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.
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