The method of fundamental solutions applied to boundary value problems on the surface of a sphere

DOI10.1016/j.camwa.2017.12.015zbMath1409.65107OpenAlexW2782752433MaRDI QIDQ1732495

Carlos J. S. Alves, Pedro R. S. Antunes

Publication date: 25 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.12.015

zbMATH Keywords

sphereboundary value problemLaplace-Beltrami operatormethod of fundamental solutions

Mathematics Subject Classification ID

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

Related Items (9)

The localized method of fundamental solutions for 2D and 3D second-order nonlinear boundary value problems ⋮ Localized boundary knot method and its application to large-scale acoustic problems ⋮ Solving boundary value problems on manifolds with a plane waves method ⋮ Some remarks on Trefftz type approximations ⋮ Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization ⋮ Localized method of fundamental solutions for three-dimensional inhomogeneous elliptic problems: theory and MATLAB code ⋮ 3D positive lattice walks and spherical triangles ⋮ On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions ⋮ Multiple reciprocity singular boundary method for 3D inhomogeneous problems

Cites Work

• Unnamed Item
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• Integral equation methods for the Yukawa-Beltrami equation on the sphere
• The method of fundamental solutions applied to boundary eigenvalue problems
• Solving partial differential equations numerically on manifolds with arbitrary spatial topologies
• The orthogonal gradients method: a radial basis functions method for solving partial differential equations on arbitrary surfaces
• On the choice of source points in the method of fundamental solutions
• Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
• Clifford analysis techniques for spherical PDE.
• On the application of the method of fundamental solutions to boundary value problems with jump discontinuities
• Is it possible to tune a drum?
• A simple embedding method for solving partial differential equations on surfaces
• A mathematical model for atmospheric ice accretion and water flow on a cold surface
• The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems
• Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on theN-dimensional unit sphere
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Variational problems and partial differential equations on implicit surfaces

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