• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1371-1377
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• 2008

In this paper, we have employed the variational iteration method to solve the boundary value problems. Numerical results reveal that it is a very effective method compared with the results obtained by using the Adomian decomposition method in Wazwaz, A. M. (2000).

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.11-18
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• 2001

In this paper, a new algorithm of coupling Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the variational formulation is presented. A global variational coupling formulation of EFGM-BEM is achieved by combining the variational form on each subregion. In the formulation, Lagrange multiplier method is introduced to satisfy the compatibility conditions between EFGM subregion and BEM subregion. Some numerical examples are studied to verify accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM direct coupling method, EFGM and BEM. The proposed method incorporating the merits of EFGM and BEM is expected to be applied to special engineering problems such as the crack propogation problems in very large domain, and underground structures with joints.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.8 s.227
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• pp.1196-1202
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• 2004

A meshfree multi-scale method has been presented for efficient analysis of elasto-plastic problems. From the variational principle, problem is decomposed into a fine scale and a coarse scale problem. In the analysis only the plastic region is discretized using fine scale. Each scale variable is approximated using meshfree method. Adaptivity can easily and nicely be implemented in meshree method. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. Iteration procedure is indispensable for the elasto-plastic deformation analysis. Therefore this kind of solution procedure is adequate to that problem. The proposed method is applied to Prandtl's punch test and shear band problem. The results are compared with those of other methods and the validity of the proposed method is demonstrated.

• Journal of Ship and Ocean Technology
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• v.12 no.2
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.431-440
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• 2009

In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].

• Journal of Communications and Networks
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• v.18 no.3
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• pp.397-410
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• 2016

This paper proposes a novel cooperative localization method for distributed wireless networks in 3-dimensional (3D) global positioning system (GPS) denied environments. The proposed method, which is referred to as hybrid ellipsoidal variational algorithm (HEVA), combines the use of non-parametric belief propagation (NBP) and variational Bayes (VB) to benefit from both the use of the rich information in NBP and compact communication size of a parametric form. InHEVA, two novel filters are also employed. The first one mitigates non-line-of-sight (NLoS) time-of-arrival (ToA) messages, permitting it to work well in high noise environments with NLoS bias while the second one decreases the number of calculations. Simulation results illustrate that HEVA significantly outperforms traditional NBP methods in localization while requires only 50% of their complexity. The superiority of VB over other clustering techniques is also shown.

• Steel and Composite Structures
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• v.14 no.5
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• pp.511-521
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• 2013

In this study we have considered the governing nonlinear equation of an eccentrically reinforced cylindrical shell. A new analytical method called He's Variational Approach (VA) is used to obtain the natural frequency of the nonlinear equation. This analytical representation gives excellent approximations to the numerical solution for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the variation approach method. It has been proved that the variational approach is very effective, convenient and does not require any linearization or small perturbation. Additionally it has been demonstrated that the variational approach is adequately accurate to nonlinear problems in physics and engineering.

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.35-40
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• 2010

In the present work, LES with new variational multiscale method is conducted on the fully developed channel flow with Reynolds number, 180 based on the friction velocity and the channel half width. Incompressible Navier-Stokes equations are integrated using finite element method with the basis function of NURBS. To solve space-time equations, Newton's method with two stage predictor multicorrector algorithm is employed. The code is parallelized using MPI. The computational domain is a rectangular box of size $2{\pi}{\times}2{\times}4/3{\pi}$ in the streamwise, wall normal and spanwise direction. Mean velocity profiles and velocity fluctuations are compared with the data of DNS. The results agree well with those of DNS and other traditional LES.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.56-59
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• 2009

In the present work, LES with new variational multiscale method is conducted on the fully developed channel flow with Reynolds number is 180 based on the friction velocity and the channel half width. Incompressible Navier-Stokes equations are integrated using finite element method with the basis function of NURBS. To solve space-time equations, Newton's method with two stage predictor multicorretor algorithm is employed. The code is parallelized using MPI. The computational domain is a rectangular box of size $2{\pi}{\times}2{\times}4/3{\pi}$ in the streamwise, wall normal and spanwise direction. Mean velocity profiles and velocity fluctuations are compared with the data of DNS. The results agree well with those of DNS and other traditional LES.