A well-conditioned method of fundamental solutions for Laplace equation

The method of fundamental solutions (MFS) is a numerical for solving boundary value problems involving linear partial differential equations. It well-known that it can be very effective assuming regularity the domain and conditions. main drawback MFS matrices involved are typically ill-conditioned this may prevent from achieving high accuracy. In work, we propose new algorithm to remove ill-conditioning classical in context Laplace equation defined planar domains. idea expand basis functions terms harmonic polynomials. Then, using singular decomposition Arnoldi orthogonalization, define well conditioned spanning same functional space as MFS’s. Several examples show when possible applied, approach much superior previous approaches, such or MFS-QR.