Diffusion problems using transient discrete source superposition

Abstract Discrete source superposition techniques seek sets of discrete, singular source strengths which satisfy the boundary conditions of a particular problem, and, necessarily, the governing differential equation. The sum of the fields produced by such sources thus provides an approximation to the required solution. In many respects these techniques are a special case of conventional boundary integral equation methods, where density distributions of smeared sources are sought. In this paper an attempt is made to extend the discrete source superposition technique to transient problems. The example addressed is the transient diffusion equation. The method developed does seem to have sòme promise. It is found that even coarse spatial discretization can yield quite accurate results, and that surprisingly large timesteps can be employed and accuracy maintained. Further, although no direct comparisons are made, the absence of spatial integrations indicates that the computational effort per timestep is likely to be less than for conventional BIE.