2024/05/24 by Bruyninckx, Kobe, Huybrechs, Daan, Meerbergen, Karl
#35J05 #65F30 #65N38 #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2405.15573
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the H-matrix format, this sparsity is exploited to achieve O(Nlog N) complexity for storage and multiplication by a vector. This is achieved purely algebraically, based on low-rank approximations of subblocks, and hence the format is also applicable to a wider range of problems. The H2-matrix format improves the complexity to O(N) by introducing a recursive structure onto subblocks on multiple levels. However, in many cases this comes with a large proportionality constant, making the H2-matrix format advantageous mostly for large problems. In this paper we investigate the usefulness of a matrix format that lies in between these two: Uniform H-matrices. An algebraic compression algorithm is introduced to transform a regular H-matrix into a uniform H-matrix, which maintains the asymptotic complexity. Using examples of the BEM formulation of the Helmholtz equation, we show that this scheme lowers the storage requirement and execution time of the matrix-vector product without significantly impacting the construction time.