Convergence of the invariant scheme of the method of fundamental solutions for two-dimensional potential problems in a Jordan region. (English) Zbl 1296.65181
In order to solve the two-dimensional Dirichlet problem of the Laplace equation in a Jordan region by the superposition of fundamental solutions, the authors use charge and collocation points obtained by a conformal mapping of the exterior of a disk onto the exterior of the problem region. In the framework of the invariant scheme, they give an approximate solution which is invariant to certain affine transformations. They demonstrate that the approximate solution of the invariant scheme converges to the exact solution exponentially.
Reviewer: Adrian Carabineanu (Bucureşti)
MSC:
| 65N80 | Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
method of fundamental solutions; charge simulation method; Laplace equation; invariant scheme; conformal mapping; convergence; Dirichlet problem; collocationReferences:
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