Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 166–178
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-432
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 166–178
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Helmholtz equation complex space irregular domain augmented immerse interface method fast Poisson solver in complex space.