Comparison of the Fast Multipole Method with Hierarchical Matrices for the Helmholtz-BEM

摘要: The simulation of the hydroacoustic sound radiation ship-like struc- tures has an ever-growing importance due to legal regulations. Using boundary element method, overall dimension problem is reduced and only inte- grals over surfaces have be considered. Additionally, Sommerfeld condition automatically satisfied by proper choice fundamental solution. However, resulting matrices are fully populated set-up time memory consumption scale quadratically with respect degrees freedom. Different fast methods been introduced for Helmholtz equation, in a quasilinear complexity. Two these considered this paper, namely multipole method hierarchical matrices. first one applies series expansion solution, whereas second pure algebraic nature represents partitions original system matrix low-rank approximations outer-product form. two compared structure, which partly immersed water. consumption, required matrix-vector product investigated. Dif- ferent frequency regimes Since diagonal known unstable low-frequency regime, types expansions necessary wideband analysis.