2,737 research outputs found
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
In this paper, we propose and study the uniaxial perfectly matched layer
(PML) method for three-dimensional time-domain electromagnetic scattering
problems, which has a great advantage over the spherical one in dealing with
problems involving anisotropic scatterers. The truncated uniaxial PML problem
is proved to be well-posed and stable, based on the Laplace transform technique
and the energy method. Moreover, the -norm and -norm error
estimates in time are given between the solutions of the original scattering
problem and the truncated PML problem, leading to the exponential convergence
of the time-domain uniaxial PML method in terms of the thickness and absorbing
parameters of the PML layer. The proof depends on the error analysis between
the EtM operators for the original scattering problem and the truncated PML
problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3)
(2020), 1918-1940).Comment: 23 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1907.0890
Adaptive Finite Element Method for Simulation of Optical Nano Structures
We discuss realization, properties and performance of the adaptive finite
element approach to the design of nano-photonic components. Central issues are
the construction of vectorial finite elements and the embedding of bounded
components into the unbounded and possibly heterogeneous exterior. We apply the
finite element method to the optimization of the design of a hollow core
photonic crystal fiber. Thereby we look at the convergence of the method and
discuss automatic and adaptive grid refinement and the performance of higher
order elements
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