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 L2-error.
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References
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E. Turkel A. Yefet (2000) ArticleTitleOn the construction of a high order difference scheme for the complex domain in cartesian grid Appl. Numer. Math. 33 113–124 Occurrence Handle10.1016/S0168-9274(99)00074-4 Occurrence Handle1770244
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Abarbanel, S., Ditkowski, A. & Yefet, A. Bounded Error Schemes for the Wave Equation on Complex Domains. J Sci Comput 26, 67–81 (2006). https://doi.org/10.1007/s10915-004-4800-x
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DOI: https://doi.org/10.1007/s10915-004-4800-x