A time-stepping DRBEM for transient heat conduction in anisotropic solids

This paper is concerned with a dual reciprocity boundary element method (DRBEM) applied to transient heat conduction problems for time-dependent, anisotropic materials. The integral equation formulation employs the fundamental solution of the Laplace equation for linear isotropic materials. As a result, from the nonlinear and also from the anisotropic parts of the governing differential equation, domain integrals arise in the boundary integral equation. These domain integrals are transformed into boundary integrals by using a new radial basis function. Furthermore, the time derivative is approximated by a time-stepping scheme, which yields additional domain integrals in the formulation. Such a domain integral at each time-step can also be transformed into boundary integrals via the same dual reciprocity method. The details of the proposed DRBEM are presented in what follows. Because of the domain integral arising from material nonlinearity, the solution is inevitably performed in an iterative manner. The usefulness of the present iterative method is demonstrated through comparison of the results obtained by a special computer code developed by the authors with those obtained by the finite element method.