Author | dc.contributor.author | Navarrete Michelini, Pablo | |
Author | dc.contributor.author | Coyle, Edward J. | es_CL |
Admission date | dc.date.accessioned | 2010-01-06T13:34:36Z | |
Available date | dc.date.available | 2010-01-06T13:34:36Z | |
Publication date | dc.date.issued | 2008-03 | |
Cita de ítem | dc.identifier.citation | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Vol.: 15, Issue: 2-3, p.: 219-247, MAR-APR, 2008 | en_US |
Identifier | dc.identifier.issn | 1070-5325 | |
Identifier | dc.identifier.uri | https://repositorio.uchile.cl/handle/2250/125038 | |
Abstract | dc.description.abstract | We study the effect of inter-grid operators—the interpolation and restriction operators—on the convergence
of two-grid algorithms for linear models. We show how a modal analysis of linear systems, along with
some assumptions on the normal modes of the system, allows us to understand the role of inter-grid
operators in the speed and accuracy of a full-multigrid step.
We state an assumption that generalizes local Fourier analysis (LFA) by means of a precise description
of aliasing effects on the system. This assumption condenses, in a single algebraic property called the
harmonic aliasing property, all the information needed from the geometry of the discretization and the
structure of the system’s eigenvectors. We first state a harmonic aliasing property based on the standard
coarsening strategies of 1D problems. Then, we extend this property to a more aggressive coarsening
typically used in 2D problems with the help of additional assumptions on the structure of the system
matrix.
Under our general assumptions, we determine the exact rates at which groups of modal components
of the error evolve and interact. With this knowledge, we are then able to design inter-grid operators
that optimize the two-grid algorithm convergence. By different choices of operators, we verify the classic
heuristics based on Fourier harmonic analysis, show a trade-off between the rate of convergence and the
number of computations required per iteration, and show how our analysis differs from LFA. | en_US |
Lenguage | dc.language.iso | en | en_US |
Publisher | dc.publisher | JOHN WILEY & SONS LTD | en_US |
Keywords | dc.subject | multigrid algorithms | en_US |
Título | dc.title | A semi-algebraic approach that enables the design of inter-grid operators to optimize multigrid convergence | en_US |
Document type | dc.type | Artículo de revista | |