Ruoyan Li^1,2, Yijun Liu^1,*, Wenjing Ye²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09472

Abstract The boundary element method (BEM) for acoustic problems is a numerical method based on solving the discretized boundary integral equation (BIE) corresponding to the Helmholtz equation. A fast direct BEM for 3D acoustic problems is proposed in this paper, which is more suitable for broadband acoustic simulation of complex structures, such as in the design and analysis of acoustic metamaterials. The main idea of the fast direct solver is based on the hierarchical off-diagonal low-rank (HODLR) matrix, randomized interpolative decomposition and fast matrix inversion formula. Several numerical examples in solving both interior and exterior acoustic More >

T. Gortsas¹, S.V. Tsinopoulos², D. Polyzos^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.4, pp. 321-343, 2015, DOI:10.3970/cmes.2015.107.321

Abstract An advanced Boundary Element method (BEM) accelerated via Adaptive Cross Approximation (ACA) and Hierarchical Matrices (HM) techniques is presented for the solution of large-scale elastostatic problems with multi-connected domains like in fiber reinforced composite materials. Although the proposed ACA/ BEM is demonstrated for two-dimensional (2D) problems, it is quite general and it can be used for 3D problems. Different forms of ACA technique are employed for exploring their efficiency when they combined with a BEM code. More precisely, the fully and partially pivoted ACA with and without recompression are utilized, while the solution of the More >

R. Q. Rodríguez^1,2, C. L. Tan², P. Sollero¹, E. L. Albuquerque³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 359-372, 2014, DOI:10.3970/cmes.2014.102.359

Abstract The efficient evaluation of the fundamental solution for 3D general anisotropic elasticity is a subject of great interest in the BEM community due to its mathematical complexity. Recently, Tan, Shiah, andWang (2013) have represented the algebraically explicit form of it developed by Ting and Lee (Ting and Lee, 1997; Lee, 2003) by a computational efficient double Fourier series. The Fourier coefficients are numerically evaluated only once for a specific material and are independent of the number of field points in the BEM analysis. This work deals with the application of hierarchical matrices and low rank More >

R. Q. Rodríguez¹, A.F. Galvis¹, P. Sollero¹, E. L. Albuquerque²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 259-274, 2013, DOI:10.3970/cmes.2013.096.259

Abstract Over recent years the rapid evolution of the computational power has motivated the development of new numerical techniques to account for engineering solutions. The Boundary Element Method (BEM) has shown to be a powerful numeric tool for the analysis and solution of many physical and engineering problems. However, BEM fully populated and non-symmetric system matrices implies in higher memory requirements and solution times. This work analyze the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross Approximation - ACA, to multiple inclusion potential problems. The use of hierarchical format is aimed at More >

D. Brunner¹, M. Junge¹, P. Rapp¹, M. Bebendorf², L. Gaul¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 131-160, 2010, DOI:10.3970/cmes.2010.058.131

Abstract The simulation of the hydroacoustic sound radiation of ship-like structures has an ever-growing importance due to legal regulations. Using the boundary element method, the overall dimension of the problem is reduced and only integrals over surfaces have to be considered. Additionally, the Sommerfeld radiation condition is automatically satisfied by proper choice of the fundamental solution. However, the resulting matrices are fully populated and the set-up time and memory consumption scale quadratically with respect to the degrees of freedom. Different fast boundary element methods have been introduced for the Helmholtz equation, resulting in a quasilinear complexity.… More >

Suely Oliveira², Fang Yang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 113-120, 2007, DOI:10.3970/icces.2007.003.113

Abstract In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H-)matrices. Previous work by the authors using this approach did not use H-matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author's previous method, an AMG method adapted to saddle point systems, and conventional iterative methods such as JOR. More >