Efficient MFS algorithms for inhomogeneous polyharmonic problems

DOI10.1007/s10915-010-9418-6zbMath1270.65075OpenAlexW2079472467MaRDI QIDQ361560

Andreas Karageorghis

Publication date: 29 August 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-010-9418-6

zbMATH Keywords

fast Fourier transformscirculant matricesmethod of fundamental solutionspolyharmonic equations

Mathematics Subject Classification ID

Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (10)

Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions ⋮ Efficient numerical methods for boundary data and right‐hand side reconstructions in elliptic partial differential equations ⋮ Method of fundamental solutions for mixed and crack type problems in the classical theory of elasticity ⋮ A direct Chebyshev collocation method for the numerical solutions of three-dimensional Helmholtz-type equations ⋮ A Kansa-radial basis function method for elliptic boundary value problems in annular domains ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ 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 ⋮ Kansa RBF collocation method with auxiliary boundary centres for high order BVPs

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the choice of source points in the method of fundamental solutions
• Matrix decomposition RBF algorithm for solving 3D elliptic problems
• The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations
• 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
• Matrix decomposition algorithms for elliptic boundary value problems: A survey
• A matrix decomposition RBF algorithm: approximation of functions and their derivatives
• Efficient Kansa-type MFS algorithm for elliptic problems
• Efficient MFS algorithms in regular polygonal domains
• The method of fundamental solutions for elliptic boundary value problems
• Error estimates for a fundamental solution method applied to reduced wave problems in a domain exterior to a disc
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• Some aspects of the method of fundamental solutions for certain harmonic problems
• A new method of fundamental solutions applied to nonhomogeneous elliptic problems
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Full identification of acoustic sources with multiple frequencies and boundary measurements
• Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation
• Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
• The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings
• A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs
• Estimation of the heat transfer coefficient by means of the method of fundamental solutions
• Recovering the source term in a linear diffusion problem by the method of fundamental solutions
• Matrix Decomposition Algorithms Related to the MFS for Axisymmetric Problems
• Polynomial particular solutions for certain partial differential operators
• A mesh free approach using radial basis functions and parallel domain decomposition for solving three‐dimensional diffusion equations

This page was built for publication: Efficient MFS algorithms for inhomogeneous polyharmonic problems