The method of fundamental solutions and compactly supported radial basis functions: A meshless approach to 3D problems. (English) Zbl 0972.65098
Brebbia, C. A. (ed.) et al., Boundary elements. XXI. Papers from the 21st international conference on the boundary element method, Oxford, Great Britain, August 1999. Southampton: WIT Press. Int. Ser. Adv. Bound. Elem. 6, 561-570 (1999).
Summary: A simple mesh/grid free numerical method for Poisson’s equation has been developed to solve large scale problems in three dimensions. in this paper, the Poisson equation is split into two parts by using the method of particular solutions; the particular solution being approximated by the dual reciprocity method (DRM). In the DRM, we choose compactly supported radial basis functions for the interpolation of the forcing term. To then achieve a true meshless method, we employ the method of fundamental solutions (MFS) in order to solve the resulting homogeneous equation. The approach developed here is especially attractive for complex-shaped boundaries in arbitrary dimensions.
For the entire collection see [Zbl 0955.00057].
For the entire collection see [Zbl 0955.00057].
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
