Solving transient diffusion problems: time-dependent fundamental solution approaches versus LTDRM approaches

Abstract

In the literature, numerical approaches for solving transient diffusion equations with the boundary element method in the time domain can be classified into two categories, those adopting time-independent fundamental solutions and those adopting time-dependent fundamental solutions. In the latter category, there are traditionally two schemes in terms for time integration, both of which require a reasonable time-step size to obtain a certain degree of accuracy, although one scheme allows a larger time step than the other. Few people seem to have realized that there is a connection between time-dependent fundamental solution approaches and the so-called LTDRM (Laplace Transform Dual Reciprocity Method) approach through the Laplace transformation. Such a connection is established here with a brief discussion of the advantages and disadvantages of each approach under different circumstances.