Singular boundary method using time-dependent fundamental solution for transient diffusion problems

This paper documents the first attempt to apply the singular boundary method (SBM) with time-dependent fundamental solution to transient diffusion equations. An inverse interpolation technique is introduced to determine the origin intensity factor of the SBM. The scheme is mathematically simple, easy-to-program, truly boundary-only, free of integration and mesh. Several examples, especially three-dimensional (3D) cases, are provided to verify time-dependent SBM strategy. The numerical results clearly demonstrate its great potential.