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Revisiting the BE SBS algorithm and applying it to solve torsion problems in composite bars: Robustness and efficiency study

机译：回顾BE SBS算法并将其应用于解决复合材料钢筋的扭转问题：鲁棒性和效率研究

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摘要

The construction of truly competitive boundary-element (BE) codes, capable of analyzing real-life engineering problems, unavoidably requires the devising of coupling strategies to make the modeling of complex heterogeneous domains user-friendly. Thereby, high-performance algorithms for solving the highly sparse resulting system of equations are essential. Moreover, as discontinuous boundary elements are necessary to alleviate the modeling process of coupled domains, efficient (low-order) quadratures for integrating singular and nearly-singular fundamental kernels over the boundary elements must be implemented. This paper newly discusses the construction of the boundary-element subregion-by-subregion (BE SBS) technique based on a BEM formulation for torsion problems in general composite bars. One also presents details of the formulation of the Krylov solvers BiCG and BiCGSTAB-(l), embedded in the coupling algorithm. In addition, the BE SBS matrix structure itself is used to form an efficient sparse incomplete LU factorization (SILU) preconditioner to accelerate the iterative solution process. Torsion problems in bars with complex composite patterns (e.g. with many different materials) are analyzed to attest the efficiency and robustness of the whole boundary-element technique.
机译：能够分析实际工程问题的真正竞争性边界元素（BE）代码的构建不可避免地需要设计耦合策略，以使对复杂异构域的建模变得用户友好。因此，用于求解高度稀疏的方程组的高性能算法至关重要。此外，由于必须使用不连续的边界元素来减轻耦合域的建模过程，因此必须实现有效的（低阶）正交函数，用于在边界元素上集成奇异和几乎奇异的基本核。本文主要讨论了基于BEM公式的边界元素子区域逐子区域（BE SBS）技术的构建，以解决一般复合材料钢筋的扭转问题。还提供了嵌入耦合算法中的克雷洛夫求解器BiCG和BiCGSTAB-（1）的公式化细节。此外，BE SBS矩阵结构本身可用于形成有效的稀疏不完全LU分解（SILU）预调节器，从而加快迭代求解过程。分析了具有复杂复合图案（例如使用多种不同材料）的钢筋的扭转问题，以证明整个边界元技术的效率和鲁棒性。

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