CAREER: Multi-Level Multi-Material Problem Solver Environment with Semisolid Material Applications and Education

在材料科学应用的计算方法和能力方面有了实质性的发展。这些方法包括物质点方法(MPM)、多时间和空间尺度方法、区域分解方法的理论和实践，以及存储容量、处理速度和分布式计算软件能力的提高。我们将在一个多级别多材料问题解算器环境(MLMM PSE)中开发和结合这些方法和功能。MLMM PSE将针对诸如裂纹扩展、颗粒材料、冲击问题、碎裂、损伤等应用。我们将展示PSE在半固态材料中的一种新的和重要的工程应用。这种组合固有的复杂性需要一个提供广泛基础设施的计算框架。作为该项目的一个计算目标，我们将在MLMM PSE中构建用于材料科学应用的基础设施。我们将创建构建MLMM PSE所必需的有效计算模块和接口。这些模块将与并行AMR和非线性求解器库集成，这将促进各种并行平台上的代码开发、效率、负载平衡和可移植性，并将支持可视化能力。作为一个理论目标，我们将设计、分析和开发创新的数值方法，以提高MLMM PSE的精度、效率、可扩展性和健壮性。我们将研究包括显式和隐式时间依赖的自适应网格和粒子细化的分层模拟。这一重要而新颖的领域提出了相当大的数学和计算挑战。作为一个教育目标，我们将为本科生开发基于网络的MLMM PSE课件，说明我们研究中出现的问题的计算解决方案。

There have been substantial developments in computational methodsand capabilities for material sciences applications. These includethe theory and practice of material point methods (MPM), multipletemporal and spatial scale methods, domain decomposition methods,together with increases in memory capacities, processing rates, andsoftware capabilities for distributed computing. We will developand combine these methods and capabilities in a Multi-LevelMulti-Material Problem Solver Environment (MLMM PSE). The MLMM PSEwill target applications such as crack propagation, granular materials,impact problems, fragmentation, damages among others. We willdemonstrate the PSE for a novel and important engineering applicationin semisolid materials.The complexity inherent in this combination demands a computationalframework that provides broad-based infrastructure. As a{\it computational aim} of this project we will construct thisinfrastructure in the MLMM PSE for material sciences applications.We will create effective computational modules and interfaces thatwill be necessary to build the MLMM PSE. These modules will beintegrated with parallel AMR and nonlinear solvers libraries, whichwill facilitate code development, efficiency, load balancing andportability on a variety of parallel platforms and will supportvisualization capabilities. As a {\it theoretical aim}, we will design,analyze, and develop innovative numerical methods to enhance accuracy,efficiency, scalability and robustness of the MLMM PSE. We willinvestigate hierarchical simulation involving explicit and implicittime dependent adaptive grid and particle refinement. This importantand novel area presents considerable mathematical and computationalchallenges. As an {\it educational aim}, we will develop withundergraduate students web-based MLMM PSE courseware that illustratesthe computational solution of problems that have arisen in our research.