Cascadic Multigrid Simulation of Incompressible Viscous Flow Problems: Performance Analysis and Parallel Workstation and Cluster Implementation

B. Kirk, K. Lipnikov, and G. Carey

Aerospace Enineering Dept, C0600
The University of Texas
Austin, TX 78712


In this investigation we examine the use of one-way cascadic multigrid strategies CMG for solution of incompressible viscous flow problems using the finite element method. The content of the presentation is as follows: First we describe the basic CMG approach for representative elliptic boundary value problems and summarize the theoretical error estimates from approximation theory, desired smoother properties, and arithmetic complexity of the method as a function of iteration parameters at each level. The extension of these error and complexity estimates to adaptive grids is also given.

In the numerical experiments, performance of the algorithm on both serial and distributed parallel systems is examined. We carry out a series of comparison studies between the CMG scheme and a standard bi-conjugate gradient solve strategy on the fine level grid. Other issues such as the treatment of the diagonal elements in the zero block corresponding to the pressure variables are also considered and the results of associated numerical studies are presented. Finally, parallel performance studies on a distributed parallel PC cluster in the CFDLab are described and both performance and flow simulation results are given for 3D applications to linear Stokes flow, low Reynolds number Navier Stokes problems, and coupled fluid-thermal problems.


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