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An Advanced ACA/BEM for Solving 2D Large-Scale Elastic Problems with Multi-Connected Domains

T. Gortsas1, S.V. Tsinopoulos2, D. Polyzos1,3
Department of Mechanical Engineering & Aeronautics, University of Patras, Patras, Greece
Department of Mechanical Engineering, Technical Research Institute, Patras, Greece
Department of Mechanical Engineering and Aeronautics, University of Patras, 26504, Patras,Greece, +0030 2610969442, Email: polyzos@mech.upatras.gr

Computer Modeling in Engineering & Sciences 2015, 107(4), 321-343. https://doi.org/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 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.

Keywords

Boundary Element Method, Hierarchical Matrices, Adaptive Cross Approximation, ACA, Large Scale Elastic Problems, Composite Materials

Cite This Article

Gortsas, T., Tsinopoulos, S., Polyzos, D. (2015). An Advanced ACA/BEM for Solving 2D Large-Scale Elastic Problems with Multi-Connected Domains. CMES-Computer Modeling in Engineering & Sciences, 107(4), 321–343.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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