Locating a complex inhomogeneous medium with an approximate factorization method

Calculation of flows in two-and three-dimensional nozzles by the approximate factorization method

Editorial

Parallel approximate factorization method for solving discrete elliptic equations

The performance of several approximate factorization methods, coupled with a e nite volume spatial discretization using Roe’ s approximate Riemann solver, are compared by means of numerical tests on a two-dimensional steady inviscid e ow past a blunt body at Mach numbers ranging from 5 to 20. The comparisons are carried out evaluating, by numerical experiments, the optimal Courant number of each method. The alternating direction implicit and the lower ‐upper symmetric Gauss ‐Seidel methods result in the most efe cient factorizations, in terms of CPU time. The former behaves smoothly with increasing Mach number, and its performance is not affected by the grid size. The latter may achieve higher efe ciency but is strongly dependent on the number of relaxation steps performed, requiring optimization in terms of Mach number and grid size. I. Introduction A N IMPLICIT time integration is usually required to improve convergence toward steady state in time-marching, shockcapturing methods. This requirement is particularly true for high Mach number real gas e ows where the practical stability limit of explicit methods is particularly severe. The large block banded linearized operators, resulting from the application of multistep implicitmethodsto multidimensionalstructuredgrids,aresolvedmost efe ciently by resorting to approximate factorization (AF). The implicit operator may be split along the grid directions, as in the early alternating direction implicit (ADI) schemes of Briley and McDonald 1 andBeamand Warming, 2 orintotwolower ‐upper(LU) factors, as in the original LU schemes of Steger and Warming 3 and Jameson and Turkel. 4 The ADI scheme, without the addition of an appropriate amount of numerical damping, may, however, become unstable in three dimensions when formulated in delta form. Therefore, the LU factorization has become increasingly popular, and many improvements to this technique have been proposed in recent years. 5 Yoon and Jameson, 6,7 combined the LU factoriza

Profile inversion in scattering theory: the TE case

An extension of the singular value decomposition (SVD) to multidimensional (m-D) arrays (tensors) has been proposed previously. This extension provide us with a new method for m-dimensional factorization, a 3-D example is given.

Design and optimization of a compact low-cost optical particle sizer

During physical simulation of light transport, we separate materials between conductors and dielectrics. The for-mer have a complex refractive index and are treated as opaque, the latter a real one and are treated as transparent.However, thin layers with a complex refractive index can become transparent if their thickness is small compared to the extinction coefficient. This happens with thin metallic layers, but also with many pigments that are semi-conductors: their extinction coefficient (the imaginary part of their refractive index) is close to zero for part of the visible spectrum. Spectral effects inside these thin layers (attenuation and interference) result in dramatic color changes.

The scope of the present work was to evaluate the role of the complex refractive index in optical diffusion studies for imaging purposes. In particular, phosphor materials and their corresponding optical transmission characteristics play significant role in x-ray detectors, cathode ray tubes, microscopy techniques, white LED applications and have an impact on other scientific fields including chemical, energy, optoelectronic and space industries. The complex refractive index is associated with the optical attenuation capabilities of phosphor materials, either scattering or absorption, which in turn influences their imaging characteristics. In order to examine the complex refractive index effects, a simulation model was developed by taking into account the following: (i) phosphors of different layer thickness, 100 μm (thin layer) and 200 μm (thick layer), (ii) packing density 50%, (iii) three values of light wavelengths 400, 550, and 700 nm, and (iv) particle diameter in the range 10–10 mm. The complex refractive index was considered to vary: (a) from 1.5 up to 2.0 the real part and (b) from 10−6 up to 10−4 the imaginary part. The role of the complex refractive index on the optical parameters was examined within the framework of Mie scattering theory. Optical diffusion was assessed through Monte Carlo simulation techniques and the most important conclusion of the results was the achievement of improved phosphor spatial resolution by increasing the real part of the refractive index and not the imaginary one.

This paper presents the application of a theoretically developed method that provides plasma parameter solution space information from measured RF attenuation that occurs during reentry. The purpose is to provide reentry plasma parameter information from the communication signal attenuation. The theoretical development centers around the attenuation and the complex index of refraction. The methodology uses an imaginary index of the refraction matching algorithm with a tolerance to find suitable solutions that satisfy the theory. The imaginary matching terms are then used to determine the real index of refraction resulting in the complex index of refraction. Then a filter is used to reject nonphysical solutions. Signal attenuation-based plasma parameter properties investigated include the complex index of refraction, plasma frequency, electron density, collision frequency, propagation constant, attenuation constant, phase constant, complex plasma conductivity, and electron mobility. RF plasma thickness attenuation is investigated and compared to the literature. Similar plasma thickness for a specific signal attenuation can have different plasma properties.

Galerkin Finite Element (FE) techniques for the solution of the transonic potential equation,in its quasi elliptic artificial density form are investigated with emphasis on the element choice and its consequences on the iterative solution with successive line relaxation (SLOR) and approximate factorization (ADI) methods.

As is well known, the mask in projection printing is a thin (about 1,am thick) object, composed of numerous variable domains. The various domains contain different complex refractive indices. These refractive indices form a discontinuous "mask function" ,appearing as a coefficient in the Maxwell-Material (MM) equation1 that describes the transmission of the electric field through the 3D mask domain. The right-hand side of this equation involves the gradient of the dot-product of the electric field with the gradient of the log of the refractive index. Within each feature, the refractive index is a constant. Therefore its gradient vanishes, and the resulting local MM equation is the wave equation. However, at a feature boundary (chrome-quartz, phase-i— phase-2, etc.) the complex refractive index is discontinuous, resulting in a highly singular delta-function-like coefficient. The trailing components of the field display the standard Maxwell discontinuity conditions, resulting in two very singular terms, i.e. a derivative of a delta function and a product of two delta functions. Such a source term, with such a remarkable oscillation, will be the origin of extreme instability in the numerical solution of the equations, no matter which direct solution algorithm is employed. Accordingly, the derivation of a preconditioner, namely a function which contains most of the unpleasantness of the equation times a function to be found, is absolutely essential to obtain accurate solutions in a reasonable time. Through an elaborate uniformly asymptotic scheme and scale analysis, we have derived such a preconditioner. The solution of the direct MM equation was compared with the solution using the preconditioner, and it gave us the confidence that we were on the right track. It actually means that one wishes to find the mask's Green function which, when convolved with the electric field incident on the mask, yields the exiting field which then enters the imaging optical system. It is the purpose of this paper to demonstrate the results obtained thus far, as well as to illustrate its implications on defocus linewidth control.

Compositional dependence of the optical parameters of Ge xSb 40− xSe 60 glasses

Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

This article represents an analytical formulation for optical properties of absorbing metallic nanoparticles in visible region of electromagnetic spectrum based on Mie theory, in order to find a clear relationship between fundamental characteristics of nanoparticles with their spectral behavior and color coordinate in CIELAB color space. Calculations were performed on nanoparticles with various diameters (d = 50, 100, and 200 nm), as well as complex refractive index with different real (n = 1.5, 2.0, 2.5, and 3.0) and imaginary (k = 0.001 and 0.1) parts. Obtained results reveal that scattering phenomena in nanoparticles are strongly linked to the particle size parameter and complex index of refraction. The results indicate that the reflectance and lightness (L*) of nanoparticles increases as a result of increase in their size and real part of complex refractive index and decrease with increasing the imaginary part of complex refractive index. The CIELAB colorimetric system was used for analysis the color of nanoparticles. According to obtained results, all nanoparticles have greenish‐blue color, and undergo color change as a result of varying in their size and the complex refractive index. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 477–483, 2016