Bounded error schemes for the wave equation on complex domains

Saul Abarbanel*, Adi Ditkowski, Amir Yefet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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

Keywords

  • Embedded methods
  • FDTD
  • Finite difference
  • Wave equation

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