Domain decomposition preconditioners for elliptic problems in two and three dimensions: First approach
In this talk, we shall describe some domain decomposition preconditioners for elliptic boundary value problems in two and three dimensions. We consider the case where more than two subdomains meet at an interior point of the original domain; this allows a subdivision into an arbitrary number of subdomains without the deterioration of the iterative convergence rates of the resulting algorithms. The described preconditioners (for both two and three dimensional applications) result in preconditioned systems whose condition number growth is bounded by c(1 + ln/sup 2/ (d/h)). Here h is the mesh size and d is roughly the size of the largest subdomain. We finally give a technique which utilizes the earlier described methods to derive even more efficient preconditioners. This technique leads to preconditioned systems whose condition number remains bounded independently of the number of unknowns. 11 refs.
- Research Organization:
- Brookhaven National Lab., Upton, NY (USA)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 7065844
- Report Number(s):
- BNL-39166; CONF-870146-1; ON: DE87005241
- Country of Publication:
- United States
- Language:
- English
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