pfft++ – A general and extensible fast integral equation solver based on a pre-corrected FFT algorithm

This paper describes an efficient algorithm to solve integral equations with complicated kernels. The algorithm can handle both piece-wise constant and high-order elements in the collocation method and the Galerkin’s method. A general and extensible fast integral equation solver has been developed using the c++ generic programming technique. Numerical experiments show that the memory usage and CPU time of the fast solver is nearly O(N) for various kernels.