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On the stability of direct time-domain boundary element methods for elastodynamics

机译：弹性力学直接时域边界元方法的稳定性

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Numerical stability has been a fundamental challenge in direct time-domain boundary element methods (TD-BEM) for elastodynamics. In this paper, an analytical framework for the evaluation of the critical aspect is presented. By casting a convolution integral-based TD-BEM algorithm in the form of a linear multi-step method with a hybrid amplification matrix and the incorporation of some fundamental characteristics of commonly-used transient Green's functions, a rigorous assessment of the problem is shown to be reducible to a standard spectral analysis in matrix theory by which the stability threshold can be clearly defined. Apt to be relevant to the evaluation of other TD-BEMs, the approach is applied to a regularized time-domain direct boundary element method with optional collocation weights and orders of solution variable projections as illustration. By virtue of the proposed formalism and a systematic parametric study, a proper resolution of the critical aspect for some past schemes as well as the versatility of the generalized TD-BEM algorithm as they pertain to the benchmark finite-domain square-bar and the infinite-domain cavity elastodynamic problems are given as examples.
机译：数值稳定性一直是弹性动力学的直接时域边界元方法（TD-BEM）的基本挑战。在本文中，提出了用于评估关键方面的分析框架。通过将基于卷积积分的TD-BEM算法转换为具有混合放大矩阵的线性多步法的形式，并结合了常用瞬态格林函数的一些基本特征，可以对问题进行严格评估可以简化为矩阵理论中的标准光谱分析，从而可以清楚地定义稳定性阈值。为了与其他TD-BEM的评估相关，该方法被应用到正则化时域直接边界元方法，并以可选的配置权重和解变量投影的顺序进行说明。通过提议的形式主义和系统的参数研究，可以合理地解决一些过去方案的关键方面，以及通用TD-BEM算法的多功能性，因为它们涉及基准有限域方杆和无限作为例子给出了域腔弹性动力学问题。

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