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- W2569872693 abstract "The constrained interpolation profile (CIP) method is a computational scheme for problems including different phases[1], and it provides possibilities to reduce computational resources for solving electromagnetic problems. The method is based on the upwind scheme with the profiles between two grid points, interpolated in terms of cubic polynomials which allow us to calculate fields at the next time step with good precision. However, propagating waves suffer from numerical dispersion, like other schemes. It is important to obatin the fomula of the numerical dispersion in order to estimate the precision of the computational results. In this paper, the numerical dispersion for the grid-aligned propagation, i.e. the propagation along the principal grid axes, is derived theoretically, and is then examined numerically. The comparison with the one of the finite-difference time-domain (FDTD) method is also performed. 2 Numerical dispersion relation of the CIP method 2.1 CIP method of the 3-rd order We consider a wave propagating to+x-direction with the velocity of c0. The field value is indicated by f(x;t) and the derivative is expressed as g(x;t) = @f=@x. Their discretized forms are given by f n i · f(i¢x;n¢t) and g n · g(i¢x;n¢t), where ¢x and ¢t are the spatial and temporal discretization, respectively. Therefore, the explicit form of the CIP updating scheme is given by the following equations: f n+1 i = A1f n i + A2f n ii1 + A3g n i + A4g n ii1 ;" @default.
- W2569872693 created "2017-01-13" @default.
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- W2569872693 date "2007-01-01" @default.
- W2569872693 modified "2023-09-27" @default.
- W2569872693 title "Numerical Dispersion of CIP Method for Electromagnetic Problems" @default.
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