Scalable Submesh Computing

University Of Colorado At Denver-Downtown Campus, Denver CO

Investigators

Abstract

We will develop new algorithms, mathematical foundations, and a new programming methodology for the fast parallel solution of elliptic problems with aspects that are crucial in practice but present serious difficulties to existing methods. We will investigate new robust iterative substructuring methods that perform well even in the presence of interface roughness on element scale. The performance of existing methods deteriorates in this case, but smooth decompositions are typically not available in practice. We also propose to investigate fast methods for the discretization and iterative solution of high frequency wave propagation and scattering problems by representing the solution locally as a combination of waves on a coarse mesh and exploiting connections with the fast multipole method. Finally, we propose to develop new programming approaches and prototype tools for latency tolerant implementation on parallel machines, transforming a high level program with new directives into multiple independent tasks queued on processors. The project will advance the state of the art in modeling complicated problems in Mechanical Engineering with irregular geometries on high-performance computers with high accuracy and efficiency, improve the technology underlying radar, sonar, and ultrasound imaging, and create a new highly efficient methodology and prototype tools for High-Performance Computing. Potential applications include computational analysis and modeling of automobiles and aircrafts and accurate high resolution ultrasound imaging. It is expected that the new methodology for High-Performance Computing will be important for futuristic technologies, where the speed of light is the limiting factor of communication between the processors, as well as for more immediate distributed computing on networks of computers.