Reduced-basis Method在特征值问题中的应用

在特征值问题中引入了一种快速计算方法——缩减基法(Reduced-basis Method,RBM),介绍了RBM的计算原理和计算过程,给出了RBM误差估计的方法。以一塔式起重机塔身结构自由振动分析为例,修正设计参数时,由RBM得到结构的固有频率和振型及该计算结果的误差限。与有限元结果相比较,RBM不仅计算速度快,计算精度也很高,还可对结果进行误差估计。

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.

Adaptive Reduced Basis Methods Applied to Structural Dynamic Analysis

The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.

The Reduced Space Method for Calculating the Periodic Solution of Nonlinear Systems

A hybrid method combined the reduced Sequential Quadratic Programming(SQP)method with the harmonic balance method has been developed to analyze the characteristics of mode localization and internal resonance of nonlinear bladed disks.With the aid of harmonic balance method,the nonlinear equality constraints for the constrained optimization problem are constructed.The reduced SQP method is then utilized to deal with the original constrained optimization problem.Applying the null space decomposition technique to the harmonic balance algebraic equations results in the vanishing of the nonlinear equality constraints and a simple optimization problem involving only upper and lower bound constraints on the optimization variables is formed and solved.Finally,numerical results are given for several test examples to validity the proposed method.The efficiency of the solution method to trace the family of energy dependent nonlinear modes is illustrated.The localization nonlinear normal modes of bladed disks related to various types of internal resonances are explored.

Studies on Reduced Extent Method for Inhibited Thermokinetics Of Enzyme－Catalyzed Reaction──Inhibition of the laccase－catalyzed oxidation of o－dihydroxybenzene by m－dihydroxybenzene

The thermokinetic reduced extent equations of reversible inhibitions for Michaiels-Menten enzymatic reaction were deduced, and then the criteria for distingushing inhibition type was given and the methods for calculating kinetic parameters, KM,Ki and Urn were suggested. This theory was applied to inverstigate the inhibited thermokinetics of laccase-catalyzed oxidation of o-dihydroxybenzene by m-dihydroxybenzene. The experimental results show the inhibition belongs to reversible competitive type, KM=6.224×10-3 mol L-1, Ki=2. 363 × 10-2 mol. L-1.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

Reduced Expanding Load Method for Simulation-Based Structural System Reliability Analysis

The current situation and difficulties of the structural system reliability analysis are mentioned. Then on the basis of Monte Carlo method and computer simulation, a new analysis method reduced expanding load method (RELM) is presented, which can be used to solve structural reliability problems effectively and conveniently. In this method, the uncertainties of loads, structural material properties and dimensions can be fully considered. If the statistic parameters of stochastic variables are known, by using this method, the probability of failure can be estimated rather accurately. In contrast with traditional approaches,RELM method gives a much better understanding of structural failure frequency and its reliability index β is more meaningful.To illustrate this new idea, a specific example is given.

Reduced-order finite element method based on POD for fractional Tricomi-type equation

The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.

Application of the Generalized Reduced Gradient Method in Mechanical Optimization Design

This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.

A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods

Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.

Sulfur-resistant methanation over MoO_3/CeO_2–ZrO_2 catalyst: Influence of Ce-addition methods

In this paper, Ce_(0.2)Zr_(0.8)O_2 composite supports were prepared by different Ce-addition methods including impregnation of cerium(CeZr-imp), impregnation of citric acid and cerium(CeZr-CA) simultaneously and deposition precipitation method(CeZr-DP), respectively. The as-prepared supports were applied to prepare 10 wt% MoO_3/Ce_(0.2)Zr_(0.8)O_2 catalysts for sulfur-resistant methanation. The N_2 adsorption/desorption,X-ray diffraction(XRD), Raman spectroscopy(RS), X-ray photoelectron(XPS), temperature-programmed reduction by hydrogen(H_2-TPR) were undertaken to get textural properties, morphological information and structures of the catalysts. The results showed that Mo O_3 was highly dispersed on the surface of these three supports and Ce was mostly of coexisted in Ce^(4+)/Ce^(3+) redox pairs. Compared with Mo/CeZrimp, the CO conversion increased by 10% and 15% for Mo/CeZr-CA and Mo/CeZr-DP, respectively. This was mainly attributed to the larger specific surface area, Ce^(3+) concentration and content of active MoS_2 on the surface of catalysts.

Excellent supercapacitive performance of a reduced graphene oxide/Ni(OH)_2 composite synthesized by a facile hydrothermal route

A reduced graphene oxide/Ni(OH)2 composite with excellent supercapacitive performance was synthesized by a facile hydrothermal route without organic solvents or templates used.XRD and SEM results reveal that the nickel hydroxide,which crystallizes into hexagonal β-Ni(OH)2 nanoflakes with a diameter less than 200 nm and a thickness of about 10 nm,is well combined with the reduced graphene oxide sheets.Electrochemical performance of the synthesized composite as an electrode material was investigated by cyclic voltammetry,electrochemical impedance spectroscopy and galvanostatic charge/discharge measurements.Its specific capacitance is determined to be 1672 F/g at a scan rate of 2 mV/s,and 696 F/g at a high scan rate of 50 mV/s.After 2000 cycles at a current density of 10 A/g,the composite exhibits a specific capacitance of 969 F/g,retaining about 86% of its initial capacitance.The composite delivers a high energy density of 83.6 W·h/kg at a power density of 1.0 kW/kg.The excellent supercapacitive performance along with the easy synthesis method allows the synthesized composite to be promising for supercapacitor applications.

