A semi-analytical approach to Green's functions for heat equation in regions of irregular shape

Initial-boundary-value problems are considered for the classical two-dimensional heat equation in regions of irregular configuration. A semi-analytical algorithm is proposed to accurately compute profiles of Green's function for such problems. The algorithm is based on a modification of the standard boundary integral equation method. To make the modification efficient, analytical representations of Green's functions are required for relevant regularly shaped regions. These are obtained in a closed form and employed then as kernels of the corresponding heat potentials, reducing the problem to a regular integral equation on a part of a boundary of the considered region.