The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations

DOI10.1016/j.enganabound.2009.04.013zbMath1244.65225OpenAlexW1984456624MaRDI QIDQ441493

Tai-Wen Hsu, Chia-Cheng Tsai, Ching-Shyang Chen

Publication date: 7 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.enganabound.2009.04.013

zbMATH Keywords

particular solutionmeshless methodsChebyshev polynomialmethod of fundamental solutionsaxisymmetric poly-Helmholtz operatoraxisymmetric polyharmonic operator

Mathematics Subject Classification ID

Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (14)

The localized method of approximated particular solutions for solving two-dimensional incompressible viscous flow field ⋮ Method of approximate particular solutions for constant- and variable-order fractional diffusion models ⋮ The plane waves method for axisymmetric Helmholtz problems ⋮ The method of particular solutions with polynomial basis functions for solving axisymmetric problems ⋮ A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions ⋮ Efficient MFS algorithms for inhomogeneous polyharmonic problems ⋮ An overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stability ⋮ Localized method of approximate particular solutions with Cole-Hopf transformation for multi-dimensional Burgers equations ⋮ A hybrid fundamental-solution-based 8-node element for axisymmetric elasticity problems ⋮ Polynomial Particular Solutions for the Solutions of PDEs with Variables Coefficients ⋮ Localized meshless methods based on polynomial basis functions for solving axisymmetric equations ⋮ Localized method of fundamental solutions for three-dimensional inhomogeneous elliptic problems: theory and MATLAB code ⋮ An efficient method of approximate particular solutions using polynomial basis functions ⋮ Fourier expansions for a logarithmic fundamental solution of the polyharmonic equation

Cites Work

• Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
• Recursive construction of particular solutions to nonhomogeneous linear partial differential equations of elliptic type
• The method of fundamental solutions for elliptic boundary value problems
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• A meshless, integration-free, and boundary-only RBF technique
• Particular solutions of Helmholtz-type operators using higher order polyharmonic splines
• Particular solutions of the multi-Helmholtz-type equation
• Heritage and early history of the boundary element method
• Particular solutions for axisymmetric Helmholtz-type operators
• A mesh-free method using hyperinterpolation and fast Fourier transform for solving differential equations
• Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
• The Numerical Evaluation of Particular Solutions for Poisson's Equation
• The method of fundamental solutions for axisymmetric potential problems
• A mesh‐free approach to solving the axisymmetric Poisson's equation
• Polynomial particular solutions for certain partial differential operators
• Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions
• BEM for thermoelasticity and elasticity with body force -- a revisit
• Trefftz method: An overview
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