The analysis of multigrid algorithms for pseudodifferential operators of order minus one
- Cornell Univ., Ithaca, NY (United States)
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{sup {minus}1/2}({Omega}). Effective multigrid algorithms are developed for this problem. These algorithms are novel in that they use the inner product on H{sup {minus}1}({Omega}) as a base inner product for the multigrid development. The authors 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. 19 refs., 1 fig., 2 tabs.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 86729
- Journal Information:
- Mathematics of Computation, Vol. 63, Issue 208; Other Information: PBD: Oct 1994
- Country of Publication:
- United States
- Language:
- English
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