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

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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.