Asynchronous integration of ordinary differential equations on multiprocessors
Asynchronous Iterations Methods have been shown to offer significant speedups in multiprocessing environments for the class of iterative methods x = F(x). For a system of equations, parallel implementation on a multiprocessor with no minimal synchronization between cooperating processes yields the most advantage. Picard or Picard-like iteration schemes for solving Ordinary Differential Equations (ODEs) fall into such a class of iterative methods. The Picard method computes a sequence of successive approximation y/sup n/(t) to the exact solution y(t) of the Initial Value Problem (IVP) /dot y/ = f(t,y), y(t/sub 0/) = y/sub 0/, where /dot y/ = dy/dt. Starting with y/sup 0/ = y(t/sub 0/), it can be shown that this sequence converges to the true solution y(t) of the IVP. We have developed an asynchronous iterative procedure that performs such an integration in a multiprocessor environment. For a given system of n IVP, each component /dot y/t = f/sub i/(t, y/sub 1/, y/sub 2/, /hor ellipsis/, y/sub n/) is integrated any time any of the y/sub j/, j /ne/ i gets updated. No synchronization other than this is maintained amongst the components. The algorithm has been implemented on an Encore Multimax which is a multiprocessor shared-memory machine. The computer code is designed to solve a given system of ODEs. The user interface to the code is similar to traditional ODEs solvers. We present a preliminary report on results obtained. 5 refs.
- Research Organization:
- Illinois Univ., Urbana (USA). Dept. of Computer Science
- DOE Contract Number:
- FG02-87ER25026
- OSTI ID:
- 5979551
- Report Number(s):
- DOE/ER/25026-31; UIUCDCS-R-89-1525; UILU-ENG-89-1744; ON: DE89014169
- Country of Publication:
- United States
- Language:
- English
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