Singular boundary method using time-dependent fundamental solution for transient diffusion problems. (English) Zbl 1403.65056
Summary: This paper documents the first attempt to apply the singular boundary method (SBM) with time-dependent fundamental solution to transient diffusion equations. An inverse interpolation technique is introduced to determine the origin intensity factor of the SBM. The scheme is mathematically simple, easy-to-program, truly boundary-only, free of integration and mesh. Several examples, especially three-dimensional (3D) cases, are provided to verify time-dependent SBM strategy. The numerical results clearly demonstrate its great potential.
MSC:
| 65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |
| 65M80 | Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs |
Keywords:
singular boundary method; diffusion; time-dependent fundamental solutions; meshless; boundary-only; origin intensity factorReferences:
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