Do you want to publish a course? Click here

3D periodic dielectric composite homogenization based on the Generalized Source Method

289   0   0.0 ( 0 )
 Added by Alexey Shcherbakov
 Publication date 2015
  fields Physics
and research's language is English




Ask ChatGPT about the research

The article encloses a new Fourier space method for rigorous optical simulation of 3D periodic dielectric structures. The method relies upon rigorous solution of Maxwells equations in complex composite structures by the Generalized Source Method. Extremely fast GPU enabled calculations provide a possibility for an efficient search of eigenmodes in 3D periodic complex structures on the basis of rigorously obtained resonant electromagnetic response. The method is applied to the homogenization problem demonstrating a complete anisotropic dielectric tensor retrieval.

rate research

Read More

In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to Vainikko (2000), to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed Generalized Source Method in the curvilinear coordinates, which has theoretical $Oleft(Nlog Nright)$ asymptotic numerical complexity, a new method formulation is developed for gratings with sharp edges. It is shown that corrugation corners can be treated as effective medium interfaces within the rationale of the method. Moreover, the given formulation is demonstrated to allow for application of the same derivation as one used in classical electrodynamics to derive the interface conditions. This yields continuous combinations of the fields and metric tensor components, which can be directly Fourier factorized. Together with an efficient algorithm the new formulation is demonstrated to substantially increase the computation accuracy for given computer resources.
The moment-of-fluid method (MOF) is an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). In MOF reconstruction, the optimized normal vector is determined from the reference centroid and the volume fraction by iteration. The state-of-art work by citet{milcent_moment--fluid_2020} proposed an analytic gradient of the objective function, which greatly reduces the computational cost. In this study, we further accelerate the MOF reconstruction algorithm by using Gauss-Newton iteration instead of Broyden-Fletcher-Goldfarb-Shanno (BFGS) iteration. We also propose an improved initial guess for MOF reconstruction, which improves the efficiency and the robustness of the MOF reconstruction algorithm. Our implementation of the code and test cases are available on our Github repository.
In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes equations and nonlinear convection-diffusion equations from the GLBM, and show that from mathematical point of view, these four analysis methods are equivalent to each other. Finally, we give some elements that are needed in the implementation of the GLBM, and also find that some available LB models can be obtained from this GLBM.
80 - Suchuan Dong , Naxian Ni 2020
We present a simple and effective method for representing periodic functions and enforcing exactly the periodic boundary conditions for solving differential equations with deep neural networks (DNN). The method stems from some simple properties about function compositions involving periodic functions. It essentially composes a DNN-represented arbitrary function with a set of independent periodic functions with adjustable (training) parameters. We distinguish two types of periodic conditions: those imposing the periodicity requirement on the function and all its derivatives (to infinite order), and those imposing periodicity on the function and its derivatives up to a finite order $k$ ($kgeqslant 0$). The former will be referred to as $C^{infty}$ periodic conditions, and the latter $C^{k}$ periodic conditions. We define operations that constitute a $C^{infty}$ periodic layer and a $C^k$ periodic layer (for any $kgeqslant 0$). A deep neural network with a $C^{infty}$ (or $C^k$) periodic layer incorporated as the second layer automatically and exactly satisfies the $C^{infty}$ (or $C^k$) periodic conditions. We present extensive numerical experiments on ordinary and partial differential equations with $C^{infty}$ and $C^k$ periodic boundary conditions to verify and demonstrate that the proposed method indeed enforces exactly, to the machine accuracy, the periodicity for the DNN solution and its derivatives.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا