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In this paper, an approach combining the DG method in space with CG method in time (CG-DG method) is developed to solve time-dependent Maxwell's equations when meta-materials are involved. Both the unconditional L2-stability and error estimate of order are obtained when polynomials of degree at most r is used for the temporal discretization and at most k for the spatial discretization. Numerical results in 3D are given to validate the theoretical results.

An implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell’s equations in metamaterials. The Maxwell’s equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most p is used for spatial approximation, our scheme is verified to converge at a rate of O(τ2+hp+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

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Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

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2 results

Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials