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Our approach is based on the combination of two powerful numerical methods, the spectral domain decomposition method and the Laplace transform method.
In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion.
Alternative variants of direct methods are the collocation methods, the spectral or pseudo-spectral methods, the probabilistic approaches, etc.
One key observation is that among the proposed methods, the spectral efficiency is maximized by FTN signaling.
Among all this wide range of methods, the spectral subtraction-based algorithm is known for its simplicity in implementation, high power in eliminating noise, and high speed.
Hence, utilizing the proposed methods, the spectral efficiency will increase more than 1% rather than other spectral efficient DCS-based approaches.
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Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented.
In the cases where the simple methods prevail, the spectral methods do not fall far behind.
Additionally, we have described two numerical methods, the finite-difference method and the spectral method, that can be used to solve different diffusion equations that arise in the computation of AFS.
Here, by using the FPI-based measurement method, the spectral dynamics of the random fibre laser just above threshold are revealed for the first time.
In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com