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We introduce the Fast Free Memory method (FFM), a new fast method for thenumerical evaluation of convolution products. Inheriting from the FastMultipole Method, the FFM is a descent-only and kernel-independent algorithm.We give the complete algorithm and the relevant complexity analysis. Whiledense matrices arise normally in such computations, the linear storagecomplexity and the quasi-linear computational complexity enable the evaluationof convolution products featuring up to one billion entries. We show how we areable to solve complex scattering problems using Boundary Integral Equationswith dozen of millions of unknowns. Our implementation is made freely availablewithin the Gypsilab framework under the GPL 3.0 license.

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