Spectral Iteration Technique Research Articles

On the Generalized Fick’s and Fourier’s Laws for an Unsteady Casson-Williamson Fluids Over a Stretching Surface: A Spectral Approach

In this comparative examination, the paradox of mass diffusion and heat conduction on the improved surface of weakly hydromagnetic and unsteady fluid flow is examined. Material relaxation time is believed to be one of the contributing factors militating against an effective heat and mass transfer. This flow process is estimated to predict accurately the fluids enhancement and condensation/evaporation properties. With a workable similarity variable, the formulated model of modified Fick’s and Fourier’s laws assumed in the Riga surface-induced flow conveying Casson-Williamson fluids with variable transport properties are transformed to the systems of ordinary differential equations. The spectral iterative technique (SLLM in particular), thus employed to analyze the flow distributions and ascertain the validity of the obtained results. However, cohesion force between the fluid particle establishes abnormalities of both Fick’s and Fourier’s laws indicating that extra time will be required for effective mass and heat convection to the immediate environment. Generalized heat flux parameter minimizes the fluid temperature and accelerated the nanoparticle concentration, relative minimization of the fluid temperature resulted to much more nanoparticle concentration. Moreover, Williamson fluid demonstrated a higher conductivity/diffusivity capacity in constract to the Casson fluid. When compared to Casson fluid, the modified Hartman number has a stronger influence on Williamson fluid.

Wiener-Hopf Analysis of Plane Wave Diffraction by an Impedance Strip Attached on a Perfectly Conducting Half-Plane

In this article, diffraction of a plane wave by an impedance strip on a perfectly conducting half-plane, which represents a metallic half-plane with a material coating near its edge, is investigated rigorously. In order to obtain an analytical solution to such a problem, where the lateral boundary conditions are different in the three-part mixed boundary-value problem, the Fourier transform and spectral iteration technique is applied. The diffracted field is analyzed numerically with respect to the surface impedance of the strip and the strip width. The results are illustrated graphically.

IMPROVED SPECTRAL ITERATION TECHNIQUE FOR THE SCATTERING BY THIN METAL PLATES

The problem of electromagnetic scattering by thin metal plates is formulated in terms of Electric Field Integral Equation and solved by an improved form of the Spectral Iteration Technique. The local solution at the edges of the plate is chosen as initial guess for the unknown surface current in order to guarantee and enhance the convergence of the iterative scheme. Numerical simulations on a square conducting plate are presented to validate the proposed approach.

Detection of small cracks and cavities using laser diffraction

A good knowledge of the evolution process of a crack or cavity is necessary for a better understanding the mechanical behavior of the damage and failure of materials and structural components. Before damage begins, the size of the initial or prescribed cracks and cavities are usually very small. These small cracks and cavities can be conveniently used as the diffraction apertures of the coherent light. By analyzing the diffraction fields, the characteristic parameters of these special diffraction apertures can be obtained and, hence, the deformation fields. Experimental tests are conducted to demonstrate the reliability and accuracy of the laser diffraction technique in detecting the evolution and propagation of a small crack or cavity. The relationships between the coherent diffraction patterns and the crack and cavity geometric parameters are established for the simple shape of the crack or cavity aperture. Moreover, the autocorrelative method and the spectral iterative technique are introduced to retrieve the small crack and cavity apertures for the complex shapes.

Diffraction of Obliquely Incident Plane Waves by Resistive and Conductive Planar Surfaces

The multiple diffraction of obliquely incident plane waves by the three-part resistive and conductive plane is evaluated via uniform asymptotic high frequency analysis. This analysis is based on a spectral iteration technique consisting of employing the Fourier Integral representation of the diffracted field through the solution of a pair of uncoupled Wiener-Hopf equations. By studying these equations iteratively, the double and triple diffracted fields are obtained through the saddle-point technique. Some numerical examples are also presented.

Electromagnetic scattering problems solved by an improved spectral iteration technique

Electromagnetic scattering problems solved by an improved spectral iteration technique

Electromagnetic scattering problems solved by an improved spectral iteration technique

AbstractThe spectral iteration technique is used to solve electromagnetic scattering problems. A detailed analysis is carried out to investigate the convergence properties of the procedure, and a static solution is proposed as an initial estimate of the current to solve divergence problems. Diffraction by strips is considered to validate the method. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 384–388, 2001.

