Solving Partial Differential Equations on Surfaces with Fundamental Solutions

DOI10.1007/978-3-030-52804-1_1zbMath1454.65183OpenAlexW3090892507MaRDI QIDQ5132502

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Publication date: 12 November 2020

Published in: Advances in Trefftz Methods and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-52804-1_1

zbMATH Keywords

collocationdual reciprocity methodembedding methodLaplace-Beltrami

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Cites Work

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• A Fast Block-Greedy Algorithm for Quasi-optimal Meshless Trial Subspace Selection
• The method of approximate particular solutions for solving certain partial differential equations
• Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
• The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces
• Dual reciprocity method using compactly supported radial basis functions
• A Kernel-Based Embedding Method and Convergence Analysis for Surfaces PDEs
• Extrinsic Meshless Collocation Methods for PDEs on Manifolds
• Some comments on the use of radial basis functions in the dual reciprocity method