Numerical Solution of Heat Transfer Boundary Value Problem for Non-homogeneous Isotropic Material in a Plane

Abstract

In this thesis we studied the numerical solution of the heat transfer boundary value problem for non-homogeneous isotropic material in a plane. We focused on one of the numerical method in solving BVPs, i.e., Boundary Element Method (BEM). The formulations of the boundary-domain integral equation (BDIE) for heat transfer problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The mesh-based discretisation of BDIE with trangular domain elements leads to a system of linear algebric equations. Then, we solved the system by LU decomposition. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed approaches. convergence of the method was discussed.