Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials

This paper presents a dual reciprocity boundary element method (DRBEM) applied to the transient heat conduction problem in temperature-dependent materials. The integral equation formulation employs the fundamental solution of the Laplace equation for homogeneous materials, and hence a domain integral arises in the boundary integral equation. This domain integral is transformed into boundary integrals by using a new set of radial basis functions. Furthermore, time derivative in the governing differential equation is approximated by the time-stepping method, and the domain integral also appears from this approximation. The domain integral corresponding to the so-called “pseudo initial condition” at each time step is also transformed into boundary integrals via the same dual reciprocity method. The details of the proposed DRBEM are presented, and a computer code is developed for three-dimensional problems. Through comparison of the results obtained by the computer code with the results by a finite difference scheme, the usefulness of the present DRBEM is demonstrated.