2D-WFMM

A wideband fast multipole method for the two-dimensional complex Helmholtz equation. 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.

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References in zbMATH (referenced in 6 articles , 1 standard article )

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  1. Li, Bin; Xiang, Shuhuang: On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels (2020)
  2. Cho, Min Hyung; Huang, Jingfang; Chen, Dangxing; Cai, Wei: A heterogeneous FMM for layered media Helmholtz equation. I: Two layers in (\mathbbR^2) (2018)
  3. Chen, Leilei; Zheng, Changjun; Chen, Haibo: A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method (2013)
  4. Davis, Christopher; Kim, June G.; Oh, Hae-Soo; Cho, Min Hyung: Meshfree particle methods in the framework of boundary element methods for the Helmholtz equation (2013)
  5. Cho, Min Hyung; Cai, Wei: A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media (2012)
  6. Cho, Min Hyung; Cai, Wei: A wideband fast multipole method for the two-dimensional complex Helmholtz equation (2010)