TY - JOUR
T1 - A semi-analytical approach to Green's functions for heat equation in regions of irregular shape
AU - Melnikov, Yu A.
AU - Reshniak, V.
PY - 2014/9
Y1 - 2014/9
N2 - 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.
AB - 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.
KW - Green's functions
KW - Regions of irregular shape
KW - Semi-analytical approach
KW - Two-dimensional heat equation
UR - http://www.scopus.com/inward/record.url?scp=84903119956&partnerID=8YFLogxK
U2 - 10.1016/j.enganabound.2014.05.012
DO - 10.1016/j.enganabound.2014.05.012
M3 - Article
AN - SCOPUS:84903119956
SN - 0955-7997
VL - 46
SP - 108
EP - 115
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
ER -