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Fast Multipole Singular Boundary Method for Large-Scale Plane Elasticity Problems

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Abstract

The singular boundary method (SBM) is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions (MFS). The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O(N3)with direct solvers or O(N2)with iterative solvers, as well as the memory requirement of O(N2). In this study, the first attempt was made to combine the fast multipole method (FMM) and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O(N). Based on the complex variable representation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, 210098, Nanjing, China

    Wenzhen Qu & Wen Chen

  2. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA

    Wenzhen Qu

Authors
  1. Wenzhen Qu
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  2. Wen Chen
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Correspondence to Wen Chen.

Additional information

Project supported by the National Basic Research Program of China (973 Project, No. 2010CB832702), the National Science Funds for Distinguished Young Scholars of China (No. 11125208), the National Natural Science Foundation of China (Nos. 11125208 and 11302069), the 111 project under Grant B12032, Jiangsu Province Graduate Students Research and Innovation Plan (No. KYZZ_0138), and the scholarship from the China Scholarship Council (CSC) (No. 201306710026).

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Qu, W., Chen, W. Fast Multipole Singular Boundary Method for Large-Scale Plane Elasticity Problems. Acta Mech. Solida Sin. 28, 626–638 (2015). https://doi.org/10.1016/S0894-9166(16)30004-0

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  • DOI: https://doi.org/10.1016/S0894-9166(16)30004-0

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