Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

Journal Article · Fri Jan 01 04:00:00 EST 1993 · Mathematics of Computation; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1993-1146834-4· OSTI ID:6647075

Bramble, J H; Leyk, Z; Pasciak, J E

The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 6647075
• Journal Information: Mathematics of Computation; (United States), Journal Name: Mathematics of Computation; (United States) Vol. 60:201; ISSN 0025-5718; ISSN MCMPAF
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CONVERGENCE
EIGENVALUES
EVALUATION
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATRICES