Implementation of a symmetric boundary element method in transient heat conduction with semi-analytical integrations

A time-convolutive variational hypersingular integral formulation of transient heat conduction over a 2-D homogeneous domain is considered. The adopted discretization leads to a linear equation system, whose coe cient matrix is symmetric, and is generated by double integrations in space and time. Assuming polyno- mial shape functions for the boundary unknowns, a set of compact formulae for the analytical time integrations is established. The spatial integrations are performed numerically using very e cient formulae just recently proposed. The competitiveness from the computational point of view of the symmetric boundary integral equa- tion approach proposed herein is investigated on the basis of an original computer implementation