Please use this identifier to cite or link to this item:
https://hdl.handle.net/10356/159512
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chu, Van Tiep | en_US |
dc.contributor.author | Hoang, Viet Ha | en_US |
dc.date.accessioned | 2022-06-27T02:24:57Z | - |
dc.date.available | 2022-06-27T02:24:57Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Chu, V. T. & Hoang, V. H. (2020). High dimensional finite elements for two-scale Maxwell wave equations. Journal of Computational and Applied Mathematics, 375, 112756-. https://dx.doi.org/10.1016/j.cam.2020.112756 | en_US |
dc.identifier.issn | 0377-0427 | en_US |
dc.identifier.uri | https://hdl.handle.net/10356/159512 | - |
dc.description.abstract | We develop an essentially optimal numerical method for solving two-scale Maxwell wave equations in a domain D⊂Rd. The problems depend on two scales: one macroscopic scale and one microscopic scale. Solving the macroscopic two-scale homogenized problem, we obtain the desired macroscopic and microscopic information. This problem depends on two variables in Rd, one for each scale that the original two-scale equation depends on, and is thus posed in a high dimensional tensorized domain. The straightforward full tensor product finite element (FE) method is exceedingly expensive. We develop the sparse tensor product FEs that solve this two-scale homogenized problem with essentially optimal number of degrees of freedom, i.e. the number of degrees of freedom differs by only a logarithmic multiplying factor from that required for solving a macroscopic problem in a domain in Rd only, for obtaining a required level of accuracy. Numerical correctors are constructed from the FE solution. We derive a rate of convergence for the numerical corrector in terms of the microscopic scale and the FE mesh width. Numerical examples confirm our analysis. | en_US |
dc.description.sponsorship | Ministry of Education (MOE) | en_US |
dc.language.iso | en | en_US |
dc.relation | MOE2017-T2-2-144 | en_US |
dc.relation.ispartof | Journal of Computational and Applied Mathematics | en_US |
dc.rights | © 2020 Elsevier B.V. All rights reserved. | en_US |
dc.subject | Science::Mathematics | en_US |
dc.title | High dimensional finite elements for two-scale Maxwell wave equations | en_US |
dc.type | Journal Article | en |
dc.contributor.school | School of Physical and Mathematical Sciences | en_US |
dc.identifier.doi | 10.1016/j.cam.2020.112756 | - |
dc.identifier.scopus | 2-s2.0-85079842855 | - |
dc.identifier.volume | 375 | en_US |
dc.identifier.spage | 112756 | en_US |
dc.subject.keywords | High Dimension | en_US |
dc.subject.keywords | Optimal Complexity | en_US |
dc.description.acknowledgement | The authors gratefully acknowledge the Tier 2 grant MOE2017-T2-2-144 awarded by the Singapore Ministry of Education. | en_US |
item.fulltext | No Fulltext | - |
item.grantfulltext | none | - |
Appears in Collections: | SPMS Journal Articles |
SCOPUSTM
Citations
50
4
Updated on Mar 26, 2024
Web of ScienceTM
Citations
50
3
Updated on Oct 24, 2023
Page view(s)
76
Updated on Mar 28, 2024
Google ScholarTM
Check
Altmetric
Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.