Dual reciprocity BEM without matrix inversion for transient heat conduction

Abstract

Presence of domain integrals in the formulation of the boundary element method dramatically decreases the efficiency of this technique. Dual reciprocity boundary element method (DRBEM) is one of the most popular methods to convert domain integrals into a series of boundary integrals. This is done at the expense of generating some additional matrices and inverting one of them. The latter feature makes the DRBEM inefficient for large-scale problems. This paper describes simple means of avoiding matrix inversion for transient heat transfer problems with arbitrary set of boundary conditions. The technique is also directly applicable to other phenomena (acoustic wave propagation, elastodynamics). For the boundary conditions of Neumann and Robin type, the proposed technique produces exactly the same results as the standard approach. In the presence of Dirichlet conditions, a lower bound on the time step has been detected in the backward difference time stepping procedure. The approach has been tested on some transient heat conduction benchmark problems and accurate results have been obtained.