Accurate solution-adaptive finite difference schemes for coarse and fine grids
(2020) In Journal of Computational Physics 410.- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e5c4d288-9715-4b5e-8b4b-6571fd250962
- author
- Linders, Viktor LU ; Carpenter, Mark H. and Nordström, Jan
- organization
- publishing date
- 2020-06
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Accuracy, Adaptivity, Convergence, Dispersion relation preserving, Finite differences, Least squares
- in
- Journal of Computational Physics
- volume
- 410
- article number
- 109393
- publisher
- Elsevier
- external identifiers
-
- scopus:85082597886
- ISSN
- 0021-9991
- DOI
- 10.1016/j.jcp.2020.109393
- language
- English
- LU publication?
- yes
- id
- e5c4d288-9715-4b5e-8b4b-6571fd250962
- date added to LUP
- 2020-04-15 16:51:56
- date last changed
- 2023-04-10 12:44:13
@article{e5c4d288-9715-4b5e-8b4b-6571fd250962,
abstract = {{<p>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.</p>}},
author = {{Linders, Viktor and Carpenter, Mark H. and Nordström, Jan}},
issn = {{0021-9991}},
keywords = {{Accuracy; Adaptivity; Convergence; Dispersion relation preserving; Finite differences; Least squares}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Journal of Computational Physics}},
title = {{Accurate solution-adaptive finite difference schemes for coarse and fine grids}},
url = {{http://dx.doi.org/10.1016/j.jcp.2020.109393}},
doi = {{10.1016/j.jcp.2020.109393}},
volume = {{410}},
year = {{2020}},
}