An iterative algorithm for singular Cauchy problems for the steady state anisotropic heat conduction equation

Abstract

In this paper, we propose an alternating iterative algorithm to solve a singular Cauchy problem for the anisotropic heat conduction equation. The numerical algorithm is based on the boundary element method (BEM), modified to take into account the form of the singularity, without substantially increasing the amount of computation involved. Two test examples, the first with a singularity caused by an abrupt change in the boundary conditions and the second with a singularity caused by a sharp re-entrant corner, are investigated. The numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed, the iterative BEM is efficient in dealing with the difficulties arising from both the instabilities produced by the boundary condition formulation and the slow rate of convergence of standard numerical methods around the singular point.