KMS Of Academy of mathematics and systems sciences, CAS
| Energy Stable Nodal Discontinuous Galerkin Methods for Nonlinear Maxwell's Equations in Multi-dimensions | |
| Lyu, Maohui1; Bokil, Vrushali A.2; Cheng, Yingda3; Li, Fengyan4 | |
| 2021-11-01 | |
| Source Publication | JOURNAL OF SCIENTIFIC COMPUTING
 |
| ISSN | 0885-7474 |
| Volume | 89Issue:2Pages:42 |
| Abstract | 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. |
| Keyword | Maxwell's equations Kerr and Raman nonlinear effects Linear Lorentz Nodal discontinuous Galerkin methods Energy stable High dimensions |
| DOI | 10.1007/s10915-021-01651-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000706173900001 |
| Publisher | SPRINGER/PLENUM PUBLISHERS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59378 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Li, Fengyan |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp LSEC, Beijing 100190, Peoples R China 2.Oregon State Univ, Coll Sci, Dept Math, Corvallis, OR 97331 USA 3.Michigan State Univ, Dept Computat Math Sci & Engn, Dept Math, E Lansing, MI 48824 USA 4.Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA |
| Recommended Citation 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. |
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