A boundary element scheme for diffusion problems using compactly supported radial basis functions

摘要

The solution of the diffusion equation using the boundary element method has a high computational cost due to the inherent time history constraint in the integral representation. This time-history dependence become impractical for problems where computations are to be performed for extended times. In general, the computation the solution at n domain points using m boundary points at the time-step requires an amount of computer operators of the order O(km~2＋knm). This paper presents a scheme that requires a computational cost of the order of only O(m~2＋nm), where the dependence from the past k-steps is removed. In the words, the computational process is reduced to that in finite differences and finite elements, where the solution at every time step is dependent from that of the previous step only. The scheme uses the time dependent fundamental solution but the time integration is performed over ne time-step only and the rest of the history integral is confuted to a domain integral which is approximated using compactly supported radial basis functions.