Two-level Iteration Research Articles

Simulating shot peening based on a dislocation density-based model with a novel time integration algorithm

Shot peening has been widely used in processing various components since it can bring in residual compressive stress and effectively refine the grain size of impacted area. To simulate grain refinement induced by shot peening, the dislocation density-based model has recently been introduced, however, the existing time integration algorithm is not stable and usually leads to divergent solutions in iterations. In this paper, a novel time integration algorithm is proposed for the dislocation density-based model. Based upon the algorithm, numerical studies on multi-shot AISI4340 steel are carried out with different coverages, velocities, shot diameters, and peening angles. It is shown that the method converges faster than the two-level iteration method, and the predicted dislocation cell structure sizes after shooting are consistent with experimental results. Besides that, increasing coverage can refine the size of a dislocation cell, which is closely dependent on the shot diameter, impact velocity, and angle. Thus, to achieve the desired grain size or the depth of refinement, it is necessary to take the shot diameter and velocity into account simultaneously.

A Two-Level Iterative Node Importance Evaluation of Aircraft Function Modules Based on Influence Matrix

Accurate evaluation of the critical nodes in the system is essential work for a multiplatform avionics system (MPAS) for resource allocation and other works. However, current evaluation methods are either limited to the aircraft level or the function module level. There is a lack of research on the evaluation using the information of these two levels. In view of this situation, this paper researches the two-level iterative method of evaluating the importance of aircraft function modules. The influence matrix was constructed by using the node access probability calculated by the PageRank algorithm and the function module weight calculated based on centrality. In addition, the importance of aircraft nodes was used to carry out two-level iteration, and finally, the importance of aircraft function modules was obtained. The experimental results show that this method can comprehensively utilize the information on aircraft cooperative network and function module cooperative network, solve the key problems of two-level iterative evaluation, and meet the requirement of evaluating critical nodes in a system.

Thermomechanical shakedown analysis considering temperature-dependent yield stress based on the primal-dual eigenstress-driven method

Many industrial structural components are loaded repeatedly in high-temperature environments. The shakedown limit under variable thermomechanical loads is a critical factor in thermomechanical elastoplastic structure design assessment. The shakedown limit is weakened due to material strength reduction at high-temperature conditions.This paper develops an efficient shakedown analysis Primal-dual Eigenstress-driven Method(PEM) algorithm for temperature-dependent yield condition, which overcomes the obstacle of the original PEM method [1] which can only deal with constant material properties. The developed temperature-dependent PEM algorithm proposes a two-level iteration algorithm to determine the shakedown limit and the time-independent residual stress field. At the inner level the theoretical framework tailored to the temperature dependence problem is derived to solve the Karush-Kuhn-Tucker (KKT) conditions of the extended temperature-dependent shakedown theorem and establish an increment algorithm for forming residual stress fields. Besides, the lower bound safe multipliers are computed to verify the residual stress field obtained by inner-level algorithm. At the outer level an efficient fixed-point algorithm is applied to search the shakedown multiplier, where the corresponding updating strategy for the yield stress with temperature is nested. For practicability, the proposed algorithm is seamlessly integrated into commercial platform ANSYS, which is applicable to industrial structures. Four numerical examples from multiple perspectives show the effectiveness of developed PEM method.

Research on patch near-field acoustic holography based on two-level iteration

In order to solve the “window effect” and “aperture repetition effect” caused by limited measurement aperture, a patch near-field acoustic holography method based on two-level iteration is proposed. After analyzing the principle and process of patch near-field acoustical holography based on orthogonal spherical wave, a patch near-field acoustical holography method based on two-level iteration is proposed. The validity of the method is verified by simulation and experiment. Compared with the reconstruction results of patch near-field acoustical holography based on orthogonal spherical wave, it shows the superiority of patch near-field acoustical holography based on two-level iteration.

Beamforming Design for Physical Layer Security in a Two-Way Cognitive Radio IoT Network With SWIPT

In this article, we study the secure beamforming design for a two-way cognitive radio (CR) Internet of Things (IoT) network aided with the simultaneous wireless information and power transfer (SWIPT). Located at the center of secondary network, the IoT controller helps to provide relay assistance and cooperative physical layer security (PLS) for two primary users (PUs) against an eavesdropper, while transmitting information and power to the other IoT devices (IoDs) with primary spectrum. To enhance the information security, we aim to maximize the secrecy sum rate (SSR) for PUs by jointly designing the beamforming matrix and vectors at the central controller. To efficiently solve the nonconvex problem, we first propose the branch-reduce-and-bound (BRB)-based algorithm to obtain an upper bound for the SSR and offer a feasible solution by Gaussian randomization, which demands two-level iteration and thus has high complexity. To strike a balance between the complexity and the performance, we then propose iterative algorithm based on constrained-convex-concave programming (CCCP) and a zero forcing (ZF)-based noniterative algorithm, the latter of which with lowest complexity is suitable for the central controller with limited-power supply. The simulation results are provided to demonstrate the effectiveness of our proposed optimization algorithms in comparison to the traditional schemes.

