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

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

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

Published online: 2016-01

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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.

  • Keywords

Helmholtz equation, complex space, irregular domain, augmented immerse interface method, fast Poisson solver in complex space.

  • AMS Subject Headings

65N06, 65N22, 65N50, 65F35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-166, author = {S.-D. M. Zhang and Z.-L. Li}, title = {An Augmented IIM for Helmholtz/Poisson Equations on Irregular Domains in Complex Space}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/432.html} }
TY - JOUR T1 - An Augmented IIM for Helmholtz/Poisson Equations on Irregular Domains in Complex Space AU - S.-D. M. Zhang & Z.-L. Li JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 166 EP - 178 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/432.html KW - Helmholtz equation, complex space, irregular domain, augmented immerse interface method, fast Poisson solver in complex space. AB -

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.

S.-D. M. Zhang and Z.-L. Li. (2016). An Augmented IIM for Helmholtz/Poisson Equations on Irregular Domains in Complex Space. International Journal of Numerical Analysis and Modeling. 13 (1). 166-178. doi:
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