Old Dominion University & ICASE, NASA Langley Research Center
Demands for massive memory and high speed typically accompany one another in scientific and engineering computations, linking space to time in algorithm design. For highest performance, some degree of programmer control should be exerted over data layout in coding for scalable distributed memory machines, even if the memory is accessible through the programming model of a global shared address space. Fortunately, the laws of nature often cooperate with a basic scaling law of computer architecture: the magnitude of interaction between two degrees of freedom in a physical system decays with their spatial separation; therefore, the frequency and volume of data exchange between different points in the computational domain can be allowed to decay with distance in a trade-off involving memory access overhead and the precision required in a final result (or the rate of convergence required from a preconditioner). For model problems, this trade-off has been formalized in convergence theorems. We have been exploring it primarily experimentally, applying domain decomposition preconditioners to multicomponent nonlinear problems from computational aerodynamics, primarily through Argonne's PETSc library. In this talk, we provide a brief algorithmic background of the pseudo-transient Newton-Krylov-Schwarz method, an even briefer background of some illustrative transonic flow physics, and some performance data for structured and unstructured grid computations, on the SP, T3E, and Origin, for up to 2.8 million vertices, on up to 512 processors. (Homepage: http://www.cs.odu.edu/~keyes/)
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 1998]