Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions

DOI10.1016/S0955-7997(00)00033-3zbMath0966.65088MaRDI QIDQ1595058

Alexander H.-D. Cheng

Publication date: 31 January 2001

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

zbMATH Keywords

biharmonic equationLaplace equationHelmholtz equationradial basis functiondual reciprocity boundary element methodpolyharmonic equationparticular solutions

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

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Cites Work

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• Towards criteria for selecting approximation functions in the dual reciprocity method
• Particular solutions of Helmholtz-type operators using higher order polyharmonic splines
• Some recent results and proposals for the use of radial basis functions in the BEM
• The annihilator method for computing particular solutions to partial differential equations
• BEM for thermoelasticity and elasticity with body force -- a revisit