2020/12/28 by Simon Dirckx, Dirckx, Simon, Daan Huybrechs +3
Engineering · Physics and Astronomy · #Electromagnetic Compatibility and Measurements #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2012.14287
openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The discretisation of boundary integral equations for the scalar Helmholtz equation leads to large dense linear systems. Efficient boundary element methods (BEM), such as the fast multipole method (FMM) and \Hmat based methods, focus on structured low-rank approximations of subblocks in these systems. It is known that the ranks of these subblocks increase linearly with the wavenumber. We explore a data-sparse representation of BEM-matrices valid for a range of frequencies, based on extracting the known phase of the Green's function. Algebraically, this leads to a Hadamard product of a frequency matrix with an \Hmat. We show that the frequency dependency of this \Hmat can be determined using a small number of frequency samples, even for geometrically complex three-dimensional scattering obstacles. We describe an efficient construction of the representation by combining adaptive cross approximation with adaptive rational approximation in the continuous frequency dimension. We show that our data-sparse representation allows to efficiently sample the full BEM-matrix at any given frequency, and as such it may be useful as part of an efficient sweeping routine.