Sidi-Israeli Quadrature Method for Steady-State Anisotropic Field Problems by Direct Domain Mapping

摘要

In this paper, the two-dimensional steady-state anisotropic field problems are transformed into the Laplace equation by direct domain mapping, and then the Sidi-Israeli quadrature method is applied to solve the weakly singular boundary integral equation of the Laplace equation. Especially, the kress's variable transformation is used for the polygon case in order to improve the accuracy by smoothing the singularities of the exact solution at the corner points of the boundary. The convergence and error analysis of numerical solutions are given by use of collective compact theory. At last, numerical examples are tested and results verify the theoretical analysis.