Wavelet solutions for the Dirichlet problem

Summary.

A modified classical penalty method for solving a Dirichlet boundary value problem is presented. This new fictitious domain penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domains. It is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast, approximate calculation of boundary integral. The compact support and orthonormality of the basis are essential for representing the boundary measure numerically, and therefore for implementing this methodology.