Singularities in anisotropic steady-state heat conduction using a boundary element method

In many heat conduction problems, boundaries with sharp corners or abrupt changes in the boundary conditions give rise to singularities of various types which tend to slow down the rate of convergence with decreasing mesh size of any standard numerical method used for obtaining the solution. In this paper, it is shown how this di9culty may beove rcomein thecaseof an anisotropic medium by a modi:ed boundary element method. The standard boundary element method is modi:ed to take account of theform of thesingularity, without appreciably increasing theamount of computation involved. Two test examples, the :rst with a singularity caused by an abrupt change in a boundary condition and the second with a singularity caused by a sharp re-entrant corner, are investigated and numerical results are presented