A fast multipole boundary element method for 2D multi-domain elastostatic problems based on a dual BIE formulation
A fast multipole boundary element method for 2D multi-domain elastostatic problems based on a dual BIE formulation
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DOI：
10.1007/s00466-008-0274-2
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发表时间：
2008-03
影响因子：
4.1
通讯作者：
Yijun Liu
中科院分区：
文献类型：
--
作者：
Yijun Liu
基于核函数的复变量表示，提出了一种新的二维弹性超奇异边界元(HBIE)快速多极公式，该公式类似于早先建立的常规边界元(CBIE)公式。将所发展的CBIE和HBIE的线性组合应用于分析含薄夹杂或开口裂纹的多域问题。设计了快速多极边界元方法的两个预条件，并讨论了它们在求解大规模问题时的有效性和效率。给出了几个数值算例，研究了基于对偶边界元格式的快速多极边界元的精度和效率。数值结果清楚地表明了快速多极边界元在求解大规模二维多域弹性问题中的潜力。该方法可用于研究复合材料、功能梯度材料和具有耦合场的微电子机械系统，这些系统通常涉及薄形状或薄夹杂物。
A new fast multipole formulation for the hypersingular BIE (HBIE) for 2D elasticity is presented in this paper based on a complex-variable representation of the kernels, similar to the formulation developed earlier for the conventional BIE (CBIE). A dual BIE formulation using a linear combination of the developed CBIE and HBIE is applied to analyze multi-domain problems with thin inclusions or open cracks. Two pre-conditioners for the fast multipole boundary element method (BEM) are devised and their effectiveness and efficiencies in solving large-scale problems are discussed. Several numerical examples are presented to study the accuracy and efficiency of the developed fast multipole BEM using the dual BIE formulation. The numerical results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale 2D multi-domain elasticity problems. The method can be applied to study composite materials, functionally-graded materials, and micro-electro-mechanical-systems with coupled fields, all of which often involve thin shapes or thin inclusions.