Reduced Detailed Mechanism for Methane Combustion

Simulated results from a detailed elementary reaction mechanism for methane-containing species in flames consisting of nitrogen (NOx), C1 or C2 fuels are presented, and compared with reduced mechanism;this mechanism have been constructed with the analysis of the rate sensitivity matrix f (PCAF method), and the computational singular perturbation (CSP). The analysis was performed on solutions of unstrained adiabatic premixed flames with detailed chemical kinetics described by GRI 3.0 for methane including NOx formation. A 9-step reduced mechanism for methane has been constructed which reproduces accurately laminar burning velocities, flame temperatures and mass fraction distributions of major species for the whole flammability range. Many steady-state species are also predicted satisfactorily. This mechanism is especially for lean flames. This mechanism is accurate for a wide range of the equivalence ratio (1, 0.9, 0.8, and 0.7) and for pressures as high as 40 atm to 60 atm. For both fuels, the CSP algorithm automatically pointed to the same steady-state species as those identified by laborious analysis or intuition in the literature and the global reactions were similar to well established previous methane-reduced mechanisms. This implies that the method is very well suited for the study of complex mechanisms for heavy hydrocarbon combustion.

BRIEF ARTICLE New reduced volume preparation regimen in colon capsule endoscopy

AIM:To evaluate the effectiveness of our proposed bowel preparation method for colon capsule endoscopy.METHODS:A pilot,multicenter,randomized controlled trial compared our proposed "reduced volume method"(group A) with the "conventional volume method"(group B) preparation regimens.Group A did not drink polyethylene glycol electrolyte lavage solution(PEGELS) the day before the capsule procedure,while group B drank 2 L.During the procedure day,groups A and B drank 2 L and 1 L of PEG-ELS,respectively,and swallowed the colon capsule(PillCam COLON capsule).Two hours later the first booster of 100 g magnesium citrate mixed with 900 mL water was administered to both groups,and the second booster was administered six hours post capsule ingestion as long as the capsule had not been excreted by that time.Capsule videos were reviewed for grading of cleansing level,RESULTS:Sixty-four subjects were enrolled,with results from 60 analyzed.Groups A and B included 31 and 29 subjects,respectively.Twenty-nine(94%) subjects in group A and 25(86%) subjects in group B had adequate bowel preparation(ns).Twenty-two(71%) of the 31 subjects in group A excreted the capsule within its battery life compared to 16(55%) of the 29 subjects in group B(ns).Of the remaining 22 subjects whose capsules were not excreted within the battery life,all of the capsules reached the left side colon before they stopped functioning.A single adverse event was reported in one subject who had mild symptoms of nausea and vomiting one hour after starting to drink PEG-ELS,due to ingesting the PEG-ELS faster than recommended.CONCLUSION:Our proposed reduced volume bowel preparation method for colon capsule without PEG-ELS during the days before the procedure was as effective as the conventional volume method.

Analysis of Reduced Switch Topology Multilevel Inverter with Different Pulse Width Modulation Technique and Its Application with DSTATCOM

Multilevel inverter has played a vital role in medium and high power applications in the recent years. In this paper, Reduced Switch Count Multi Level Inverter structure (RSCMLI) topology is presented with different pulse width modulation techniques. The harmonic level analysis is carried out for the reduced switch count multilevel inverter with the different PWM technique such as with Alternate Phase Opposition Disposition (APOD) method, In Phase Disposition (IPD) method and multi reference pulse width modulation method for five level, seven level , nine level and eleven level inverter. The simulation results are compared with the cascaded H Bridge Multi Level Inverter (CHBMLI). The nine level RSCMLI inverter with APOD method is used for the Distribution Static Synchronous Compensator (DSTATCOM) application in the nonlinear load connected system for power factor improvement. The result shows that the harmonic level and the number of switches required for RSCMLI is reduced compared to CHBMLI. RSCMLI employed in DSTATCOM improves the power factor and harmonic level of the system when it is connected to the nonlinear load.

Finite Element Model Updating of Complicated Beam-Type Structures Based on Reduced Super Beam Model

A finite element model updating technique for complicated beam-type structures is presented in this study.Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory.Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model.Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters.Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.

Multigrid One-Shot Method for PDE-Constrained Optimization Problems

This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.

The Clinical Observation of 80 Patients with Diseases of Lumbar Vertebrae Treated by Reinforcing and Reducing Methods of Mani

ＴｈｅＣｌｉｎｉｃａｌＯｂｓｅｒｖａｔｉｏｎｏｆ８０ＰａｔｉｅｎｔｓｗｉｔｈＤｉｓｅａｓｅｓｏｆＬｕｍｂａｒＶｅｒｔｅｂｒａｅＴｒｅａｔｅｄｂｙＲｅｉｎｆｏｒｃｉｎｇａｎｄＲｅｄｕｃｉｎｇＭｅｔｈｏｄｓｏｆＭａｎｉｐｕｌａｔｉｏｎＳｅｌｅｃｔｅｄＣｏ...