A general algorithm for the numerical evaluation of domain integrals in 3D boundary element method for transient heat conduction

In this paper, a general algorithm is proposed for evaluating domain integrals in 3D boundary element method. These integrals are involved in the solution of transient heat conduction problems when using a time-dependent boundary integral equation method named as pseudo-initial condition method. Accurate evaluation of domain integrals is of great importance to the successful implementation of this method. However, as the time-dependent kernel in the domain integral is close to singular when small time step is used, a straightforward application of Gaussian quadrature may produce large errors, and thus lead to instability of the analysis. To overcome this drawback, a coordinate transformation coupled with an element subdivision technique is presented. The coordinate transformation makes the integrand of domain integral more smooth; meanwhile, the element subdivision technique considers the relations between the size of the element and the time step. With the proposed method, more Gaussian points are shifted towards the source point, thus more accurate results can be obtained. Numerical examples demonstrate that the calculation accuracy of domain integrals and the stability of analysis for transient heat conduction problems are improved by the proposed algorithm when small time step is used.