This is the first part of a three part sequence of lectures, which deal with topics arising in the parallel implementation computational fluid dynamics (CFD) algorithms. CFD has many applications ranging from modeling the airflow around a hypersonic plane of the future to modeling flow of water in a pipe. In our series of lectures the focus is on unstructured grid technology. Many of the applications are derived from areodynamics.
Unstructured grid techmologies give rise to many challenging problems in a parallel implementation. Here we will address the question of how to distribute such unstructured computational domains over a large number of processors in a MIMD machine with distributed memory. A graph theoretical framework for these problems will be established. Based on this framework three decomposition algorithms will be introduced: recursive coordinate bisection, recursive graph bisection, and recursive spectral bisection (RSB)
RSB will be discussed in some more detail. It is based on the computation of an eigenvector of the Laplacian matrix associated with the graph. Some theoretical background about Laplacian matrices will be reviewed. Numerical comparisons on large scale two and three dimensional problems demonstrate the efficiency of the spectral bisection algorithm.
H. Simon, "Partitioning of Unstructured Problems for Parallel Processing", Computing Systems in Engineering, No 2/3, pages 135 -148, 1991.
Jim Demmel's lecture notes on graph partitioning.
T. Barth, "Parallel CFD Algorithms on Unstructured Meshes", in Special Course on Parallel Computing in CFD, AGARD Lecture Notes, AGARD-R-807, Advisory Group for Aerospace Research and Development, Neuilly-sur-Seine, France 1994. (These lecture notes are available as "VKI lecture notes" in postscript from Tim's homepage).
METIS graph partitioning Package, by G. Karypis and V. Kumar, Univ. of Minnesota.
CHACO graph partitioning, by B. Hendrickson and R. Leland, Sandia Natl. Labs.
JOSTLE graph partitioning, by C. Walshaw, M. Cross, and M. Everett at the University of Greenwich in the UK.