A boundary element method for the solution of the transient diffusion equation in two dimensions

The main advantage of using potential or boundary element methods for generating numerical solutions to linear elliptic partial differential equations is that the dimension of the problem is reduced by one. This feature not only reduces the number of algebraic equations to be solved, but, in two and three space dimensions, it also eliminates the problems of mesh generation. Both of these factors contribute to reducing the computational cost. A potential method is described which provides numerical solutions of the transient diffusion equation for two-dimensional problems. The solutions are generally as accurate as conventional techniques whilst retaining the advantage of a reduction in dimensionality throughout the time domain. The numerical study, however, also indicates that the method may have limitations, particularly when there are discontinuities at the boundaries.