A novel model order reduction framework via staggered reduced basis space-time finite elements in linear first order transient systems

R. Deokar, K. K. Tamma

Research output: Research - peer-reviewArticle

Abstract

A novel model order reduction framework for space and time domain discretizations is proposed. Iterative convergence of a Galerkin approximation in space and a Least Squares Petrov Galerkin approximation in time is obtained through a staggered reduced basis method in space-time. In every iteration, one of the two domains (space or time) is refined; and the other is reduced and a posteriori error indicators in space and time are used to drive the convergence iterations. Numerical results for 2D heat transfer and convection-diffusion problems demonstrate the significant computational efficiency of the proposed methodology. Comparisons of wall-clock times and solution accuracy with traditional time integration algorithms has been presented to validate the efficacy of the proposed framework and demonstrate computational savings of an order of magnitude.

LanguageEnglish (US)
Pages991-1005
Number of pages15
JournalInternational Journal of Heat and Mass Transfer
Volume117
DOIs
StatePublished - Feb 1 2018

Fingerprint

Heat convection
Computational efficiency
Clocks
Heat transfer
iteration
approximation
clocks
convection
heat transfer
methodology

Keywords

  • A posteriori error estimation
  • Computational thermal/fluid dynamics
  • Proper orthogonal decomposition
  • Space-time discretization
  • Space-time finite elements

Cite this

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title = "A novel model order reduction framework via staggered reduced basis space-time finite elements in linear first order transient systems",
abstract = "A novel model order reduction framework for space and time domain discretizations is proposed. Iterative convergence of a Galerkin approximation in space and a Least Squares Petrov Galerkin approximation in time is obtained through a staggered reduced basis method in space-time. In every iteration, one of the two domains (space or time) is refined; and the other is reduced and a posteriori error indicators in space and time are used to drive the convergence iterations. Numerical results for 2D heat transfer and convection-diffusion problems demonstrate the significant computational efficiency of the proposed methodology. Comparisons of wall-clock times and solution accuracy with traditional time integration algorithms has been presented to validate the efficacy of the proposed framework and demonstrate computational savings of an order of magnitude.",
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AB - A novel model order reduction framework for space and time domain discretizations is proposed. Iterative convergence of a Galerkin approximation in space and a Least Squares Petrov Galerkin approximation in time is obtained through a staggered reduced basis method in space-time. In every iteration, one of the two domains (space or time) is refined; and the other is reduced and a posteriori error indicators in space and time are used to drive the convergence iterations. Numerical results for 2D heat transfer and convection-diffusion problems demonstrate the significant computational efficiency of the proposed methodology. Comparisons of wall-clock times and solution accuracy with traditional time integration algorithms has been presented to validate the efficacy of the proposed framework and demonstrate computational savings of an order of magnitude.

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