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Volume 32, Issue 5
Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem

Tian Luan, Fuming Ma & Minghui Liu

DOI: 10.4208/jcm.1403-m4404

J. Comp. Math., 32 (2014), pp. 491-506.

Published online: 2014-10

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  • Abstract

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.

  • Keywords

Helmholtz equation, Ultra weak variational formulation, Plane wave function, Evanescent wave function, Absorbing boundary condition.

  • AMS Subject Headings

65N12, 65N55.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-491, author = {Tian Luan, Fuming Ma and Minghui Liu}, title = {Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {5}, pages = {491--506}, abstract = {

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1403-m4404}, url = {http://global-sci.org/intro/article_detail/jcm/9900.html} }
TY - JOUR T1 - Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem AU - Tian Luan, Fuming Ma & Minghui Liu JO - Journal of Computational Mathematics VL - 5 SP - 491 EP - 506 PY - 2014 DA - 2014/10 SN - 32 DO - http://doi.org/10.4208/jcm.1403-m4404 UR - https://global-sci.org/intro/article_detail/jcm/9900.html KW - Helmholtz equation, Ultra weak variational formulation, Plane wave function, Evanescent wave function, Absorbing boundary condition. AB -

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.

Tian Luan, Fuming Ma and Minghui Liu. (2014). Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem. Journal of Computational Mathematics. 32 (5). 491-506. doi:10.4208/jcm.1403-m4404
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