The Fast and Free Memory Method for the efficient computation of convolution kernels

Abstract: We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the complete algorithm and the relevant complexity analysis. While dense matrices arise normally in such computations, the linear storage complexity and the quasi-linear computational complexity enable the evaluation of convolution products featuring up to one billion entries. We show how we are able to solve complex scattering problems using Boundary Integral Equations with dozen of millions of unknowns. Our implementation is made freely available within the Gypsilab framework under the GPL 3.0 license.