On bivariate poly-sinc collocation applied to patching domain decomposition

Abstract

An efficient direct domain decomposition method is developed coupled with Poly-Sinc approximation over complex geometry. We solve 2D Poisson equations in L-Shaped geometry. The spatial domains of interest are decomposed into several non-overlapping rectangular subdomains. In each sub-domain, a Poly-Sinc collocation scheme is used to approximate the solution of the governing equation. Sinc points are used for the spatial discretization. We use the Dirichlet boundary conditions on interface and using the first-order normal derivatives as transmission conditions. The boundary conditions will keep the continuities of variables and the continuities of the derivatives. Three test examples are used to verify the accuracy and efficiency. We compare the errors derived from Poly-Sinc approximations with errors obtained by either Sinc or finite difference approximations. The results indicate that the present method is efficient, stable, and accurate.

Poly-Sinc Solution of Stochastic Elliptic Differential Equations

“…In [20], a collocation method based on the use of bivariate Poly-Sinc interpolation defined in ( 16) is introduced to solve elliptic equations defined on rectangular domains. In [22], Poly-Sinc collocation domain decomposition method for elliptic boundary value problems is investigated on complicated domains. The idea of the collocation method is to reduce the boundary value problem to a system of algebraic equations which have to be solved subsequently.…”