Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/150429
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dc.contributor.authorHuang, Canen_US
dc.contributor.authorWang, Li-Lianen_US
dc.date.accessioned2021-06-04T08:20:11Z-
dc.date.available2021-06-04T08:20:11Z-
dc.date.issued2019-
dc.identifier.citationHuang, C. & Wang, L. (2019). An accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media. Advances in Computational Mathematics, 45(2), 707-734. https://dx.doi.org/10.1007/s10444-018-9636-2en_US
dc.identifier.issn1019-7168en_US
dc.identifier.urihttps://hdl.handle.net/10356/150429-
dc.description.abstractIn this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media in two-dimensional setting. Our starting point is to derive a new model involving only one unknown field from the original model with three unknown fields: electric, magnetic fields, and the induced electric polarization (described by a global temporal convolution of the electric field). This results in a second-order integral-differential equation with a weakly singular integral kernel expressed by the Mittag-Lefler (ML) function. The most interesting but challenging issue resides in how to efficiently deal with the singularity in time induced by the ML function which is an infinite series of singular power functions with different nature. With this in mind, we introduce a spectral-Galerkin method using Fourier-like basis functions for spatial discretization, leading to a sequence of decoupled temporal integral-differential equations (IDE) with the same weakly singular kernel involving the ML function as the original two-dimensional problem. With a careful study of the regularity of IDE, we incorporate several leading singular terms into the numerical scheme and approximate much regular part of the solution. Then, we solve the IDE by a multi-step well-conditioned collocation scheme together with mapping technique to increase the accuracy and enhance the resolution. We show that such an enriched collocation method is convergent and accurate.en_US
dc.description.sponsorshipMinistry of Education (MOE)en_US
dc.language.isoenen_US
dc.relationRG 15/12en_US
dc.relationMOE2017-T2-2-014en_US
dc.relationMOE2018-T2-1-059en_US
dc.relation.ispartofAdvances in Computational Mathematicsen_US
dc.rights© 2018 Springer Science Business Media, LLC, part of Springer Nature. All rights reserved.en_US
dc.subjectScience::Mathematicsen_US
dc.titleAn accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive mediaen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.identifier.doi10.1007/s10444-018-9636-2-
dc.identifier.scopus2-s2.0-85053799357-
dc.identifier.issue2en_US
dc.identifier.volume45en_US
dc.identifier.spage707en_US
dc.identifier.epage734en_US
dc.subject.keywordsCole-Cole Mediaen_US
dc.subject.keywordsDispersiveen_US
dc.description.acknowledgementThe research of author Can Huang is supported by the National Natural Science Foundation of China (no. 11401500, 91630204, 11771363). The research of author Li-Lian Wang is partially supported by Singapore MOE AcRF Tier 1 Grant (RG 15/12) and Singapore MOE AcRF Tier 2 Grants (MOE2017-T2-2-014 and MOE2018-T2-1-059).en_US
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