  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.
