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Autori principali: Dai, Ruiyang, Després, Bruno
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2405.07811
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author Dai, Ruiyang
Després, Bruno
author_facet Dai, Ruiyang
Després, Bruno
contents We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of the infinite moment linear system looses the skew-symmetry property with respect to the Gram matrix. Then we propose an original closed formula for the scalar product of any pair of asymmetric basis functions. It makes possible the construction of two simple modifications of the linear systems which recover the skew-symmetry property. By construction the new methods are quadratically stable with respect to the natural $L^2$ norm. We explain how to generalize to other transport equations encountered in numerical plasma physics. Basic numerical tests with oscillating electric fields of different nature illustrate the unconditional stability properties of our algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2405_07811
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the quadratic stability of asymmetric Hermite basis with application to plasma physics with oscillating electric field
Dai, Ruiyang
Després, Bruno
Numerical Analysis
We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of the infinite moment linear system looses the skew-symmetry property with respect to the Gram matrix. Then we propose an original closed formula for the scalar product of any pair of asymmetric basis functions. It makes possible the construction of two simple modifications of the linear systems which recover the skew-symmetry property. By construction the new methods are quadratically stable with respect to the natural $L^2$ norm. We explain how to generalize to other transport equations encountered in numerical plasma physics. Basic numerical tests with oscillating electric fields of different nature illustrate the unconditional stability properties of our algorithms.
title On the quadratic stability of asymmetric Hermite basis with application to plasma physics with oscillating electric field
topic Numerical Analysis
url https://arxiv.org/abs/2405.07811