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Search Results: 1 - 10 of 22627 matches for " Reduced-Basis Method "
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A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods  [PDF]
Yonghui Huang, Yi Huang
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2015, DOI: 10.4236/alamt.2015.53010
Abstract: 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.
Adaptive Reduced Basis Methods Applied to Structural Dynamic Analysis  [PDF]
Yonghui Huang, Yi Huang
American Journal of Computational Mathematics (AJCM) , 2015, DOI: 10.4236/ajcm.2015.53029
Abstract: 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.
A reduced basis element method for the steady Stokes problem: Application to hierarchical flow systems
Alf E. L?vgren,Yvon Maday,Einar M. R?nquist
Modeling, Identification and Control , 2006, DOI: 10.4173/mic.2006.2.1
Abstract: The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations (Fink & Rheinboldt (1983), Noor & Peters (1980), Prud’homme et al. (2002)), and its applications extend to, for example, control and optimization problems. The basic idea is to first decompose the computational domain into a series of subdomains that are similar to a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same governing partial differential equation, but solved for different choices of some underlying parameter. In this work, the parameters are representing the geometric shape associated with a computational part. The approximation corresponding to a new shape is then taken to be a linear combination of the precomputed solutions, mapped from the reference domain for the part to the actual domain. We extend earlier work (Maday & R nquist (2002), Maday & R nquist (2004)) in this direction to solve incompressible fluid flow problems governed by the steady Stokes equations. Particular focus is given to constructing the basis functions, to the mapping of the velocity fields, to satisfying the inf-sup condition, and to 'gluing' the local solutions together in the multidomain case (Belgacem et al. (2000)). We also demonstrate an algorithm for choosing the most efficient precomputed solutions. Two-dimensional examples are presented for pipes, bifurcations, and couplings of pipes and bifurcations in order to simulate hierarchical flow systems.
一种分析区间参数结构可靠性的减基快速计算方法 A rapid reduced basis method for analysis of interval parameter structural reliability
A rapid reduced basis method for analysis of interval parameter structural reliability

- , 2017, DOI: 10.7511/jslx201701010
Abstract: 将减基法与蒙特卡洛模拟结合,提出了一种快速计算区间不确定结构可靠性的方法。该方法分为离线和在线计算两个阶段,离线阶段利用减基法建立减基空间,进而形成减缩模型;而在线阶段则将减缩模型融入蒙特卡洛方法,进而快速求解区间失效概率及相应的区间参数失效域。该方法在减基空间而非有限元空间中分析区间结构的可靠性,减少了求解时间,提高了计算效率,通过算例验证了该方法的可行性和有效性。
A rapid method is proposed for computing interval reliability of uncertain structures by combination of reduced basis method and Monte Carlo simulation.The method is divided into two parts off-line and on-line.In off-line part,the reduced space and reduced model are constructed using reduced basis method.Then in on-line part,the formed reduced model is incorporated into Monte Carlo simulation for efficiently computing the interval reliability and corresponding parameterized reliability region.This method can reduce computational time and improve efficiency,since it deals with interval reliability problem in reduced basis space rather than finite element space.The example in the paper illustrates feasibility and validity of this method.
Rapid computation of structural static extreme response based on reduced basis method

- , 2015, DOI: 10.7511/jslx201501016
Abstract: 针对参数化结构系统的响应极值问题,提出了一种适用于快速分析结构静态响应极值的计算方法.该方法在有限元模型基础上,利用减基法原理建立减缩的优化模型,并结合遗传算法快速、准确地获取结构在测点处的静态响应极值,同时,为了更贴近工程应用,在建立优化模型和设计优化步骤时,考虑了求解多测点情况下的最大静态响应极值.算例分析和结果比较,表明该方法在保证响应极值求解精度的同时,具有极大的时效性.
A suitable method based on the reduced basis conception,is proposed for efficiently analyzing and computing the structural static extreme response.In this method,the finite element model is established firstly,and then the reduced basis method and genetic algorithm are used together to construct a reduced optimization model,which could rapidly obtain the structural static extreme response at single-observation point.To further improve engineering application of this method,the largest extreme displacement response under multi-observation-point situation is taken into consideration in development of the optimization model and procedure.The examples in this paper demonstrate the high accuracy and efficiency of this method.
Reduced Detailed Mechanism for Methane Combustion  [PDF]
Abdelouahad Ait Msaad, Abdeltif Belcadi, Mustapha Mahdaoui, Elhoussin Aaffad, M’hamed Mouqallid
Energy and Power Engineering (EPE) , 2012, DOI: 10.4236/epe.2012.41004
Abstract: 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.
Analysis of Reduced Switch Topology Multilevel Inverter with Different Pulse Width Modulation Technique and Its Application with DSTATCOM  [PDF]
Sambasivam Rajalakshmi, Parthasarathy Rangarajan
Circuits and Systems (CS) , 2016, DOI: 10.4236/cs.2016.79208
Abstract: 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) methodand 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 systemfor 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.
Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem  [PDF]
Sharaf Mohmoud, Mohamed Gubara
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.710092
Abstract: 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.
Multigrid One-Shot Method for PDE-Constrained Optimization Problems  [PDF]
Subhendu Bikash Hazra
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.330216
Abstract: 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.
Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
Sanjay Mehrotra,Zhifeng Li
Algorithms , 2010, DOI: 10.3390/a3030224
Abstract: The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n) improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n 0.5.
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