Maxim Pisarenco

Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures

This paper extends the area of application of the Fourier modal method (FMM) from periodic structures to aperiodic ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched layers at the lateral sides of the computational domain and reformulating the governing equations in terms of a contrast field that does not contain the incoming field. As a result of the reformulation, the homogeneous system of second-order ordinary differential equations from the original FMM becomes non-homogeneous. Its solution is derived analytically and used in the established FMM framework. The technique is demonstrated on a simple problem of planar scattering of TE-polarized light by a single rectangular line.

Efficient solution of Maxwell's equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method

The aperiodic Fourier modal method in contrast-field formulation is a numerical discretization and solution technique for solving scattering problems in electromagnetics. Typically, spectral discretization is used in the finite periodic direction and spatial discretization in the orthogonal direction. In the light of the fact that the structures of interest often have a large width-to-height ratio and that the two discretization approaches have different computational complexities, we propose exchanging the directions for spatial and spectral discretization. Moreover, if the scatterer has repeating patterns, swapping the discretization directions facilitates the reuse of previous computations. Therefore, the new method is suited for scattering from objects with a finite number of periods, such as gratings, memory arrays, metamaterials, etc. Numerical experiments demonstrate a considerable reduction of the computational costs in terms of time and memory. For a specific test case considered in this paper, the new method (based on alternative discretization) is 40 times faster and requires 100 times less memory than the method based on classical discretization.

A Numerical Method for the Solution of Time‐Harmonic Maxwell Equations for Two‐Dimensional Scatterers

The Fourier modal method (FMM) is a method for efficiently solving Maxwell equations with periodic boundary conditions. In a recent paper [1] the extension of the FMM to non‐periodic structures has been demonstrated for a simple two‐dimensional rectangular scatterer illuminated by TE‐polarized light with a wavevector normal to the third (invariant) dimension. In this paper we present a generalized version of the aperiodic Fourier modal method in contrast‐field formulation (aFMM‐CFF) which allows arbitrary profiles of the scatterer as well as arbitrary angles of incidence of light.

Efficient computation of three-dimensional flow in helically corrugated hoses including swirl

In this article we propose an e cient method to compute the friction factor of helically corrugated hoses carrying flow at high Reynolds numbers. A comparison between computations of several turbulence models is made with experimental results for corrugation sizes that fall outside the range of validity of the Moody diagram. To do this e ciently we implement quasi-periodicity. Using the appropriate boundary conditions and matching body force, we only need to simulate a single period of the corrugation to find the friction factor for fully developed flow. A second technique is introduced by the construction of an appropriately twisted wedge, which allows us to furthermore reduce the problem by a further dimension while accounting for the Beltrami symmetry that is present in the full three-dimensional problem. We make a detailed analysis of the accuracy and timesaving that this novelty introduces. We show that the swirl inside the flow, which is introduced by the helical boundary, has a positive e ect on the friction fac

Friction Factor Estimation for Turbulent Flows in Corrugated Pipes With Rough Walls

The motivation of the investigation is critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, twoequation turbulence models (k e and k w) are used in the computations. First, fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: the friction factor in a flexible corru

Compact discrepancy and chi-squared principles for over-determined inverse problems

Abstract We discuss and analyze the classical discrepancy principle and the recently proposed and closely related chi-squared principle for selecting the regularization parameter of an inverse problem. Some properties that deteriorate the performance of these methods for over-determined inverse problems are highlighted. We propose a so-called compact version of the discrepancy and chi-squared principles and demonstrate that for over-determined inverse problems the propagation of measurement uncertainty into the determination of the regularization parameter can be partly suppressed. This is achieved by expanding the cost function in terms of the singular vectors of the system matrix and by replacing the solution independent stochastic term by its statistical expectation. Although the motivation of the method requires a singular value decomposition, we show that in practice this step can be avoided. The performance of the regular and compact discrepancy and chi-squared principles is demonstrated on two benchmark problems. The compact versions of the discrepancy and chi-squared principles (i.e. with suppression of uncertainty) are shown to always improve the quality of the regularized solutions.

Near-to far-field transformation in the aperiodic Fourier modal method

This paper addresses the task of obtaining the far-field spectrum for a finite structure given the near-field calculated by the aperiodic Fourier modal method in contrast-field formulation (AFMM-CFF). The AFMM-CFF efficiently calculates the solution to Maxwells equations for a finite structure by truncating the computational domain with perfectly matched layers (PMLs). However, this limits the far-field solution to a narrow strip between the PMLs. The Greens function for layered media is used to extend the solution over the whole super- and substrate. The approach is validated by applying it to the problem of scattering from a cylinder for which the analytical solution is available. Moreover, a numerical study is conducted on the accuracy of the approximate far-field computed with the super-cell Fourier modal method by using the AFMM-CFF with near- to far-field transformation as a reference.