A Fast Boundary Element Method for the Analysis of Fiber-Reinforced Composites Based on a Rigid-Inclusion Model

By Yijun Liu, Naoshi Nishimura, Y. Otani, Toru Takahashi, Xiaolin Chen, H. Munakata. 2005

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A new fast multipole boundary element method for solving large‐scale two‐dimensional elastostatic problems (2006, background): “Expansions using solid harmonic functions with about 10–15 terms and about 20 iterations are often found to be sufficient for the convergence with a tolerance of 10−6 in the solutions of large 3-D problems with more than 10 million BEM equations [22, 23].”
The fast multipole boundary element method for potential problems: A tutorial (2006, background): “Most recently, composite material models containing tens of thousands of fibers [18] [19] and models of electromagnetic wave scatterings from a full Engineering Analysis with Boundary Elements 30 (2006) 371–381 www.elsevier.com/locate/enganabound 0955-7997/$ -see front matter q 2006 Elsevier Ltd.”
A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain (2008, methodology): “The FMM then naturally led to fast multipole boundary element methods (FM-BEMs), whose scope and capabilities have rapidly progressed, especiall y in connection with application in electromagnetics [21, 31, 32, 53], but also in other fields including acoustics [14, 36, 48] and computational mechanic”