Abstract
We discuss the Fourier-Infinite-Element method, which combines the Fourier method and the infinite element method, for sloving the Poisson equation with singularities caused by the presence of a corner. In the infinite element method the underlying domain is divided into infinitely many pieces. This leads to a system of the infinitely many equations in which the matrix is of block tridiagonal form. In spite of this fact, it is the nature of these block matrices that allows the problem to be expressed by three-term inhomogeneous recurrence relations. The required solution of this problem is generated by using an algorithm based on Gaussian elimination and rapidly obtained by using fast sine transform. In this paper we also discuss the approach for estimating automatically the truncation error of the proposed algorithm.
