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. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5306227
- Report Number(s):
- UCRL-LR-108186; ON: DE92000096
- Resource Relation:
- Other Information: Thesis (M.S.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Domain decomposition techniques for solving elliptic partial differential equations on multiprocessors
PSolve: A concurrent algorithm for solving sparse systems of linear equations
Related Subjects
ITERATIVE METHODS
ALGORITHMS
PARTIAL DIFFERENTIAL EQUATIONS
ARRAY PROCESSORS
BOUNDARY-VALUE PROBLEMS
CONVERGENCE
ELLIPTICAL CONFIGURATION
PARALLEL PROCESSING
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers