Analysis of a Parallelized Nonlinear Elliptic Boundary Value Problem Solver with Application to Reacting Flows
Abstract
A parallelized finite difference code based on Newton's method for systems of non-linear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters (including discrete problem dimensions, convergence parameters, and machine characteristics) is derived for algorithms based on stripwise and boxwise decompositions of the domain and a 1:1 assignment of the strip or box subdomains to processors. Sensitivity of the cost function to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of 19 equations with very expensive function evaluations (a reacting flow model of engineering interest which motivates the work. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedups of O(n), where n is mesh resolution in one direction, for reasonable n. To realize speedups of O (n sq), the total number of mesh points, only hypercubes appear attractive. These results must be qualified by hardware assumptions, including sufficient local memory per processor to hold all of the data defined on the associated subdomain, and selection of machine parameters typical of presently commercially available components. CFD.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1987
- Accession Number
- ADA211487
Entities
People
- David E. Keyes
- Mitchell D. Smooke