Corrected fundamental solution for numerical solution of elliptic PDEs

Corrected fundamental solution (CFS) is a meshless method for homogeneous elliptic problems that corrects the density function in a simple layer potential integral. In the CFS method, we apply a new expansion of density function with variable coefficients which are approximated in a finite subspace of a complete space. These coefficients are determined by the moving least square method (MLS), using a suitable weight function that its support is in the real and artificial domain.