Development of numerical scheme using boundary element method for heat conduction problems

Abstract

This paper deals with the boundary element method solution of set of parabolic differential equations of heat conducting problems with continuous and discontinuous boundary conditions. Time-dependent terms have been used as a non-homogeneous forcing function by changing a parabolic differential equation into a Poisson's equation. The suggested approach for solving the Poisson equation has been modified which decreases the number of algebraic equations and reduces the computational time. The constant coefficient matrix and LU decomposition provide an economical means for the solution of the concern problem. The discretization of the boundary of parabolic differential equations with respect to (w.r.t.) time is one of the main features of this article. Direct determination of unknown at interior points is also trademark of the proposed method. The method has been supported by examples, which include discontinuous boundary conditions and non-homogeneous forcing terms to highlight its effectiveness and accuracy.