Maxwell’s Equations with Impedance Boundary Conditions: Discontinuous Galerkin and Reduced Basis Methods
نویسنده
چکیده
We consider Maxwell’s equations with impedance boundary conditions on a polyhedron with polyhedral holes. Well-posedness of the variational formulation is proven and a discontinuous Galerkin (dG) approximation is introduced. We prove well-posedness of the dG problem as well as a priori error estimates. Next, we use the frequency ω as a parameter in a multi-query context. For this purpose, we derive a Reduced Basis Method (RBM) based upon the dG formulation as well as the corresponding a posteriori error bound. Numerical results indicate the efficiency and the robustness of the scheme.
منابع مشابه
Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions
In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell’s equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in ...
متن کاملThe Time-Harmonic Discontinuous Galerkin Method as a Robust Forward Solver for Microwave Imaging Applications
Novel microwave imaging systems require flexible forward solvers capable of incorporating arbitrary boundary conditions and inhomogeneous background constitutive parameters. In this work we focus on the implementation of a time-harmonic Discontinuous Galerkin Method (DGM) forward solver with a number of features that aim to benefit tomographic microwave imaging algorithms: locally varying high-...
متن کاملA domain decomposition strategy for solving time-harmonic Maxwell’s equations discretized by a discontinuous Galerkin method
A domain decomposition strategy is introduced in order to solve time-harmonic Maxwell’s equations discretized by a discontinuous Galerkin method. Its principles are explained for a 2D model problem and its efficacy is demonstrated on 2D and 3D examples.
متن کاملOptimized Schwarz Methods for Maxwell’s Equations with Non-zero Electric Conductivity
The study of optimized Schwarz methods for Maxwell’s equations started with the Helmholtz equation, see [2, 3, 4, 11]. For the rot-rot formulation of Maxwell’s equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizatio...
متن کاملOptimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials
Abstract. Simulation of electromagnetic wave propagation in metamaterials leads to more complicated time domain Maxwell’s equations than the standard Maxwell’s equations in free space. In this paper, we develop and analyze a non-dissipative discontinuous Galerkin (DG) method for solving the Maxwell’s equations in Drude metamaterials. Previous discontinuous Galerkin methods in the literature for...
متن کامل