An efficient numerical evaluation of the Green's function for the Helmholtz operator on periodic structures

DOI10.1016/0021-9991(86)90093-8zbMath0647.65084OpenAlexW2068945551WikidataQ61761182 ScholiaQ61761182MaRDI QIDQ1104718

Ping Sheng, Gerard R. Richter, Kirk E. Jordan

Publication date: 1986

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(86)90093-8

zbMATH Keywords

convergence accelerationboundary integral methodMaxwell's equationsGreen functionHelmholtz operatorNumerical examplesEwald's methodpseudo-periodic boundary conditionsslowly convergent infinite series

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Electromagnetic theory (general) (78A25) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (12)

Unnamed Item ⋮ A fast Fourier transform accelerated Ewald summation technique for the vector electromagnetic rectangular cavity Green's function ⋮ Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method ⋮ Spectrally-accurate numerical method for acoustic scattering from doubly-periodic 3D multilayered media ⋮ Fast algorithms for Helmholtz Green's functions ⋮ Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects ⋮ Fast algorithms for implementation of the Green's function ⋮ An integral representation of the Green function for a linear array of acoustic point sources ⋮ A hybrid finite/boundary element method for periodic structures on non-periodic meshes using an interior penalty formulation for Maxwell's equations ⋮ Stable and efficient evaluation of periodized Green's functions for the Helmholtz equation at high frequencies ⋮ Diffraction by a truncated planar array of dipoles: a Wiener-Hopf approach ⋮ Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

Cites Work

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