A stochastic spectral projection method for solving PDEs in domains composed by overlapping discs, spheres, and half-spaces

A new mesh-free stochastic spectral method based on a spectral inversion of the Poisson integral formula is suggested. We consider the cases of Laplace equation and the system of elasticity equations for domains consisting of overlapping discs, half-planes, spheres, and half-spaces. A randomized projection method we developed in Sabelfeld and Loshchina (2010) [21] is used to solve the system of linear equations approximating the integral equations whose phase space is the intersection surfaces of the domains.

► A new spectral method based on the inversion of the Poisson integral is suggested. ► Laplace and systems of isotropic elasticity equations are considered. ► Domains consisting of overlapped discs, half-planes and half-spaces are treated. ► A randomized solver and Monte Carlo integration are used in the implementation.