This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor 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.
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