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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations


Authors: S. C. Brenner, J. Cui, Z. Nan and L.-Y. Sung
Journal: Math. Comp. 81 (2012), 643-659
MSC (2010): Primary 65N30, 65N15, 35Q60
Published electronically: August 30, 2011
MathSciNet review: 2869031
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Abstract: We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a $ P_1$ finite element method.


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Additional Information

S. C. Brenner
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: brenner@math.lsu.edu

J. Cui
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Address at time of publication: Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455
Email: jcui@ima.umn.edu

Z. Nan
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: zhenan@math.lsu.edu

L.-Y. Sung
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sung@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02540-8
PII: S 0025-5718(2011)02540-8
Keywords: Maxwell’s equations, Hodge decomposition, finite element
Received by editor(s): January 11, 2010
Received by editor(s) in revised form: March 1, 2011
Published electronically: August 30, 2011
Additional Notes: This work was supported in part by the National Science Foundation under Grant Nos. DMS-07-13835 and DMS-10-16332, and by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.
Article copyright: © Copyright 2011 American Mathematical Society