A spectral iterative domain decomposition technique for the incompressible Navier–Stokes equations

An efficient iterative domain decomposition technique associated with high order spectral methods is described for the resolution of the incompressible Navier–Stokes equations. This corresponds to an extension of the patching-collocation approach proposed by Zanolli (1987) for linear problems, and based on a relaxation parameter. Particular attention is focused on its efficiency for Neumann boundary conditions, as in the pressure Poisson equation. In such a case, it is shown that the convergence of the solution can be obtained after a limited number of internal iterations. Moreover, the present procedure is efficient in parallel computing. Applications to the prediction of the Hopf bifurcation occurring in a tall differentially heated cavity are presented for a low-Prandtl number fluid.

An Improved Form of the Spectral Iteration Technique

An iterative approach to the solution of the first kind integral equations arising in electromagnetic scattering problems is considered. The analysis is carried out in the spectral domain, where integral equations can be transformed into algebraic equations, suitable for easy manipulations on computers. The proposed iteration scheme assumes the static solution as initial estimate of the unknown current distribution on the scatterer. With this choice, the procedure is guaranteed not to diverge and the convergence is significantly enhanced. As a matter of fact, static solution enforces the correct edge behaviour solving the Electric Field Integral Equation (EFIE) with respect to the regular part of the current density. Diffraction by strips of both small and large dimensions (compared to the wavelength) is considered as illustrative example of the method. The procedure is applicable to more complex structures like printed circuits on stratified dielectric support, where the Green's function is known in the spectral domain.

Plane-wave diffraction by a two-part impedance strip

A uniform asymptotic high-frequency solution is developed for the diffraction of (E-polarised) electromagnetic plane waves by a two-part impedance strip. Uniform expressions for the interactions up to third order between the edges of the strip, including the conversion of surface-wave fields into space-wave fields, and vice-versa, via edge or junction diffraction, are obtained. The solution is based on a spectral iteration technique consisting of taking the spectral representation of the n-tuply diffracted field by one edge as the incident held for a half-plane (or a two-part plane) associated with the other edge (or junction) where the (n+1)th diffraction will take place. The analysis is then performed through the Wiener-Hopf technique for the (n+1)th diffraction. Bistatic diffraction patterns are obtained for different values of the surface impedances of the strip.

The diffraction of an E-polarized plane wave by a resistive strip located on a dielectric interface

Uniform asymptotic expressions for the doubly diffracted fields excited on the edges of a resistive strip located on a dielectric interface are obtained using a spectral iteration technique. The incident electric field is assumed to be parallel to the edges of the strip. The results also include the contribution of the surface wave fields to the secondary diffraction.

Matrix interpretation of the spectral iteration technique for 3D dielectric scatterers in the resonance region

The matrix interpretation of the spectral iteration technique (MSIT) has recently been shown to provide rapid convergence for the electromagnetic problems associated with 2D homogeneous dielectric scatterers in the resonance region for both TM and TE incidence. The MSIT is presented in a form suitable for use on 3D homogeneous dielectric and lossy-dielectric scatterers. Rapid convergence on test problems in the resonance region is demonstrated with significantly fewer than 3√(N) iterations, where N is the number of unknowns, needed for electrically large scatterers. The bistatic RCS computed from the MSIT for spheres with a range of permittivities and diameters up to 2λ0 are shown to be in good agreement with analytic solutions. Current distributions from some initial tests on lossy-dielectric thin plates show well-behaved and symmetric results.

Secondary Diffraction of a Plan Wave by a Metal-Backed Dielectric Strip

This paper deals with the secondary diffraction of an H- polarized plane-wave by a metal strip with a thin coating of high contrast dielectric material. After simulating the effect of the coating by an impedance boundary condition, the secondary diffracted field is evaluated uniformly by making use of a new spectral iteration technique proposed recently by the authors.

