An ACA accelerated MFS for potential problems

The MFS is a popular meshless boundary collocation method but encounters troublesome fully-populated interpolation matrix, whose operation count and memory requirement for interpolation matrices buildup are of order O(N2). This is computationally prohibitively expensive. The adaptive cross approximation (ACA), a kernel-independent fast algorithm, was devised to reduce both CPU time and memory requirement in solving dense matrix systems from O(N2) to O(N logβN) by a pseudo-skeletal entries approximation. This paper makes a first attempt to apply the ACA to remedy the expensive matrix computation and accelerate the solution of the MFS in potential problems, and further improves the ACA in generating the admissible cluster pairs. The MFS accelerated by the present improved ACA are tested to three benchmark cases. Numerical results show that the proposed methodology is computationally more efficient than the conventional scheme.