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Iterative methods to solve the linear system

In particular, this is true for all formulations described in Sec. 2.4.3.I. Then for any of the equivalent systems of DDA equations (Eqs. 2.14, 2.18, 2.19) A is complex-symmetric if and only if 6, is complex-symmetric for all i. The latter is true for all cases except chiral and non-diagonal anisotropic absorbing materials. Moreover, when is complex-symmetric, it can be decomposed as 6, =, leading to [Pg.96]

An important consequence of this analysis is that the spectrum of A, and thus convergence should not depend significantly on the discretization. This fact was also confirmed empirically [56, 67, 68], Budko et al. [69] derived optimal value of y when using the general overrelaxation iterative method. This estimate of y is similar but always greater than Eq. [2.36], since this stationary iterative method also constructs the solution in the Krylov subspace but not in the most optimal way. [Pg.97]

To estimate the required number of iterations Nuer one can combine Eq. (2.36] with commonly used value of 10 for convergence threshold of the iterative solver  [Pg.97]

Applicability of Eq. (2.37) is illustrated by comparison with simulation data [67] in Fig. 2.1. Shown data is for nanospheres discretized with 128 dipoles per diameter however, a particular value of this parameter is not important, as discussed above. More details about these data are given in Sec. 2.6. The estimate describes well the general behavior of Niter versus A,—it is accurate within the factor of two and lies in between the two tested DDA formulations. [Pg.97]

This allows one to quickly estimate Niter for any other metal in the near-infrared using its Drude parameters. Unfortunately, the Drude model is usually inaccurate for ro cop and, hence, does not provide an accurate estimate of the wavelength position of the transitions in Fig. 2.2. If a nanoparticle is located in dielectric medium [Pg.98]


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