Mapping unstructured grid computations to massively parallel computers
This thesis investigates the 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, a highly parallel heuristic mapping algorithm is developed, called Cyclic Pairwise Exchange (CPE), and its place in the taxonomy is discussed. 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 twofold for the test problems used. Finally, CPE is used 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. Rows of the matrix are mapped to processors and an inner-product based matrix-vector multiplication is used. This method is demonstrated to be an order of magnitude faster than methods based on scan operations for the test cases used here.
- Research Organization:
- Rensselaer Polytechnic Inst., Troy, NY (United States)
- OSTI ID:
- 5569644
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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