抄録
We present an efficient algorithm based on the Legendre-Galerkin approximation for solving the Poisson equation on a fan-shaped domain. The key to the efficiency of our algorithm is to map the domain to a rectangular domain by using a new type of the double exponential formula. Some numerical results show that the convergence rate of our algorithm is nearly exponential. As an application, we also discuss the approach for solving the Poisson equation on triangular domains by using the Legendre-Galerkin method in conjunction with the Schwarz Alternating method.
