SCREMS: Developing Computational Mathematics at the University of Florida

该补助金为佛罗里达大学数学系的计算资源提供资金。 提出了四个需要新资源的研究项目：第一个项目是稀疏矩阵算法，将最新的优化策略和多级并行算法结合到稀疏矩阵算法中，特别强调可以利用并可以应用于并行计算架构的技术。第二个项目的目标是发展一套新的方法来解决复杂结构上的偏微分方程。第三个项目围绕算法重建人体内部区域的三维断层图像。第四个研究纳米尺度的材料，使用基于数学合理简化的模拟。研究活动的成功将通过生物医学工程，计算机科学，电气工程和医学的合作产生超越计算数学的影响。考虑的具体应用包括对空中交通管制的潜在益处的闪电模拟，对心律失常患者潜在益处的心脏消融技术的生物医学工程，用于医学成像的改进的断层重建算法可能导致更好的诊断工具，以及对纳米尺度材料的性质的更好预测，这些材料具有挑战性，难以用当前技术制造。学生和年轻的研究人员将受益于新的资源，通过严格的数学课程培训，结合实际的计算培训，使用大规模应用中出现的问题。

This grant provides funding for augmenting the computational resourcesin the Mathematics Department of the University of Florida. Fourresearch projects which require the new resources are proposed: Thefirst project on sparse matrix algorithms incorporates state of theart optimization strategies and multilevel heuristics into sparsematrix algorithms, with particular emphasis on techniques that canexploit and can be applied to parallel computing architectures. Thesecond project aims to develop a new set of methods for solvingpartial differential equations on complicated structures. The thirdproject centers around algorithms for the reconstruction of threedimensional tomographic images of internal regions of the humanbody. The fourth investigates nano-scale materials using simulationsbased on mathematically sound simplifications.The success of the research activities will have impact beyondcomputational mathematics through collaborations in biomedicalengineering, computer science, electrical engineering, andmedicine. Specific applications considered include the simulation oflightning with potential benefits to air traffic control, thebiomedical engineering of cardiac ablation technology potentiallybenefiting patients with arrhythmias, improved tomographicreconstruction algorithms for medical imaging potentially leading tobetter diagnostic tools, and better predictions for the properties ofnano-scale materials which are challenging to fabricate with currenttechnology. Students and young researchers will benefit from the newresources by rigorous training in mathematical courses combined withpractical computational training using problems arising fromlarge-scale applications.