A two-level iteration approach for modeling and analysis of rapid response process with multiple deteriorating patients

In acute care, a patient’s clinical deterioration is often a precursor to serious and often fatal outcomes. To reduce the severity and frequency of negative outcomes, care providers need to response rapidly by providing quick evaluation, triage, and treatment to patients with declining conditions. However, a provider’s availability to respond can be constrained when multiple patients are deteriorating at the same time. To study the multiple patients rapid response process, we introduce a network model with complex structures, such as split, merge, and parallel. Iterative methods are presented to evaluate the mean decision time (i.e., the average time from the detection of a patient’s declining to a physician’s treatment decision being made). It is shown that such methods lead to convergent results and high accuracy in performance evaluation. Such a model provides a quantitative tool for healthcare professionals to design and improve rapid response systems.

TWO-LEVEL ITERATION PENALTY AND VARIATIONAL MULTISCALE METHOD FOR STEADY INCOMPRESSIBLE FLOWS

In this paper, we study two-level iteration penalty and variational multiscale method for the approximation of steady Navier-Stokes equations at high Reynolds number. Comparing with classical penalty method, this new method does not require very small penalty parameter &#949;. Moreover, two-level mesh method can save a large amount of CPU time. The error estimates in <b>H</b>¹ norm for velocity and in <i>L</i>² norm for pressure are derived. Finally, two numerical experiments are shown to support the efficiency of this new method.

A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints

This paper proposes a combination of trial-and-error congestion pricing schemes that have been studied in the literature. It not only considers the minimization of the total system cost but also addresses the capacity constraints. A two-level iteration method is proposed for solving the hybrid problem, in which the approximate subgradient projection method is used for the outer level iteration phase, and the partial linearization method is used for the inner level iteration phase. We prove the convergence of the two-level iteration method, under the condition that the subproblem for the inner level iteration is only solved approximately, which makes the method efficient and practical. A numerical example is presented to illustrate the application of the two-level iteration method to the trial-and-error congestion pricing scheme.

Two-level iteration penalty methods for the incompressible flows

In this article, we present a new iteration penalty method for incompressible flows based on the iteration of pressure with a factor of penalty parameter, which was first developed for Stokes flows by Cheng and Abdul (2006) [14]. The stability and error estimates of numerical solutions in some norms are derived for this one-level method. Then, combining the techniques of two-level method and linearization with respect to the nonlinear convective term, we propose two-level Stokes/Oseen/Newton iteration penalty methods corresponding to three different linearization method, and show the stability and error estimates of these three methods. Finally, some numerical tests are given to demonstrate the effect of penalty parameter and the efficiency of the new methods.

Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows

We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.

Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.

Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh sizeHin combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh sizeh. The error estimate obtained in this paper shows that ifH,h, andεcan be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints

Underground constructions, such as shafts, courtain walls, foundations, pipes and tunnels, use structural elements that are supported by a geological medium (soil or rock) or are used to support the geological medium loads. If the geological medium is unable to react under tension, the structural element is subjected to unilateral contact constraints and, during the deformation process, may loose contact with the surrounding medium at one or more regions. The present work proposes an alternative numerical methodology for the geometrically nonlinear analysis of structural systems under unilateral contact constraints. The nonlinear problem involves two different types of variables: the displacement field and the length and position of the contact regions. In order to solve the resulting algebraic nonlinear equations with contact constraints and obtain the structural equilibrium configuration, the present work proposes a two-level iteration solution strategy at each load step. The first solves the contact problem as a linear complementary problem using Lemke’s algorithm. The second updates the displacement field. A nonlinear beam-column element is used to model the structure, while a bed of springs is used to model the geological medium. The use of an updated Lagrangian formulation, together with continuation and optimization techniques minimize the errors along the equilibrium paths and enables one to trace convoluted non-linear equilibrium paths with a varying number of contact regions. Special attention is given to the behavior of curved unidimensional support systems such as arches and rings. The nonlinear behavior of four such support systems is studied. The results clarify the influence of the foundation position (above or below the structure) and its stiffness on the nonlinear behavior and stability of curved structures. Comparison of the present results with those found in literature demonstrates the accuracy and versatility of the proposed numerical strategy in the analysis of structural elements with unilateral contact constraints.

Exact subgrid interface correction schemes for elliptic interface problems

We introduce a nonconforming finite-element method for second order elliptic interface problems. Our approach applies to problems in which discontinuous coefficients and singular sources on the interface may give rise to jump discontinuities in either the solution or its normal derivative. Given a standard background mesh and an interface that passes between elements, the key idea is to construct a singular correction function that satisfies the prescribed jump conditions, providing accurate subgrid resolution of the discontinuities. Utilizing the closest point extension and an implicit interface representation by the signed distance function, an algorithm is established to construct the correction function. The result is a function that is supported only on the interface elements, represented by the regular basis functions, and bounded independently of the interface location with respect to the background mesh. In the particular case of a constant second-order coefficient, our regularization by a singular function is straightforward, and the resulting left-hand side is identical to that of a regular problem without introducing any instability. The influence of the regularization appears solely on the right-hand side, which simplifies the implementation. In the more general case of discontinuous second-order coefficients, a normalization is invoked which introduces a constraint equation on the interface. This results in a problem statement similar to that of a saddle-point problem. We employ two-level iteration as the solution strategy, which exhibits aspects similar to those of iterative preconditioning strategies.

Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems

Nonsymmetric saddle point problems arise in a wide variety of applications in computational science and engineering. The aim of this paper is to discuss the numerical behavior of several nonsymmetric iterative methods applied for solving the saddle point systems via the Schur complement reduction or the null-space projection approach. Krylov subspace methods often produce the iterates which fluctuate rather strongly. Here we address the question whether large intermediate approximate solutions reduce the final accuracy of these two-level (inner–outer) iteration algorithms. We extend our previous analysis obtained for symmetric saddle point problems and distinguish between three mathematically equivalent back-substitution schemes which lead to a different numerical behavior when applied in finite precision arithmetic. Theoretical results are then illustrated on a simple model example.

Transient response of finned-tube condenser in household refrigerators

A distributed parameter model for prediction of the transient performance of a condenser is presented. The model is capable of predicting the refrigerant temperature distribution, tube wall temperature, quality of refrigerant, inventory mass of refrigerant as a function of position and time. An efficient two-level iteration method is proposed to obtain the numerical solution of the model without solving a large set of non-linear equations simultaneously. A finned tube condenser of 12 ft 3 refrigerator with R12 as working fluid was chosen as a sample and some tests were carried out to determine its transient response. The examination of results indicates that the theoretical model provides a reasonable prediction of dynamic response compared to the experimental data. Transient behavior of temperature, pressure, mass flow rate, mass of liquid and vapor of refrigerant, quality, heat transfer in household refrigerators have been presented. Also time-dependent displacement of interface between saturated and superheated regions has been shown. Extensive examinations of theoretical and experimental results show that with utilization of a controllable compressor, power consumption can be reduced.

Transient response of dry expansion evaporator in household refrigerators

A distributed parameter model for prediction of the transient performance of an evaporator is presented. The model is capable of predicting the refrigerant temperature distribution, tube wall temperature, quality of refrigerant, inventory mass of refrigerant as a function of position and time. An efficient two-level iteration method is proposed to obtain the numerical solution of the model without solving a large set of non-linear equations simultaneously. A round bound evaporator of 12 ft3 refrigerator with R12 as working fluid were chosen as a sample and some tests were carried out to determine its transient response. The results indicate that the theoretical model provides a reasonable prediction of dynamic response compared with the experimental data. Transient behaviour of temperature, pressure, mass flow rate, mass of liquid and vapour of refrigerant, quality, heat transfer in household refrigerators have been presented. Also time dependent displacement of interface between saturated and superheated regions has been shown. Extensive investigation of theoretical and experimental results shows that with a controllable compressor, power consumption can be reduced.

Transient response of dry expansion evaporator in household refrigerators

A distributed parameter model for prediction of the transient performance of an evaporator is presented. The model is capable of predicting the refrigerant temperature distribution, tube wall temperature, quality of refrigerant, inventory mass of refrigerant as a function of position and time. An efficient two-level iteration method is proposed to obtain the numerical solution of the model without solving a large set of non-linear equations simultaneously. A round bound evaporator of 12 ft 3 refrigerator with R12 as working fluid were chosen as a sample and some tests were carried out to determine its transient response. The results indicate that the theoretical model provides a reasonable prediction of dynamic response compared with the experimental data. Transient behaviour of temperature, pressure, mass flow rate, mass of liquid and vapour of refrigerant, quality, heat transfer in household refrigerators have been presented. Also time dependent displacement of interface between saturated and superheated regions has been shown. Extensive investigation of theoretical and experimental results shows that with a controllable compressor, power consumption can be reduced.

Acceleration of the non-symmetrized two-level iteration

In this paper we discuss two-level multiplicative Schwarz methods, which result in unsymmetric systems in their solution spaces. We introduce a new algorithm to accelerate this iteration by applying the conjugate gradient (CG) scheme to a subspace. It will be shown that this algorithm possesses a CG-type convergence rate. Our algorithm has obvious advantages over the existing Schwarz-CG algorithms. Its application to two-level grid methods will be also considered.

Hierarchical SIR and rate control on the forward link for CDMA data users under delay and error constraints

We study the signal-to-interference ratio (SIR) and rate control for code division multiple access (CDMA) data users on the forward link under average or peak power constraints. The quality of service (QoS) for data users is specified by delay and error rate constraints as well as a family of utility functions representing the throughput and fairness among the data users. It is found that the optimal SIR and rate control algorithm has a hierarchical structure which can be easily implemented in a distributed manner. The SIR targets can be adjusted independently by the mobiles using information specific to the individual users. The data rates can be adjusted jointly by the base station based on limited feedback from the mobiles. We also propose a two-level iteration algorithm for both the mobile and the base station to efficiently compute the SIR and data rates. Our results show that a flexible tradeoff between total system throughput (sum of rates achieved) and fairness (similarity in data rates) can be achieved by choosing appropriate utility functions used in this scheme.