Accurate solution-adaptive finite difference schemes for coarse and fine grids

Viktor Linders; Mark H. Carpenter; Jan Nordström

doi:10.1016/j.jcp.2020.109393

Accurate solution-adaptive finite difference schemes for coarse and fine grids

Viktor Linders, Mark H. Carpenter, Jan Nordström

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

2 Citations (Scopus)

Abstract

We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

Original language	English
Article number	109393
Journal	Journal of Computational Physics
Volume	410
DOIs	https://doi.org/10.1016/j.jcp.2020.109393
Publication status	Published - 1 Jun 2020
Externally published	Yes

Keywords

Accuracy
Adaptivity
Convergence
Dispersion relation preserving
Finite differences
Least squares

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2020.109393

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abstract = "We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.",

keywords = "Accuracy, Adaptivity, Convergence, Dispersion relation preserving, Finite differences, Least squares",

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AU - Carpenter, Mark H.

AU - Nordström, Jan

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N2 - We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

AB - We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

KW - Accuracy

KW - Adaptivity

KW - Convergence

KW - Dispersion relation preserving

KW - Finite differences

KW - Least squares

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JO - Journal of Computational Physics

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ER -

Accurate solution-adaptive finite difference schemes for coarse and fine grids

Abstract

Keywords

ASJC Scopus subject areas

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