A numerical algorithm to reduce ill-conditioning in meshless methods for the Helmholtz equation

DOI10.1007/s11075-017-0465-zzbMath1402.65180OpenAlexW2788891133MaRDI QIDQ1989945

Pedro R. S. Antunes

Publication date: 29 October 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0465-z

zbMATH Keywords

plane wavesHelmholtz equationill-conditioningmethod of fundamental solutions

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (14)

Numerical calculation of extremal Steklov eigenvalues in 3D and 4D ⋮ A meshfree method with plane waves for elastic wave propagation problems ⋮ Coupling FEM with a multiple-subdomain Trefftz method ⋮ Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains ⋮ Stable approximation of Helmholtz solutions in the disk by evanescent plane waves ⋮ Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis ⋮ Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions ⋮ A roadmap for generalized plane waves and their interpolation properties ⋮ Fast boundary-domain integral method for unsteady convection-diffusion equation with variable diffusivity using the modified Helmholtz fundamental solution ⋮ A plane wave least squares method for the Maxwell equations in anisotropic media ⋮ On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions ⋮ Trefftz co-chain calculus ⋮ A well-conditioned method of fundamental solutions for Laplace equation ⋮ Multiple reciprocity singular boundary method for 3D inhomogeneous problems

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