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  • Open Access



    Dave Martina,b,† , Hicham Chaoukia,b, Jean-Loup Roberta, Donald Zieglerc, Mario Fafarda,b

    Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-9, 2016, DOI:10.5098/hmt.7.31

    Abstract The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust… More >

  • Open Access



    Dave Martina,b,† , Hicham Chaoukia,b, Jean-Loup Roberta, Donald Zieglerc, Mario Fafarda,b

    Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-11, 2016, DOI:10.5098/hmt.7.40

    Abstract A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were… More >

  • Open Access


    Optimal Control and Spectral Collocation Method for Solving Smoking Models

    Amr M. S. Mahdy1,*, Mohamed S. Mohamed1, Ahoud Y. Al Amiri2, Khaled A. Gepreel1

    Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 899-915, 2022, DOI:10.32604/iasc.2022.017801

    Abstract In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through… More >

  • Open Access


    A Parameter-Free Approach to Determine the Lagrange Multiplier in the Level Set Method by Using the BESO

    Zihao Zong, Tielin Shi, Qi Xia*

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 283-295, 2021, DOI:10.32604/cmes.2021.015975

    Abstract A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method. It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method. It first computes the difference between the volume of current design and the upper bound of volume. Then, the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material. Numerical examples proved that this approach is effective to constrain the volume. More importantly, there is no parameter in the proposed approach, which makes it convenient to use.… More >

  • Open Access


    Partitioned Formulation for Solving 3D Frictional Contact Problems with BEM using Localized Lagrange Multipliers

    L. Rodríguez-Tembleque1, J.A. González1, R. Abascal1, K.C. Park2, C.A. Felippa2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.2, No.1, pp. 21-28, 2007, DOI:10.3970/icces.2007.002.021

    Abstract This work presents an interface treatment method based on localized Lagrange Multipliers (LLM) to solve frictional contact problems between two 3D elastic bodies. The connection between the solids is done using a displacement frame intercalated between the interfaces meshes, and the LLM are collocated at the interface nodes. The Boundary Elements Method (BEM) is used to compute the influence coefficients of the surface points involved, and contact conditions are imposed using projection functions. The LLM provides a partitioned formulation which preserves software modularity, facilitates non-matching meshes treatment and passes the contact patch test [4]. More >

  • Open Access


    Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

    Andrew Lundberg1, Pengtao Sun1,∗, Cheng Wang2, Chen-song Zhang3

    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 35-62, 2019, DOI:10.32604/cmes.2019.04804

    Abstract The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated. More >

  • Open Access


    Topology optimization of finite similar periodic continuum structures based on a density exponent interpolation model

    Jian Hua Rong1,2,3, Zhi Jun Zhao4, Yi Min Xie5, Ji Jun Yi1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 211-231, 2013, DOI:10.3970/cmes.2013.090.211

    Abstract Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural… More >

  • Open Access


    Fuzzy Optimization of Multivariable Fuzzy Functions

    Şahin Emrah Amrahov1, Iman N.Askerzade1

    CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.1, pp. 1-10, 2010, DOI:10.3970/cmes.2010.070.001

    Abstract In this paper we define multivariable fuzzy functions (MFF) and corresponding multivariable crisp functions (MCF). Then we give a definition for the maximum value of MFF, which in some cases coincides with the maximum value in Pareto sense. We introduce generalized maximizing and minimizing sets in order to determine the maximum values of MFF. By equating membership functions of a given fuzzy domain set and the corresponding maximizing set, we obtain a curve of equal possibilities. Then we use the method of Lagrange multipliers to solve the resulting nonlinear optimization problem when the membership functions are differentiable. We finally present… More >

  • Open Access


    Error Analysis of Trefftz Methods for Laplace's Equations and Its Applications

    Z. C. Li2, T. T. Lu3, H. T. Huang4, A. H.-D. Cheng5

    CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 39-82, 2009, DOI:10.3970/cmes.2009.052.039

    Abstract For Laplace's equation and other homogeneous elliptic equations, when the particular and fundamental solutions can be found, we may choose their linear combination as the admissible functions, and obtain the expansion coefficients by satisfying the boundary conditions only. This is known as the Trefftz method (TM) (or boundary approximation methods). Since the TM is a meshless method, it has drawn great attention of researchers in recent years, and Inter. Workshops of TM and MFS (i.e., the method of fundamental solutions). A number of efficient algorithms, such the collocation algorithms, Lagrange multiplier methods, etc., have been developed in computation. However, there… More >

  • Open Access


    A Reduction Algorithm of Contact Problems for Core Seismic Analysis of Fast Breeder Reactors

    Ryuta Imai1, Masatoshi Nakagawa2

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 253-282, 2012, DOI:10.3970/cmes.2012.084.253

    Abstract In order to evaluate seismic response of fast breeder reactors, finite element analysis for core vibration with contact/impact is performed so far. However a full model analysis of whole core vibration requires huge calculation times and memory sizes. In this research, we propose an acceleration method of reducing the number of degrees of freedom to be solved until converged for nonlinear contact problems. Furthermore we show a sufficient condition for the algorithm to work well and discuss its efficiency and a generalization of the algorithm. In particular we carry out the full model analysis to show that our method can… More >

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