Domain decomposition techniques for solving elliptic partial differential equations on multiprocessors
Historically, multiprocessing has long been thought of as an excellent approach for increasing performance. Unfortunately, classical sequential algorithms are not easily translated into parallel algorithms for solving a single problem on several processors. Particularly, solving a matrix problem on a multiprocessor is nontrivial, but successful implementation of matrix iterative algorithms on multiprocessors could significantly increase the performance of the numeric hydrodynamic codes. Therefore, the algorithms must be rewritten to realize the full potential of multiprocessor architectures. This thesis will describe and analyze results from a simulation study of certain matrix iterative methods that could be efficiently implemented on an arbitrary multiprocessor configuration. Chapter one and chapter two present the background matrix theory and notation. Chapter three presents possible splittings for the preconditioned conjugate gradient method and reports numerical results. In addition, this chapter introduces the Schwarz Alternating Principle, the Schwarz numeric iteration, and interesting results for arbitrarily splitting a domain for multiprocessing. Throughout this paper, the Laplace equation with Dirichlet boundary conditions is used as a numerical model for simulation and developing insight into domain decomposition for multiprocessing.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6115805
- Report Number(s):
- UCRL-53578; ON: DE85004448
- Resource Relation:
- Other Information: Portions are illegible in microfiche products. Original copy available until stock is exhausted. Thesis
- Country of Publication:
- United States
- Language:
- English
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