An Advanced ACA/BEM for Solving 2D Large-Scale Elastic Problems with Multi-Connected Domains
T. Gortsas, S.V. Tsinopoulos, D. Polyzos

doi:10.3970/cmes.2015.107.321
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 107, No. 4, pp. 321-343, 2015
Download Full length paper in PDF format. Size = 9,770,551 bytes
Keywords Boundary Element Method; Hierarchical Matrices; Adaptive Cross Approximation; ACA; Large Scale Elastic Problems; Composite Materials
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 final linear system of equations is accelerated via an iterative GMRES solver. The proposed methodology is demonstrated with the solution of large scale, plane strain elastic problems dealing with the bending of unidirectional fiber composite plates with large numbers of periodically or randomly distributed cylindrical elastic fibers embedded in a matrix medium.

PDF download PDF