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Radial basis functions for solving near singular Poisson problems. (English) Zbl 1018.65131
Summary: We investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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