On round-off error for adaptive finite element methods

J. Alvarez-Aramberri; D. Pardo; Maciej Paszynski; Nathan Collier; Lisandro Dalcin; Victor M. Calo

doi:10.1016/j.procs.2012.04.162

On round-off error for adaptive finite element methods

J. Alvarez-Aramberri, D. Pardo, Maciej Paszynski, Nathan Collier, Lisandro Dalcin, Victor M. Calo

Research output: Contribution to journal › Conference article › peer-review

10 Scopus citations

Abstract

Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.

Original language	English
Pages (from-to)	1474-1483
Number of pages	10
Journal	Procedia Computer Science
Volume	9
DOIs	https://doi.org/10.1016/j.procs.2012.04.162
State	Published - 2012
Externally published	Yes
Event	12th Annual International Conference on Computational Science, ICCS 2012 - Omaha, NB, United States Duration: Jun 4 2012 → Jun 6 2012

Funding

This work has been partially supported by a Ph.D grant from University of Basque Country UPV/EHU and by the Spanish Ministry of Science and Innovation under the project MTM2010-16511. The authors wish to express their gratitude to Ion Zaballa for helpful discussions. ∗The work reported in this paper was funded by the Spanish Ministry of Science and Innovation under the project MTM2010-16511. Email address: [email protected] (J. Alvarez-Aramberria, D. Pardoa,b,∗, Maciej Paszynskic, Nathan Collierd, Lisandro Dalcine, and Victor M. Calod)

Funders	Funder number
University of Basque Country UPV
Euskal Herriko Unibertsitatea
Ministerio de Ciencia e Innovación	MTM2010-16511

Keywords

Condition number
Finite element methods (FEM)
Hp-adaptivity
Round-off error

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10.1016/j.procs.2012.04.162

Cite this

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title = "On round-off error for adaptive finite element methods",

abstract = "Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.",

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author = "J. Alvarez-Aramberri and D. Pardo and Maciej Paszynski and Nathan Collier and Lisandro Dalcin and Calo, {Victor M.}",

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AU - Alvarez-Aramberri, J.

AU - Pardo, D.

AU - Paszynski, Maciej

AU - Collier, Nathan

AU - Dalcin, Lisandro

AU - Calo, Victor M.

PY - 2012

Y1 - 2012

N2 - Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.

AB - Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.

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KW - Finite element methods (FEM)

KW - Hp-adaptivity

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T2 - 12th Annual International Conference on Computational Science, ICCS 2012

Y2 - 4 June 2012 through 6 June 2012

ER -

On round-off error for adaptive finite element methods

Abstract

Funding

Keywords

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