A triple reciprocity method in Laplace transform boundary element method for three-dimensional transient heat conduction problems

In this paper, a boundary element method employing the Laplace transform is developed to solve the three-dimensional transient heat conduction problems. The fundamental solution for the modified Helmholtz equation is adopted in order to derive the basic integral equations. Due to the effects of initial temperature and heat generation, the domain integrals appearing in the integral equation will degrade the advantages of boundary element method. Therefore, a new triple reciprocity formulation in Laplace domain is proposed to convert the domain integrals into boundary integrals. The higher order fundamental solutions required in the triple reciprocity method can be obtained from the original fundamental solution by multiplying a constant term, which leads to a much simpler formulation in the Laplace domain. Then, the inverse transformation can be used to obtain the solutions in the time domain. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. In summary, the triple reciprocity formulation is a useful approach to capture the transient heat conduction responses.