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.