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            <title xml:lang="en">Improving Yee's scheme with asymptotic dispersion correction for time-harmonic Maxwell's equations</title>
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              <p>In this paper, we show how to reduce the dispersion error associated to Yee's nite dierence scheme applied to time-harmonic Maxwell's equations in one, two and three spatial dimensions. Our method, called asymptotic dispersion correction, is based on the introduction of a shifted angular frequency depending on a free parameter in the Yee stencil. The optimal parameter, called the asymptotically optimal shift, is next explicitly determined by minimizing the dispersion error for small enough meshsize or, equivalently, for large enough number of grid points per wavelength. Numerical experiments are provided and show that the relative error is reduced when using the optimal shifted angular frequency as soon as the number of grid points per wavelength is large enough.</p>
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