Mosaic-based waveguide lenses designed by the adjoint method based on the finite-element scheme.

The authors discuss ion-milled planar waveguide lenses in GaAs which exhibit a considerably higher efficiency than that previously reported for those lenses and near diffraction-limited spot size. The authors also report the performance characteristics of these latest lenses, including single lenses and lens array of analog Fresnel, chirp grating, and hybrid types as well as a collimation-Fourier transformation lens-pair, together with the detailed design and fabrication procedures. A simple theoretical model for the lens efficiency is also formulated to assist in the lens design. Ion milling has been shown to be a simple and versatile technique for fabrication of waveguide lenses in GaAs and applicable to any other substrate material. Such ion-milled waveguide lenses should facilitate realization of a variety of monolithically integrated optic device modules and circuits in GaAs and other related substrates with applications to communications, signal processing, and computing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Lenses are among the key components in optical signal processing and computing systems(1). Realization of such optical systems in a waveguide substrate has long been considered one of the major applications of integrated optics. Recently, the prospects for this realization are significantly advanced through progress in guided-wave microoptic components of both active and passive types. Aside from the study on integrated acoustooptic RF spectrum analyzers(2) that has become an international effort, serious attempts to utilize the integrated optic devices for optical computation of both analog and digital data are also being made at various research institutions. Accordingly, it is of great importance to develop viable techniques for fabrication of waveguide lenses with application to optical computing. A variety of planar waveguide lenses including the geodesic, chirp-grating, Fresnel, and Luneburg types have been reported in the literature. A common characteristic of these lenses is a relatively long focal length and a relatively small numerical aperture. It is to be noted that a channel waveguide lens involving multiple coupled-waveguides has also been proposed most recently(3). In this paper we report on the single-mode planar waveguide microlenses and microlens arrays in LiNbO3 that are formed using titanium indiffused-proton exchange technique(4). These waveguide lenses have demonstrated desirable properties including very short focal length, large numerical aperture, very small focal spot size for a wide range of focal length, and low optical insertion loss at the 6328 Å He-Ne laser wavelength.

The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics. Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function q 1 , as appropriately normalised kernel function, which inherently satisfies all the specific requirements on q 1 : The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic plastic fracture mechanics, including the combination with elastic plastic constitutive models is straightforward. • New algorithm to calculate J-Integral developed in Smoothed Particle Hydrodynamics (SPH). • New approach for calculating gradient of J-Integral weighting function q 1 analytically. • Confirmed accuracy of J-integral results from SPH compared to FEM results.

Ultracompact multiway ultrasonic power splitters based on phononic crystal with a triangular lattice

The relation between finite element methods and nodal methods in transport theory

We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field B \mathbfit {B} and the current density j \mathbfit {j} as discretization variables. We show that Gauss’s law for the magnetic field, namely ∇ ⋅ B = 0 \nabla \cdot \mathbfit {B}=0 , and the energy law for the entire system are exactly preserved in the finite element schemes. Based on some new basic estimates for H ( d i v ) H(\mathrm {div}) finite elements, we show that the new finite element scheme is well-posed. Furthermore, we show the existence of solutions to the nonlinear problems and the convergence of the Picard iterations and the finite element methods under some conditions.

Motor design can be said as multi-modal optimization problem, as many performances should be considered. In addition, a time-consuming finite element method (FEM) is required for accurate analysis of the motor, and such computational burden becomes worse when the FEM is applied to multi-modal optimization problem. In this paper, adaptive-sampling kriging algorithm (ASKA) is proposed to relieve the computation cost of multi-modal optimization problem. The ASKA utilizes kriging interpolation model with generated samples by Compact Search Sampling (CSS) and Exclusive Space-filling Method (ESM). The CSS improves the accuracy of the solutions by generating samples near the expected solutions, and the ESM guarantees the diversity of solutions by generating samples far from existing samples, avoiding solution-near area. Using CSS and ESM, the ASKA adjusts the number of samples effectively and reduces function call considerably. The superior performance of the ASKA was verified by mathematical test functions with complex objective function regions. To validate the feasibility of actual electric machines, the ASKA was applied to optimal design of permanent magnet assisted synchronous reluctance motors for electric vehicles and optimum design with diminished torque ripple is derived.

The purpose of this paper is to present a parameter identification method to determine the force of a blast and the elastic modulus of the ground using the measurements of a dynamic elastic wave, the adjoint equation method of optimal control theory, and the finite element method. Before the excavation of rocky ground, it is important to estimate the ground properties. In this paper, the elastic modulus is determined as the performance function is minimized using a technique based on the first‐order adjoint method. The performance function is a square sum of the discrepancies between the computed and the observed values of the velocities. After the determination of the magnitude of the blasting force, we can determine the elastic modulus of the rock. As the basic equation to calculate the velocities of dynamic elastic body, elastic equilibrium equations with linear viscosity are employed. The adjoint equation method has been utilized in order to calculate the gradient of the performance function with respect to the parameters. The gradient of the performance function is calculated using the first‐order adjoint equation. The weighted gradient method is applied for minimization. In order to solve the state equations in space and time, the finite element method and the Newmark \documentclass{article}\usepackage{amssymb}\footskip=0pc\pagestyle{empty}\begin{document}$\frac{1}{4}$\end{document} method are used. In this paper, we tested the practical application of our proposed method for determination of the elastic modulus of rock at the Ikawa tunnel located in the Tokushima prefecture, Japan. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Energy-preserving finite element methods for a class of nonlinear wave equations

