A non-intrusive model order reduction boundary element method for frequency sweeps of 2D acoustics

Abstract

The boundary element method (BEM) is one of the most commonly used prediction technique to deal with acoustic problems governed by the Helmholtz equation. Its use, however, suffers from the disadvantage that the system of equations have to be reformulated for each frequency of interest due to the frequency-dependent property. This undermines the inherent efficiency of frequency sweep analyses of BE models. Additionally, the resulting coefficient matrices are fully-populated, non-symmetric and complex-valued. In order to enable the traditional BEM to be applied for large-scale acoustic problems, a non-intrusive model order reduction boundary element method under the offline–online framework is proposed. In the offline phase, a proper reduced-order basis (ROB) which spans a projection subspace is constructed via the Arnoldi method. A newly developed cutoff technique is incorporated to reduce the involved computational complexity. Once a low-rank ROB is determined, the full-order frequency-decoupled system matrices based on the series expansions are projected onto the spanned subspace column-by-column to favor the memory requirement. In the online phase, fast frequency sweep analyses with a direct solver can be achieved because only the compact reduced-order model needs to be confronted. The high performance of the proposed solution approach in the context of single-frequency and multi-frequency analyses of two-dimensional (2D) BE models with the number of degrees of freedom ranging from a few hundred up to one hundred thousand is demonstrated by various problem settings, including both interior and exterior acoustic fields with different boundary conditions.