Compression of the Fast Multipole Method using the Singular Value Decomposition

In this work a new matrix compression algorithm to improve the efficiency of the fast multipole method (FMM) is presented. The method is based on the application of the singular value decomposition (SVD) to the plane wave FMM aggregation matrices. These matrices are low-ranked, which is exploited to provide alternative sets of orthonormal singular basis functions. By choosing only the most relevant singular functions, a much more compact representation is obtained. The new formulation provides a reduction close to one order of magnitude both in computational cost and memory requirements without compromising at all the accuracy of the solution.