Bounded error schemes for the wave equation on complex domains

Saul Abarbanel, Adi Ditkowski, Amir Yefet

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)67-81
Number of pages15
JournalJournal of Scientific Computing
Volume26
Issue number1
DOIs
StatePublished - Jan 2006
Externally publishedYes

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.

FundersFunder number
U.S. Department of EnergyDOE-DE-FG02-95ER25239
National Aeronautics and Space Administration
Air Force Office of Scientific ResearchAFOSR-F49620-95-1-0074

    Keywords

    • Embedded methods
    • FDTD
    • Finite difference
    • Wave equation

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