Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.

Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy cons...

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Autores principales:	Xiuling Yin, Yanqin Liu, Jingjing Zhang, Yanfeng Shen, Limei Yan
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/4379092b710d4cc69d720f677a797648
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spelling	oai:doaj.org-article:4379092b710d4cc69d720f677a7976482021-12-02T20:17:31ZExponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.1932-620310.1371/journal.pone.0256108https://doaj.org/article/4379092b710d4cc69d720f677a7976482021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0256108https://doaj.org/toc/1932-6203Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.Xiuling YinYanqin LiuJingjing ZhangYanfeng ShenLimei YanPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 8, p e0256108 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Xiuling Yin Yanqin Liu Jingjing Zhang Yanfeng Shen Limei Yan Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
description	Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.
format	article
author	Xiuling Yin Yanqin Liu Jingjing Zhang Yanfeng Shen Limei Yan
author_facet	Xiuling Yin Yanqin Liu Jingjing Zhang Yanfeng Shen Limei Yan
author_sort	Xiuling Yin
title	Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
title_short	Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
title_full	Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
title_fullStr	Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
title_full_unstemmed	Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.
title_sort	exponentially fitted multisymplectic scheme for conservative maxwell equations with oscillary solutions.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/4379092b710d4cc69d720f677a797648
work_keys_str_mv	AT xiulingyin exponentiallyfittedmultisymplecticschemeforconservativemaxwellequationswithoscillarysolutions AT yanqinliu exponentiallyfittedmultisymplecticschemeforconservativemaxwellequationswithoscillarysolutions AT jingjingzhang exponentiallyfittedmultisymplecticschemeforconservativemaxwellequationswithoscillarysolutions AT yanfengshen exponentiallyfittedmultisymplecticschemeforconservativemaxwellequationswithoscillarysolutions AT limeiyan exponentiallyfittedmultisymplecticschemeforconservativemaxwellequationswithoscillarysolutions
_version_	1718374340570906624

Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions.

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