error.

KW - Embedded methods

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KW - Finite difference

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Bounded error schemes for the wave equation on complex domains

Abstract

Bibliographical note

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Keywords

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