Accuracy measures and fourier analysis for the full multigrid algorithm

Carmen Rodrigo; Francisco J. Gaspar; Cornelis W. Oosterlee; Irad Yavneh

doi:10.1137/100786101

Accuracy measures and fourier analysis for the full multigrid algorithm

Carmen Rodrigo^*
, Francisco J. Gaspar
, Cornelis W. Oosterlee
, Irad Yavneh

^*Corresponding author for this work

Centro Universitario de la Defensa, Zaragoza
University of Zaragoza
extern
Technion-Israel Institute of Technology

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted E^l _FMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating E^l_FMG, and the resulting estimates are confirmed by numerical tests.

Original language	English
Pages (from-to)	3108-3129
Number of pages	22
Journal	SIAM Journal on Scientific Computing
Volume	32
Issue number	5
DOIs	https://doi.org/10.1137/100786101
Publication status	Published - 2010
Externally published	Yes

Keywords

Discretization error
FMG measure
Full multigrid algorithm
Local Fourier analysis

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10.1137/100786101

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title = "Accuracy measures and fourier analysis for the full multigrid algorithm",

abstract = "The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted El FMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating ElFMG, and the resulting estimates are confirmed by numerical tests.",

keywords = "Discretization error, FMG measure, Full multigrid algorithm, Local Fourier analysis",

author = "Carmen Rodrigo and Gaspar, \{Francisco J.\} and Oosterlee, \{Cornelis W.\} and Irad Yavneh",

year = "2010",

doi = "10.1137/100786101",

language = "English",

volume = "32",

pages = "3108--3129",

journal = "SIAM Journal on Scientific Computing",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - Accuracy measures and fourier analysis for the full multigrid algorithm

AU - Rodrigo, Carmen

AU - Gaspar, Francisco J.

AU - Oosterlee, Cornelis W.

AU - Yavneh, Irad

PY - 2010

Y1 - 2010

N2 - The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted El FMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating ElFMG, and the resulting estimates are confirmed by numerical tests.

AB - The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted El FMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating ElFMG, and the resulting estimates are confirmed by numerical tests.

KW - Discretization error

KW - FMG measure

KW - Full multigrid algorithm

KW - Local Fourier analysis

UR - https://www.scopus.com/pages/publications/78149339708

U2 - 10.1137/100786101

DO - 10.1137/100786101

M3 - Article

AN - SCOPUS:78149339708

SN - 1064-8275

VL - 32

SP - 3108

EP - 3129

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 5

ER -

Accuracy measures and fourier analysis for the full multigrid algorithm

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Keywords

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