An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems

Xie，Xiang; Liu，Yijun

2021

10.1016/j.cma.2020.113532

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING   影响因子和分区

0045-7825

1879-2138

The classical boundary element method (BEM) is widely used to obtain detailed information on the acoustic performance of large-scale dynamical systems due to the nature of semi-analytical characteristic. Its use, however, results in asymmetric and dense system matrix, which makes original full-order model evaluation very time consuming and memory demanding. Moreover, the frequency sweep analysis which is indispensable for the assessment of noise emission levels and the design of high-quality products requires the repetitive assembly and solution of system of equations, which further increases the computational complexity. In order to alleviate these problems, an adaptive structure-preserving model order reduction method is presented, which is based on an offline–online solution framework. In the offline phase, we first factor out the frequency term as a scalar function from the BE integral kernels of the Burton–Miller formulation, followed by integration to set up the system matrices. A global frequency-independent orthonormal basis is then constructed via the second-order Arnoldi (SOAR) method to span a projection subspace, onto which the frequency-decoupled system matrices are projected column by column to solve the memory problem arising from the frequency-related decomposition. In addition, the number of iterations required for convergence can be automatically determined by exploiting the condition number of an upper Hessenberg matrix in SOAR. In the online stage, a reliable reduced-order model can be quickly recovered by the sum of those offline stored reduced matrices multiplied by frequency-dependent coefficients, which is favored in many-query applications. Two academic benchmarks and a more realistic problem are investigated in order to demonstrate the potentials of the proposed approach.

Adaptive model order reduction Boundary element method Burton–Miller formulation Frequency sweep Second-order Arnoldi

SCI ; EI

英语

第一 ; 通讯

National Natural Science Foundation of China[12002146,11972179] ; China Postdoctoral Science Foundation[2020M672696]

Engineering ; Mathematics ; Mechanics

Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics

WOS:000600286800008

ELSEVIER SCIENCE SA

20204509468166

Dynamical systems ; Product design ; Quality control ; Matrix algebra ; Number theory ; Sailing vessels

Small Marine Craft:674.1 ; Production Engineering:913.1 ; Quality Assurance and Control:913.3 ; Algebra:921.1 ; Numerical Methods:921.6

COMPUTER SCIENCE

2-s2.0-85095438223

Scopus

Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Xie，Xiang,Liu，Yijun. An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2021,373.

Xie，Xiang,&Liu，Yijun.(2021).An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,373.

Xie，Xiang,et al."An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 373(2021).