Scalable Submesh Computing

我们将开发新的算法、数学基础和新的编程方法，用于椭圆问题的快速并行解决，这些问题在实践中至关重要，但对现有方法来说存在严重困难。我们将研究新的鲁棒迭代子结构方法，即使在元素尺度上存在接口性也能表现良好。在这种情况下，现有方法的性能会下降，但在实践中通常无法实现平滑分解。我们还建议研究高频波传播和散射问题的离散化和迭代解的快速方法，将解局部表示为粗网格上的波的组合，并利用快速多极方法的联系。最后，我们建议开发新的编程方法和原型工具，用于并行机器上的延迟容忍实现，将具有新指令的高级程序转换为在处理器上排队的多个独立任务。该项目将在高精度和高效率的高性能计算机上推进机械工程中不规则几何复杂问题建模的最新技术，改进雷达、声纳和超声成像技术，并为高性能计算创造新的高效方法和原型工具。潜在的应用包括汽车和飞机的计算分析和建模，以及精确的高分辨率超声成像。预计高性能计算的新方法将对未来技术很重要，在未来技术中，光速是处理器之间通信的限制因素，以及对计算机网络上更直接的分布式计算也很重要。

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.