A Fast Free Memory Method for an Efficient Computation of Convolution Kernels

Abstract

We introduce the Fast Free Memory method (FFM), a new implementation of the Fast Multipole Method (FMM) for the evaluation of convolution products. The FFM aims at being easier to implement while maintaining a high level of performance, capable of handling industrially-sized problems. The FFM avoids the implementation of a recursive tree and is a kernel independent algorithm. We give the algorithm and the relevant complexity estimates. The quasi-linear complexity enables the evaluation of convolution products with up to one billion entries. We illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of unknowns. Our implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.