Evaluating 2D domain integrals by sinh transformation for transient heat conduction problem

The time-dependent boundary element method (BEM) is widely used to solve transient heat conduction problem. The integrands of the domain integrals in the time-dependent BEM are close to singular when small time step is used. A straightforward computation of these integrals using Gaussian quadrature will produce large errors. To evaluate domain integrals accurately and efficiently, the sinh transformation combined with element subdivision method is proposed in this paper. With the sinh transformation, the integrands of the domain integrals become smoother. Meanwhile, the Gaussian points are shifted towards the source point due to the element subdivision. Thus, the 2D domain integrals in the time-dependent BEM can be computed accurately. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.