Scattering from periodic strip gratings via the secant-spectral iterative method

The secant method is used in an iterative algorithm for calculating the electromagnetic scattering from planar, periodic gratings. Results are compared with the moment method and the contraction-corrector spectral-iteration technique (SIT) methods. The secant approach does not depend on the evaluation of numerical derivatives to achieve convergence like the contraction-corrector SIT method. Suggestions for applying this method to more complicated structures are included. >

Convergence criteria for the extended matrix version of the spectral iteration technique (EM scattering)

An extended matrix version of the spectral iteration technique (SIT) has been reported recently, where it was shown to offer the possibility of significantly improving the convergence rate for homogeneous dielectric or conducting scatterers by introducing a taper. It is shown that there are good grounds for introducing such a taper, and that it can sometimes significantly improve the convergence of the method. For example, if a 64*64 grid size allows (with a taper) convergence in five iterations whereas a 42*42 grid size requires 23 iterations, a noticeable improvement in total computer time is effected. Also, there are cases where a taper must be introduced if the SIT method is to converge at all, without the application of a full orthogonalization procedure. The technique requires a correct choice of arbitrary values in the extended matrix, and guidelines are presented for such a choice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A spectral iteration technique for analyzing scattering from circuit analog absorbers

An iterative technique is described for solving for the current and field distributions in a structure composed of a periodic array of sheet conductors, deposited on a dielectric layered substrate, whether or not backed by a conductor. The incident field must be a plane wave but can be oblique. The periods array is taken into account by use of a Floquet mode field formalism, and an iterative method has been chosen that permits a numerical solution on personal computers by avoiding matrix inversions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comments, with reply, on "A generalization of Van den Berg's integral-square error computational technique for scattering" by A.J. Mackay and A. McCowen

The commenters note that if the conjugate gradient method were used in the above named work (ibid., vol.AP-35, p.213-20, Feb. 1987) its use automatically enforces the orthogonality of the authors' functions, without requiring any additional storage. In replying the authors agree that it was perhaps an oversight not to compare Van den Berg's method with the conjugate gradient method. However, they note that it was not their aim to provide such a comparison, but only to show how improvements could be made to the spectral iteration technique (SIT).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Matrix interpretation of the spectral iteration technique (electromagnetic scattering)

A matrix interpretation of the spectral iteration technique is presented to illustrate improvements in accuracy and convergence for both transverse magnetic and transverse electric waves incident on two-dimensional homogeneous scatterers producing solutions identical to a method of moments scheme. In this scheme, it is possible to improve the convergence rate of the technique by the use of nonphysical Green's function terms in the extended matrix. These terms result in the generation of a nonphysical field outside the scatterer, while still maintaining the correct solution of the current. Although the problem of nonconvergence has not been entirely overcome, a particular taper method used in the examples provided shows an improvement over their nontapered counterparts.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A spectral iterative technique with Gram-Schmidt orthogonalization

Iterative schemes based on the minimization of the integrated square error are discussed. In each iteration a basis function is generated in such a way that it is linearly related to the residual error of the previous iteration. A complete orthogonalization of all these basis functions leads to an optimal convergent scheme for some choices of the basis functions. In order to reduce the computer storage needed to store all of the basis functions, an incomplete orthogonalization scheme that still yields an efficient computational method is presented. In this scheme, a limited number of basis functions has to be stored. Some numerical results with respect to some representative field problems illustrate the performance of the various versions of the iterative schemes suggested here. >

The conjugate gradient spectral iterative technique for planar structures

It is shown that using the spectral iterative technique (SIT) to solve the first-kind integral equation is equivalent to the Neumann iterative solution of a related second-kind integral equation. It is thus shown that SIT only converges when the norm of the operator in the second-kind equation is small enough. Applying a conjugate gradient technique to the second-kind equation results in a convergent iterative scheme. Some representative numerical results show a superiority in the rate of convergence of the conjugate gradient scheme for the second-kind equation (CGSIT-scheme) when compared with the convergence of the conjugate scheme for the original first-kind equation (CG-scheme). The CGSIT-scheme combines the advantages of the conjugate gradient method with those of the spectral iterative technique. >