TY - JOUR
T1 - A Fast Free Memory Method for an Efficient Computation of Convolution Kernels
AU - Aussal , Matthieu
AU - Bakry , Marc
JO - Journal of Computational Mathematics
VL - 6
SP - 1093
EP - 1116
PY - 2023
DA - 2023/11
SN - 41
DO - http://doi.org/10.4208/jcm.2202-m2021-0324
UR - https://global-sci.org/intro/article_detail/jcm/22105.html
KW - Convolution product, Fast multipole method, Boundary integral equations,
Open-source.
AB - <p style="text-align: justify;">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.</p>