Robust Structured Multigrid Algorithms for Mechanics of Heterogeneous Media

异质介质力学的鲁棒结构化多重网格算法

• 批准号: RGPIN-2014-06032
• 负责人: MacLachlan, Scott
• 金额: $ 3.93万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634914
• 关键词: Robust; Structured; Multigrid; Algorithms; Mechanics

With the steady increase in modern computing resources has come an increased demand for high-fidelity computational simulation tools in many areas of science and engineering. This demand is driven by the need for understanding physical processes at scales where prototype engineering or lab-scale experimentation are impractical or intractable, but where the underlying physical processes are well-enough understood to yield accurate mathematical models on which to base a computational approach. Such simulation has, indeed, been a driving force in computation throughout its history, and modern simulation toolkits include highly detailed models that, consequently, have high computational costs associated with them. The principle focus of this proposal is the development, analysis, and implementation of computer algorithms to accelerate these computations.A wide class of physical problems are modeled by a similar family of mathematical equations, focusing on the dynamics of incompressible fluids and incompressible solid bodies. These equations naturally model physical energy-minimization principles coupled with the constraint of conservation of mass. While the equivalent unconstrained energy minimization problems are in a class for which efficient simulation techniques are known, the constrained versions of interest here are not. Thus, the focus of this research is in the extension of these approaches to the constrained minimization models associated with these problems. Two key aspects will be studied, focusing on the development of so-called optimal algorithms for these simulations, and on developing these algorithms to take full advantage of modern computational hardware.The algorithms in this research program are focused on the multigrid methodology, named after the multiple scales of a problem that are used in order to achieve an efficient solution algorithm. For problems with variable material properties, the key challenges in applying the multigrid approach are in developing appropriately averaged models to account for long-distance behaviour, and in developing efficient complementary techniques for resolving short-distance behaviour. In this proposal, a major focus is given to doing the latter in a way that greatly leverages modern high-performance computing architectures to produce algorithms that are efficient both in theory and in practice.The results of the proposed research promise to provide both a strong step forward in the academic study of these problems and software that can be directly applied in other science and engineering disciplines, and in industrial practice. Thus, the expected economic benefit is significant, particularly to the high-technology and bio-technology sectors. The proposed work will directly result in the training of several students, at the undergraduate and graduate levels, in key skills in the emerging discipline of computational science and engineering, enabling them to fill high-demand roles in these industries, essential for the Canadian information economy.

随着现代计算资源的稳定增长，在许多科学和工程领域，对高保真计算模拟工具的需求增加。这种需求是由理解原型工程或实验室规模实验不切实际或棘手的尺度上的物理过程所驱动的，但是可以很好地理解基本的物理过程以产生准确的数学模型，以基于计算方法。确实，这种模拟在整个历史上都是计算的推动力，现代模拟工具包包括高度详细的模型，因此具有与之相关的高计算成本。该提案的主要重点是计算机算法的开发，分析和实施以加速这些计算。广泛的物理问题是通过类似的数学方程式来建模的，重点是不可压缩的流体和不可压缩的固体身体。这些方程自然地模拟了物理能量最小化原理，并结合质量保护的约束。尽管已知有效的仿真技术的类别中，等效的不受限制的能量最小化问题却尚不清楚。因此，这项研究的重点是将这些方法扩展到与这些问题相关的受约束最小化模型。将研究两个关键方面，重点是为这些模拟的所谓最佳算法开发，并开发这些算法以充分利用现代计算硬件。该研究计划中的算法侧重于以多种量表的问题命名的Multigrid方法，该方法用于获得有效的解决方案的多个问题，以实现有效的解决方案。对于具有可变材料属性的问题，应用多机方法的主要挑战是开发适当的平均模型来说明长距离行为，并开发有效的互补技术来解决短途行为。在该提案中，重点是以一种极大地利用现代高性能计算体系结构的方式进行后者，以产生在理论上和实践中有效效率的算法。拟议的研究的结果有望在对这些问题和软件的学术研究中既可以在其他科学和工程学实践和工业实践中都能直接应用这些问题，并在工业阶段和工业实践中直接应用。因此，预期的经济利益是重要的，特别是对于高科技和生物技术领域。拟议的工作将直接导致在本科和研究生级别的几名学生培训计算科学和工程学的新兴学科中的关键技能，从而使他们能够在这些行业中填补对加拿大信息经济至关重要的高调角色。