PARALLEL ALGORITHMS FOR MEDICAL IMAGE REGISTRATION

这个子项目是许多研究子项目中利用 资源由NIH/NCRR资助的中心拨款提供。子项目和 调查员(PI)可能从NIH的另一个来源获得了主要资金， 并因此可以在其他清晰的条目中表示。列出的机构是 该中心不一定是调查人员的机构。 这项建议的目标是发展多万亿浮点算法，高精度的边界体积问题的解定义在复杂几何上的椭圆算子的公式，具有非均匀和多物理连续。为了测试所提出的方法，将检查两个具体的应用：流固相互作用问题和非线性静电模拟。这些应用涉及复杂的三维几何、非线性算子和多物理耦合。他们的解决方案带来了突出的算法和并行可伸缩性挑战。在椭圆算子的理论和计算方面有大量的工作。用于大规模、高保真模拟的主要计算工具是多重网格和基于网格的离散化的区域分解方法。另一类算法基于笛卡尔网格，但不容易扩展到具有动态界面的问题的可扩展算法。另一类求解器是基于积分方程式的。积分方程解算器的特点是算法复杂度最优、并行可伸缩性、超代数精度和稳健性。这项研究将利用PI最近在核独立快速多极子方法方面所做的工作，该方法允许使用几种不同的椭圆算子来模拟具有多达21亿个未知数和多达3000个处理器的问题，实现持续的1万亿浮点/S效率(SC05)。此外，PI的小组还开发了大规模并行八叉树结构和2：1的平衡精化算法。PI在使用PSC资源方面有丰富的经验。在过去的十年里，他一直是一个活跃的用户。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The objective of this proposal is to develop multiteraflop algorithms the high-accuracy solution of boundary volume problems formulations of elliptic operators defined on complex geometries with inhomogeneous and multiphysics continua. To test the proposed methodologies two specific applications will be examined: fluid-solid interaction problems, and nonlinear electrostatic simulations. These applications involve complicated 3D geometries, nonlinear operators and multiphysics coupling. Their solution presents outstanding algorithmic and parallel scalability challenges. There is extensive work on the theory and computation of elliptic operators. The main computational tools for large scale, high-fidelity simulations are multigrid and domain decomposition methods for grid-based discretizations. A different class of algorithms is based on Cartesian grids, but does not readily extend to scalable algorithms for problems with dynamic interfaces. Another category of solvers is based on integral equation formulations. The features of integral equation solvers are optimal algorithmic complexity, parallel scalability, superalgebraic accuracy, and robustness. This research will capitalize on recent work of the PI on kernel-independent fast multipole methods that allowed simulations with several different elliptic operators for problems with up to 2.1 billion unknowns and on up to 3000 processors, achieving a sustained 1 Teraflop/s efficiency (SC05). In addition the PI's group has developed a massively parallel octree construction and 2:1 balance refinement algorithm. The PI has extensive experience in using PSC resources. He has been an active user for the last ten years.