A domain decomposition algorithm for solving large elliptic problems
AN algorithm which efficiently solves large systems of equations arising from the discretization of a single second-order elliptic partial differential equation is discussed. The global domain is partitioned into not necessarily disjoint subdomains which are traversed using the Schwarz Alternating Procedure. On each subdomain the multigrid method is used to advance the solution. The algorithm has the potential to decrease solution time when data is stored across multiple levels of a memory hierarchy. Results are presented for a virtual memory, vector multiprocessor architecture. A study of choice of inner iteration procedure and subdomain overlap is presented for a model problem, solved with two and four subdomains, sequentially and in parallel. Microtasking multiprocessing results are reported for multigrid on the Alliant FX-8 vector-multiprocessor. A convergence proof for a class of matrix splittings for the two-dimensional Helmholtz equation is given. 70 refs., 3 figs., 20 tabs.
- Research Organization:
- Lawrence Livermore National Lab., CA (United States)
- Sponsoring Organization:
- DOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5306227
- Report Number(s):
- UCRL-LR-108186; ON: DE92000096
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
BOUNDARY-VALUE PROBLEMS
CONFIGURATION
CONVERGENCE
DIFFERENTIAL EQUATIONS
ELLIPTICAL CONFIGURATION
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING