Scalable Parallel Multilevel Algorithms for the Solution and Optimization of Partial Differential Equations

9973276这项建议集中在由最优控制和物理问题的变分公式产生的偏微分方程组的并行隐式求解中涉及的几个基本计算问题。研究的目标包括但不限于：(1)建立和分析由偏微分方程组定义的系统的优化和求解的可证明的高效、健壮和可伸缩的多层算法。(2)包含上述算法的软件的开发及其在制造业、工程界和科学界的传播。拟议的软件将扩展加州大学圣地亚哥分校调查人员开发的现有PLTMG、MC和SNOPT代码的范围和有效性。(3)吸引高级研究生进入这一研究领域，该领域一般涉及科学和工程中出现的系统的分析和计算研究。研究人员结合了优化、偏微分方程数值方法和并行计算方面的专业知识。这项研究计划旨在为研究生提供广泛的教育经验，在一个环境中，这些不同的方面的科学计算集成在一起。这项研究的一个主要目标是将新成果转移到制造业、工程界和科学界。数学软件是技术转移最有效的手段之一。相反，有效的算法开发的一个关键组成部分是与面对现实世界问题的工程师和科学家密切联系。调查人员将继续并扩大他们与其他应用科学和技术领域的研究人员的合作，包括制造、环境建模、电力优化、生物分子建模、计算机图形学、固体力学、航空航天和金融。所有这些应用程序都受益于现有的算法和软件，并对它们做出了贡献。

9973276This proposal focuses on several fundamental computational issues involved in the parallel implicit solution of partial differential equations arising from optimal control and the variational formulation of physical problems. The goals of the research include, but are not limited to, the following: (1) The formulation and analysis of provably efficient, robust and scalable multilevel algorithms for the optimization and solution of systems defined by partial differential equations. (2) The development of software embodying the above algorithms and its dissemination within the manufacturing, engineering and scientific community. The proposed software will extend the scope and effectiveness of the existing codes PLTMG, MC, and SNOPT that have been developed by the investigators at UC San Diego. (3) The attraction of advanced graduate students into this research area, which generally concerns the analysis and computational study of systems arising in the sciences and engineering.The investigators have combined expertise in optimization, numerical methods for partial differential equations, and parallel computation. This research program is intended to provide graduate students with a broad educational experience in an environment in which these different aspects of scientific computation are integrated. A key aim of the research is the transfer of new results to the manufacturing, engineering and scientific community. Mathematical software is one of the most effective means of technology transfer. Conversely, a crucial component of effective algorithm development is close association with engineers and scientists facing real-world problems. The investigators will continue and broaden their collaboration with researchers in other areas of applied science and technology, including manufacturing, environmental modeling, electrical power optimization, biomolecular modeling, computer graphics, solid mechanics, aerospace and finance. All these applications have benefited from and contributed to existing algorithms and software.