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Volume 25, Issue 3
The Use of Plane Waves to Approximate Wave Propagation in Anisotropic Media

Tomi Huttunen & Peter Monk

J. Comp. Math., 25 (2007), pp. 350-367.

Published online: 2007-06

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  • Abstract

In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media (however error estimates are not yet available) and completely describe the new scheme. We then consider TM mode scattering, show how these results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.

  • Keywords

Ultra weak, Maxwell, Plane wave, Anisotropic medium.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-350, author = {Tomi Huttunen and Peter Monk}, title = {The Use of Plane Waves to Approximate Wave Propagation in Anisotropic Media}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {3}, pages = {350--367}, abstract = {

In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media (however error estimates are not yet available) and completely describe the new scheme. We then consider TM mode scattering, show how these results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8696.html} }
TY - JOUR T1 - The Use of Plane Waves to Approximate Wave Propagation in Anisotropic Media AU - Tomi Huttunen & Peter Monk JO - Journal of Computational Mathematics VL - 3 SP - 350 EP - 367 PY - 2007 DA - 2007/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8696.html KW - Ultra weak, Maxwell, Plane wave, Anisotropic medium. AB -

In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media (however error estimates are not yet available) and completely describe the new scheme. We then consider TM mode scattering, show how these results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.

Tomi Huttunen and Peter Monk. (2007). The Use of Plane Waves to Approximate Wave Propagation in Anisotropic Media. Journal of Computational Mathematics. 25 (3). 350-367. doi:
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