Accelerating boundary element methods in wideband frequency sweep analysis by matrix-free model order reduction

Abstract

In frequency-domain acoustic simulations, a wideband frequency sweep analysis is often required. This becomes particularly challenging for boundary element methods (BEM), as the system matrix has a complex dependency on frequency. Previous attempts have been made to accelerate the frequency sweep analysis for the conventional BEM i.e., without fast multipole or ℋ-matrices accelerations, which restrains the applications to limited scale problems due to the dense system matrix. This paper investigates and incorporates a rational Krylov projection based model order reduction (MOR) technology i.e., matrix-free method into various BEM formulations to address the critical challenge of accelerating frequency sweep analysis. Operating on the transfer functions of the BEM system’s input and output, the matrix-free MOR avoids the direct interference with the BEM kernels, which makes it feasible and attractive to work with existing fast BEM techniques such as ℋ-matrices and fast multipole method. The combined holistic BEM solution retains the merits of the acceleration from both MOR and fast BEM techniques. Significant speed-ups have been achieved by the matrix-free MOR for wideband BEM simulations. Numerical examples are presented to demonstrate the capability of the presented holistic approach in simulating various acoustic problems, including interior–exterior models, complex geometries and frequency dependent boundary conditions.