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Nonlinear reaction-diffusion equations are an important and interesting class of problems. However, we almost never know the solution of a nonlinear reaction-diffusion model and consequently numerical computation is a principal tool for analysis. But the same features that make analysis difficult also make numerics difficult. To be on a firm scientific… (More)

- Roy D. Williams
- Concurrency - Practice and Experience
- 1991

If a finite element mesh has a sufficiently regular structure, it is easy to decide in advance how to distribute the mesh among the processors of a distributed-memory parallel processor, but if the mesh is unstructured, the problem becomes much more difficult. The distribution should be made so that each processor has approximately equal work to do, and… (More)

We describe a MIMD parallel code to solve a general class of ordinary dierential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial dierential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and exibility of the software. We… (More)

- J Häuser, M Spel, J Muylaert, R D Williams
- 1994

Extended Abstract 1 The ParNSS Code ParNSS is an acronym for Parallel Navier-Stokes Solver: it solves the Reynolds averaged Navier-Stokes equations on a multiblock grid topology. Our objectives in producing this code are for a solver that combines sophisticated fluid-flow simulation with sophisticated software engineering. ParNSS can solve complex physics –… (More)

- R. D. Williams
- C3P
- 1989

DIME (Distributed Irregular Mesh Environment) is a user environment written in C for manipulation of an unstructured triangular mesh in two dimensions. The mesh is distributed among the separate memories of the processors, and communication between processors is handled by DIME; thus the user writes C-code referring to the elements and nodes of the mesh and… (More)

- R. D. Williams
- 1989

DIME is a programming environment for manipulation of irregular triangular meshes with a distributed memory machine. We have added a software layer DIMEFEM which manipulates Finite Element representations of functions and allows the stating and solving of variational statements. An application of DIMEFEM is an incompressible Navier-Stokes solver with a… (More)

- Jochem Häuser, Thorsten Ludewig, +4 authors Jean Muylaert
- 1999

The Java programming language has a number of features that make it attractive for writing high-quality, portable parallel programs. A pure object formulation, strong typing and the exception model make programs easier to create, debug, and maintain. The elegant threading provides a simple route to parallelism on shared-memory machines. Anticipating great… (More)

- Roy D. Williams
- Concurrency - Practice and Experience
- 1992

This paper concerns parallel, local computations with a data structure such a graph or mesh, which may be structured or unstructured. The target machine is a distributed-memory parallel processor with vector or pipeline hardware on the processors, but software based on voxel databases also runs efficiently on shared-memory and uniprocessor machines with and… (More)

In this article we discuss a strategy for speeding up the solution of the Navier-Stokes equations on highly complex solution domains such as complete aircraft, spacecraft, or turbomachinery equipment. We have used a nite-volume code for the non-turbulent Navier-Stokes equations as a testbed for implementation of linked numerical and parallel processing… (More)

The purpose of this paper is to predict the efficiency of the Navier-Stokes code NSS*, which will run on an MIMD architecture parallel machine. Computations are performed using a three-dimensional overlapping structured multi-block grid. Each processor works with some of these blocks, and exchanges data across the boundaries of the blocks. The efficiency of… (More)