Mapping unstructured grid computations to massively parallel computers. Ph. D. Thesis - Rensselaer Polytechnic Inst. , Feb. 1992

Thesis/Dissertation · Mon Jun 01 04:00:00 EDT 1992

OSTI ID:7169948

Hammond, S W

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

• Research Organization: Research Inst. for Advanced Computer Science, Moffett Field, CA (United States)
• OSTI ID: 7169948
• Report Number(s): N-92-29109; NASA-CR--190551; NAS--1.26:190551; RIACS-TR--92.14; CNN: NCC2-387
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
DATA PROCESSING
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATRICES
MECHANICAL STRUCTURES
MECHANICS
MESH GENERATION
OPTIMIZATION
PARALLEL PROCESSING
PROCESSING
PROGRAMMING
SCALARS
SPECTRA
TASK SCHEDULING