Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions

doi:10.1007/s10915-021-01651-4

	Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions
	Lyu, Maohui 2; Bokil, Vrushali A.1; Cheng, Yingda 4; Li, Fengyan 3
刊名	JOURNAL OF SCIENTIFIC COMPUTING
	2021-11-01
卷号	89 期号:2 页码:42
关键词	Maxwell's equations Kerr and Raman nonlinear effects Linear Lorentz Nodal discontinuous Galerkin methods Energy stable High dimensions
ISSN号	0885-7474
DOI	10.1007/s10915-021-01651-4
英文摘要	In this work, we extend the energy stable discontinuous Galerkin (DG) schemes proposed in Bokil et al. (J Comput Phys 350:420-452, 2017), for the time domain Maxwell's equations augmented with a class of nonlinear constitutive polarization laws, to higher dimensions. The nontrivial discrete temporal treatment of the nonlinearity in the ordinary differential equations that encode the Kerr and Raman effects (Bokil et al. 2017), is first generalized to higher spatial dimensions. To further improve the computational efficiency in dealing with the nonlinearity, we apply nodal DG methods in space. Energy stability is proved for the semi-discrete in time and in space schemes as well as for the fully-discrete schemes. Under some assumptions on the strength of nonlinearity, error estimates are established for the semi-discrete in space methods, and, in particular, optimal accuracy is achieved for the methods on Cartesian meshes with Q(k)-type elements and alternating fluxes. Attention is paid to the role of the nodal form of the DG discretizations in the analysis. We numerically validate the accuracy, energy stability, and computational efficiency of the proposed schemes using manufactured solutions. We further illustrate the performance of the methods through physically relevant experiments involving spatial soliton propagation and airhole scattering in realistic glasses.
资助项目	China Postdoctoral Science Foundation[2020TQ0344] ; NSFC[11871139] ; NSFC[12101597] ; NSF[DMS-1720116] ; NSF[DMS-2012882] ; NSF[DMS-1453661] ; NSF[DMS-2011838] ; NSF[DMS-1719942] ; NSF[DMS-1913072]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER/PLENUM PUBLISHERS
WOS记录号	WOS:000706173900001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59377]
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Fengyan
作者单位	1.Oregon State Univ, Coll Sci, Dept Math, Corvallis, OR 97331 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp LSEC, Beijing 100190, Peoples R China 3.Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA 4.Michigan State Univ, Dept Computat Math Sci & Engn, Dept Math, E Lansing, MI 48824 USA
推荐引用方式 GB/T 7714	Lyu, Maohui,Bokil, Vrushali A.,Cheng, Yingda,et al. Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions[J]. JOURNAL OF SCIENTIFIC COMPUTING,2021,89(2):42.
APA	Lyu, Maohui,Bokil, Vrushali A.,Cheng, Yingda,&Li, Fengyan.(2021).Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions.JOURNAL OF SCIENTIFIC COMPUTING,89(2),42.
MLA	Lyu, Maohui,et al."Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions".JOURNAL OF SCIENTIFIC COMPUTING 89.2(2021):42.