Hybrid Approximation Hierarchical Boundary Element Methods for Acoustic Problems

A multipole expansion approximation boundary element method (MEA BEM) based on the hierarchical matrices (H-matrices) and the multipole expansion theory was proposed previously. Though the MEA BEM can obtain higher accuracy than the adaptive cross-approximation BEM (ACA BEM), it demands more CPU time and memory than the ACA BEM does. To alleviate this problem, in this paper, two hybrid BEMs are developed taking advantage of the high efficiency and low memory consumption property of the ACA BEM and the high accuracy advantage of the MEA BEM. Numerical examples are elaborately set up to compare the accuracy, efficiency and memory consumption of the ACA BEM, MEA BEM and hybrid methods. It is indicated that the hybrid BEMs can reach the same level of accuracy as the ACA BEM and MEA BEM. The efficiency of each hybrid BEM is higher than that of the MEA BEM but lower than that of the ACA BEM. The memory consumptions of the hybrid BEMs are larger than that of the ACA BEM but less than that of the MEA BEM. The algorithm used to approximate the far-field submatrices corresponding to the cells and their nearest interactional cells determines the accuracy, efficiency and memory consumption of the hybrid BEMs. The proposed hybrid BEMs have both operation and storage logarithmic-linear complexity. They are feasible.

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