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A Galerkin approximation for integro-differential equations in electromagnetic scattering from a chiral medium |
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| Authors: | Dinh-Liem Nguyen Thanh-Nhan Nguyen Minh-Phuong Tran |
| Institution: | 1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA.dlnguyen@umich.edu;3. Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam.;4. Department of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam. |
| Abstract: | We consider the scattering of time-harmonic electromagnetic waves from a chiral medium. It is known for the Drude–Born–Fedorov model that the forward scattering problem can be described by an integro-differential equation. In this paper we study a Galerkin finite element approximation for this integro-differential equation. Our Galerkin scheme, which relies on a suitable periodization of the integral equation, enables the use of the fast Fourier transform and a simple numerical implementation. We establish a quasi-optimal convergence analysis for the Galerkin method. Explicit formulas for the discrete scheme are also provided. |
| Keywords: | Chiral media electromagnetic scattering numerical analysis integral equations Galerkin approximations Drude–Born–Fedorov model |