Preconditioning Second-Order Elliptic Operators: Experiment and Theory

Autor:	Sze-Ping Wong, Thomas A. Manteuffel, Wayne Joubert, Seymour V. Parter
Rok vydání:	1992
Předmět:	Pure mathematics Elliptic operator Current (mathematics) Conjugate gradient method Mathematical analysis Order (ring theory) Uniform boundedness Development (differential geometry) Boundary value problem Condition number Mathematics
Zdroj:	SIAM Journal on Scientific and Statistical Computing. 13:259-288
ISSN:	2168-3417 0196-5204
DOI:	10.1137/0913014
Popis:	In an earlier work Manteuffel and Parter discussed the role of boundary conditions in obtaining elliptic operators B so that the preconditioned operators $B_h^{ - 1} A_h $ or $A_h B_h^{ - 1} $ have uniformly bounded $L_2 $ condition number. Here A is the original elliptic operator and $A_h $ and $B_h $ are discretizations. Certain computations, mostly one-dimensional, were undertaken to illustrate and understand these results. These computational experiments provided several surprises. This current work describes those experiments and some subsequent experiments together with theoretical explanations of these surprising results. One of the main points of this report is the discussion of interaction of experimental results with the ensuing development of the theory.
Databáze:	OpenAIRE
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