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A wideband fast multipole method for the two-dimensional complex Helmholtz equation. (English) Zbl 1219.65140

Summary: A wideband fast multipole method (FMM) for the 2D Helmholtz equation is presented. It can evaluate the interactions between \(N\) particles governed by the fundamental solution of 2D complex Helmholtz equation in a fast manner for a wide range of complex wave number \(k\), which was not easy with the original FMM due to the instability of the diagonalized conversion operator. This paper includes the description of theoretical backgrounds, the FMM algorithm, software structures, and some test runs.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Software:

FMM-Yukawa; 2D-WFMM; FIFA
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References:

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