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 difficulty may be overcome in the case of an anisotropic medium by a modified boundary element method. The standard boundary element method is modified to take account of the form of the singularity, without appreciably increasing the amount of computation involved. Two test examples, the first 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.
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