Lee, Barry | Search NASA

DOE OSTI2016

Summary Report: Multigrid for Systems of Elliptic PDEs

We are interested in determining if multigrid can be effectively applied to the system. The conclusion that I seem to be drawn to is that it is impossible to develop a blackbox multigrid solver for these general systems. Analysis of the system of PDEs must be conducted first to determine pre-processing procedures on the continuous problem before applying a multigrid method. Determining this pre-processing is currently not incorporated in black-box multigrid strategies. Nevertheless, we characterize some system features that will make the system more amenable to multigrid approaches, techniques that may lead to more amenable systems, and multigrid procedures that are generally more appropriate for these systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

Towards Real-Time High Performance Computing For Power Grid Analysis

Real-time computing has traditionally been considered largely in the context of single-processor and embedded systems, and indeed, the terms real-time computing, embedded systems, and control systems are often mentioned in closely related contexts. However, real-time computing in the context of multinode systems, specifically high-performance, cluster-computing systems, remains relatively unexplored. Imposing real-time constraints on a parallel (cluster) computing environment introduces a variety of challenges with respect to the formal verification of the system's timing properties. In this paper, we give a motivating example to demonstrate the need for such a system--- an application to estimate the electromechanical states of the power grid--- and we introduce a formal method for performing verification of certain temporal properties within a system of parallel processes. We describe our work towards a full real-time implementation of the target application--- namely, our progress towards extracting a key mathematical kernel from the application, the formal process by which we analyze the intricate timing behavior of the processes on the cluster, as well as timing measurements taken on our test cluster to demonstrate use of these concepts.

High performance computing, real-time-computing, p↗