Efficient Kansa-type MFS algorithm for elliptic problems

DOI10.1007/s11075-009-9334-8zbMath1190.65184OpenAlexW2064482754MaRDI QIDQ973855

Andreas Karageorghis

Publication date: 26 May 2010

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

Full work available at URL: https://doi.org/10.1007/s11075-009-9334-8

zbMATH Keywords

numerical examplesfast Fourier transformsHelmholtz equationelliptic boundary value problemscirculant matricesmethod of fundamental solutionsmatrix decomposition algorithm

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for discrete and fast Fourier transforms (65T50) 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 (8)

The method of approximate particular solutions for solving certain partial differential equations ⋮ Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems ⋮ Efficient MFS algorithms for inhomogeneous polyharmonic problems ⋮ A Kansa-radial basis function method for elliptic boundary value problems in annular domains ⋮ Matrix decomposition algorithms for elliptic boundary value problems: A survey ⋮ A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations ⋮ Extending the method of fundamental solutions to non-homogeneous elastic wave problems ⋮ Kansa-RBF Algorithms for Elliptic Problems in Axisymmetric Domains

Uses Software

• Matlab

Cites Work

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• Matrix decomposition RBF algorithm for solving 3D elliptic problems
• Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods
• A time-marching MFS scheme for heat conduction problems
• A matrix decomposition RBF algorithm: approximation of functions and their derivatives
• Efficient MFS algorithms in regular polygonal domains
• The method of fundamental solutions for elliptic boundary value problems
• The method of fundamental solutions for scattering and radiation problems.
• Some aspects of the method of fundamental solutions for certain harmonic problems
• A new method of fundamental solutions applied to nonhomogeneous elliptic problems
• Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs
• Matrix Decomposition Algorithms Related to the MFS for Axisymmetric Problems

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