Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The analysis of multigrid algorithms for pseudodifferential operators of order minus one


Authors: James H. Bramble, Zbigniew Leyk and Joseph E. Pasciak
Journal: Math. Comp. 63 (1994), 461-478
MSC: Primary 65N55
MathSciNet review: 1254145
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Multigrid algorithms are developed to solve the discrete systems approximating the solutions of operator equations involving pseudodifferential operators of order minus one. Classical multigrid theory deals with the case of differential operators of positive order. The pseudodifferential operator gives rise to a coercive form on $ {H^{ - 1/2}}(\Omega )$. Effective multigrid algorithms are developed for this problem. These algorithms are novel in that they use the inner product on $ {H^{ - 1}}(\Omega )$ as a base inner product for the multigrid development. We show that the resulting rate of iterative convergence can, at worst, depend linearly on the number of levels in these novel multigrid algorithms. In addition, it is shown that the convergence rate is independent of the number of levels (and unknowns) in the case of a pseudodifferential operator defined by a single-layer potential. Finally, the results of numerical experiments illustrating the theory are presented.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N55

Retrieve articles in all journals with MSC: 65N55


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1254145-2
PII: S 0025-5718(1994)1254145-2
Article copyright: © Copyright 1994 American Mathematical Society