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首页> 外文学位 >A unified mathematical framework of continuous and discontinuous time integrators and domain decomposition techniques for scalable high performance structural dynamics simulations.
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A unified mathematical framework of continuous and discontinuous time integrators and domain decomposition techniques for scalable high performance structural dynamics simulations.

机译：连续和不连续时间积分器和域分解技术的统一数学框架，用于可扩展的高性能结构动力学仿真。

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摘要

The present research provides a unified theoretical framework and computational developments involving the fundamental concepts and methodology leading to a viable computational technology to significantly enhance the state-of-the-art in computational structural dynamics. The research individually addresses developments in: (i) time discretized operators, and (ii) scalable computational models in the terascale range.; The basic factors considered in the developments of time discretized operators are: (i) new avenues and framework leading to computational algorithms with good accuracy while preserving the underlying physics, (ii) a class of optimal algorithms for practical applications, and (iii) ease of implementation with increased functionality. The distinguishing features include: (a) new unified mathematical framework for generalized time continuous/discontinuous time integration operators that do not exist and/or have not been adequately explored/exploited to date including various existing computational algorithms as subsets, (b) the design leading to high-order accurate continuous/discontinuous time integration operators with/without spurious roots, (c) new and practical implementation methodology leading to the notion of a reduced complexity in programming environment, and (d) new unified hierarchical set of energy conserving/decaying discontinuous time integration operators.; The key factors considered in the developments of scalable computational models in the terascale range include: (i) a framework towards a unified domain decomposition approach suitable for heterogeneous situations, and (ii) the overall scalability of the entire transient analysis with focus on structural dynamics applications. The scalability metrics such as numerical scalability, parallel scalability, and memory utilization scalability are particularly addressed with the final objectives of providing for the first time a viable computational technology that ensures scalability of the entire analysis. In this regard, the distinguishing features include: (a) a generalized variational domain decomposition framework that permits congruent/non-congruent meshes and simultaneously yields various existing methods as subsets, and (b) an integrated computational technology that integrates parallel explicit/implicit time integration operators via a unified family of time discretized computational algorithms, domain decomposition techniques and graph partitioning.; The results of various contributions of this research in each of the topical areas demonstrate and validate the proposed developments including the integrated computational technology for large-scale structural dynamics on high performance computing platforms.
机译：本研究提供了统一的理论框架和涉及基础概念和计算方法的计算开发，从而导致了可行的计算技术，从而显着提高了计算结构动力学的最新水平。这项研究分别针对以下方面的发展：（i）时间离散算子和（ii）万亿级的可伸缩计算模型。时间离散算子的发展中考虑的基本因素是：（i）导致计算算法具有较高准确性的新途径和框架，同时保留了基本的物理原理;（ii）一类用于实际应用的最佳算法，并且（iii）功能增强的实现方式。区别特征包括：（a）用于尚不存在和/或迄今尚未充分探索/利用的广义时间连续/不连续时间积分算子的新统一数学框架，包括各种现有的计算算法作为子集，（b）设计导致具有/没有虚假根源的高阶准确连续/不连续时间积分算子，（c）新的实际实现方法导致编程环境复杂性降低的概念，以及（d）新的节能统一层级集合/衰减的不连续时间积分算子。在万亿级范围内的可伸缩计算模型的开发中考虑的关键因素包括：（i）面向适用于异构情况的统一域分解方法的框架，以及（ii）整个瞬态分析的整体可伸缩性，重点是结构动力学应用程序。诸如数字可伸缩性，并行可伸缩性和内存利用率可伸缩性之类的可伸缩性指标特别针对最终目的，即首次提供可确保整个分析的可伸缩性的可行计算技术的最终目标。在这方面，其显着特征包括：（a）允许全等/非全等网格并同时产生各种现有方法作为子集的广义变分域分解框架，以及（b）整合了并行显式/隐式时间的集成计算技术通过统一的时间离散计算算法家族，域分解技术和图分区集成运营商。这项研究在每个主题领域的各种贡献的结果证明并验证了所提出的发展，包括在高性能计算平台上用于大规模结构动力学的集成计算技术。

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