Volume 13, Issue 1
An Augmented IIM for Helmholtz/Poisson Equations on Irregular Domains in Complex Space

S.-D. M. Zhang and Z.-L. Li

Int. J. Numer. Anal. Mod., 13 (2016), pp. 166-178

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  • Abstract

In this paper, an augmented immersed interface method has been developed for Helmholtz/Poisson equations on irregular domains in complex space. One of motivations of this paper is for simulations of wave scattering in different geometries. This paper is the first immersed interface method in complex space. The new method utilizes a combination of methodologies including the immersed interface method, a fast Fourier transform, augmented strategies, least squares interpolations, and the generalized minimal residual method (GMRES) for a Schur complement system, all in complex space. The new method is second order accurate in the L^∞ norm and requires O(N log(N)) operations. Numerical examples are provided for a variety of real or complex wave numbers.

  • History

Published online: 2016-01

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