Scalable Submesh Computing

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We will develop new algorithms, mathematical foundations, and a newprogramming methodology for the fast parallel solution of ellipticproblems with aspects that are crucial in practice but present seriousdifficulties to existing methods. We will investigate new robust iterativesubstructuring methods that perform well even in the presence of interfaceroughness on element scale. The performance of existing methodsdeteriorates in this case, but smooth decompositions are typically notavailable in practice. We also propose to investigate fast methods for thediscretization and iterative solution of high frequency wave propagationand scattering problems by representing the solution locally as acombination of waves on a coarse mesh and exploiting connections with thefast multipole method. Finally, we propose to develop new programmingapproaches and prototype tools for latency tolerant implementation onparallel machines, transforming a high level program with new directivesinto multiple independent tasks queued on processors.The project will advance the state of the art in modeling complicatedproblems in Mechanical Engineering with irregular geometries onhigh-performance computers with high accuracy and efficiency, improve thetechnology underlying radar, sonar, and ultrasound imaging, and create anew highly efficient methodology and prototype tools for High-PerformanceComputing. Potential applications include computational analysis andmodeling of automobiles and aircrafts and accurate high resolutionultrasound imaging. It is expected that the new methodology forHigh-Performance Computing will be important for futuristic technologies,where the speed of light is the limiting factor of communication betweenthe processors, as well as for more immediate distributed computing onnetworks of computers.