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A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs

Alves, Carlos J. S.; Valtchev, Svilen S.

Advances in Meshfree Techniques (Ed. Leitao, Vma et Al.). Computational Methods in Applied Sciences, 5 (2007), 241-256

A Kansa type modification of the Method of Fundamental Solutions (MFS) is presented. This allows us to apply the MFS to a larger class of elliptic problems. In the case of inhomogeneous problems we reduce to a single linear system, contrary to previous methods where two linear systems are solved, one for the particular solution and one for the homogeneous solution of the problem. Here the solution is approximated using fundamental solutions of the Helmholtz equation. Several numerical tests in 2D will be presented in order to illustrate the convergence of the method. Mixed, Dirichlet-Neumann, boundary conditions will be considered.