Prediction of Temperature Distribution and Displacement of Carbon Steel Plates by FEM

Objectives: In this study, two new power splitters integrated with a novel half mode substrate integrated waveguide (HMSIW) and composite right/left-handed transmission lines (CRLH-TL) cells are presented, realized and compared to a conventional Substrate Integrated Waveguide (SIW) one. Methods: The SIW technology is characterized by a high Q factor and a low return loss, but it suffers from the massive size particularly in low frequencies bands, so to achieve practically 50% miniaturization in size with keeping the high performances of the SIW technique, HMSIW origins from SIW has been utilized. otherwise, so as to reduce the HMSIW device, size, Composite Right/Left-Handed Transmission Lines (CRLH-TL) cells are applied. The designs are printed on a Roger RT/duroid 6010 and performed within an HFSS environment based on the finite element method (FEM). Simulations and measurements of the three power dividers are presented over a frequency band from 2.2 GHz to 2.6 GHz. Findings: The novel proposed component achieves about 70% and 90% of size reduction compared to, respectively, the HMSIW and SIW power splitters. The simulated and measured results are in close agreement. Application: Compared to the SIW power divider and the HMSIW one the novel proposed device is characterized by a compact size and an easy fabrication process. So that it will enable a convenient reduction of size, loss and cost in millimeter-wave and microwave systems.Keywords: Power Divider, HMSIW, SIW, CRLH-TL Cells, Tapered Transition

In this paper, a controllable hybrid plasmonic integrated circuit (CHPIC) composed of hybrid plasmonic waveguide (HPW)-based rhombic nano-antenna, polarization beam splitter, coupler, filter, and sensor has been designed and investigated for the first time. In order to control the power into a corresponding input port, a graphene-based 1 × 3 power splitter with switchable output has been exploited. The functionality of each device has been studied comprehensively based on the finite element method and the advantages over state-of-the-art have been compared. Moreover, the effect of connection of CHPIC to the photonic and plasmonic waveguides has been studied to exhibit the capability of variety excitation methods of the CHPIC. Furthermore, the performance of the proposed CHPIC connected to inter/intra wireless transmission links has been investigated. The wireless transmission link consists of two HPW-based nano-antennas as transmitter and receiver with the maximum gain and directivity of 10 dB and 10.2 dBi, respectively, at 193.5 THz. The suggested CHPIC can be used for applications such as optical wireless communication and inter/intra-chip optical interconnects.

Design of single-polarization coupler based on dual-core photonic band-gap fiber implied in resonant fiber optic gyro

As is well known, one of the main challenges in dealing with the time‐fractional diffusion‐wave equation is that the solutions have weak regularity at the initial values. This necessitates the use of nonuniform grids for error analysis. However, the theoretical analysis of nonuniform grids is relatively complex and lacks efficient and stable numerical methods. The main research problem addressed in this article is the time‐fractional diffusion‐wave equation on nonuniform grids. We use the order reduction method and discrete complementary convolution kernel to discretize the Caputo derivative of the equation and obtain the L1‐type finite element method on nonuniform grids. The properties related to discrete complementary convolutional kernels are often used for algorithm convergence analysis, which simplifies the process of finite element theory analysis and is efficient and innovative. This article demonstrates the solvability, stability, and convergence of the L1‐type finite element schemes on nonuniform grids. Finally, the consistency between the proposed finite element scheme and the convergence order results obtained from theoretical analysis was verified through experiments.

A simplified method has been developed for assessing the loading of the load-bearing systems of passenger cars under thermal loading with a fire spot with limited properties. A system of simplifications for realizing a combustion spot is substantiated. A method for its implementation is proposed. The description of the object of research is given with the necessary thoroughness of presentation. A finite element scheme has been developed and adapted, taking into account the application of thermal loads in the system of an industrial software complex that implements the finite element method. Verification of the finite element scheme was carried out taking into account full-scale normative experiments. A conclusion is made about the possibility of the applicability of the finite element scheme for the study. Numerical experiments have been carried out to assess the carrying capacity of the body of a double-deck passenger car when it is exposed to a combustion center with known thermal parameters. The experiments were built and performed in a finite element method system. The results of simulations in the affected zone of the alleged fire were obtained for the conditional spot of its location. Comparison of the results with the static loading mode of the car body is considered. The analysis of the results obtained is carried out. A conclusion is given on the effect of a small localization fire on the carrying capacity of the car body. The proposed method is evaluated taking into account the possibility of further use