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  • Open Access


    Efficient Multigrid Method Based on Adaptive Weighted Jacobi in Isogeometric Analysis

    ShiJie Luo1, Feng Yang1, Yingjun Wang1,*

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09474

    Abstract The isogeometric analysis Method (IGA) is an efficient and accurate engineering analysis method. However, in order to obtain accurate analysis results, the grid must be refined, and the increase of the number of refinements will lead to large-scale equations, which will increase the computational cost. Compared with the traditional equation solvers such as preconditioned conjugate gradient method (PCG), generalized minimal residual (GMRES), the advantage of multigrid method is that the convergence rate is independent of grid scale when solving large-scale equations. This paper presents an adaptive weighted Jacobi method to improve the convergence of geometric… More >

  • Open Access


    Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

    Arash Mehraban1, Henry Tufo1, Stein Sture2, Richard Regueiro2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1283-1303, 2021, DOI:10.32604/cmes.2021.017476

    Abstract Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive. To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with respect to strain energy error are investigated for polynomial order p = 1, 2, 3, 4 for compressible elasticity, and p = 2, 3, 4 for nearly-incompressible elasticity, on different number More >

  • Open Access


    High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

    Luciano Pereira da Silva1,*, Bruno Benato Rutyna1, Aline Roberta Santos Righi2, Marcio Augusto Villela Pinto3

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 699-715, 2021, DOI:10.32604/cmes.2021.014239

    Abstract In this article, we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes. The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high. We can obtain sparse matrices by applying compact schemes. In this article, we compare compact and exponential finite difference schemes of fourth order. The numerical solutions are calculated in quadruple precision (Real * 16 or extended precision) in FORTRAN language, and iteratively obtained until reaching the round-off error magnitude around 1.0E −32. This procedure is performed to ensure More >

  • Open Access


    A Multigrid Coupled DEIM Method for High-Efficient Simulation of Compressible Gas Porous Flow

    Jingfa Li1, Daobing Wang1, Bo Yu1,*, Shuyu Sun2, Dongliang Sun1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.23, No.1, pp. 3-3, 2021, DOI:10.32604/icces.2021.08209

    Abstract In natural gas engineering, the numerical simulation plays a significant role in the exploration, production and optimization of natural gas reservoir. However, numerical simulations of compressible gas flow in porous media are always expensive due to the gas compressibility and nonlinear properties. To save the computational cost, in this work we present a multigrid coupled discrete empirical interpolation method (MG-DEIM) to speedup the simulation of compressible gas porous flow. In this MG-DEIM framework, the core idea is that the multigrid method based on the full approximate scheme (FAS) is used to solve the flow equation… More >

  • Open Access


    Geometric Multigrid Method for Isogeometric Analysis

    Houlin Yang1, Bingquan Zuo1,2,*, Zhipeng Wei1,2, Huixin Luo1,2, Jianguo Fei1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 1033-1052, 2021, DOI:10.32604/cmes.2021.014493

    Abstract The isogeometric analysis method (IGA) is a new type of numerical method solving partial differential equations. Compared with the traditional finite element method, IGA based on geometric spline can keep the model consistency between geometry and analysis, and provide higher precision with less freedom. However, huge stiffness matrix from the subdivision progress still leads to the solution efficiency problems. This paper presents a multigrid method based on geometric multigrid (GMG) to solve the matrix system of IGA. This method extracts the required computational data for multigrid method from the IGA process, which also can be… More >

  • Open Access


    Performance of Geometric Multigrid Method for Two-Dimensional Burgers’ Equations with Non-Orthogonal, Structured Curvilinear Grids

    Daiane Cristina Zanatta1,*, Luciano Kiyoshi Araki2, Marcio Augusto Villela Pinto2, Diego Fernando Moro3

    CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.3, pp. 1061-1081, 2020, DOI:10.32604/cmes.2020.012634

    Abstract This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were discretized by Finite Volume Method (FVM) with second-order approximation scheme and deferred correction. Moreover, the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids. Furthermore, the influence of some parameters of geometric multigrid method, as well as lexicographical Gauss–Seidel (Lex-GS), η-line Gauss–Seidel (η-line-GS), Modified Strongly Implicit (MSI) and modified incomplete LU decomposition (MILU) solvers on the Central Processing… More >

  • Open Access


    Mesh Quality Improvement for Unstructured Quadrilateral Multigrid Analysis

    Y. Wada1, T. Hayashi2, M. Kikuchi3

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.8, No.4, pp. 127-132, 2008, DOI:10.3970/icces.2008.008.127

    Abstract Due to more complex and severe design, more effective and faster finite element analyses are demanded. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with different node densities and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to More >

  • Open Access


    H-matrix preconditioners for saddle-point systems from meshfree discretization 1

    Suely Oliveira2, Fang Yang2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 113-120, 2007, DOI:10.3970/icces.2007.003.113

    Abstract In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H-)matrices. Previous work by the authors using this approach did not use H-matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author's previous method, an AMG method adapted to saddle point systems, and conventional iterative methods such as JOR. More >

  • Open Access


    On the Robustness of the xy-Zebra-Gauss-Seidel Smoother on an Anisotropic Diffusion Problem

    Michely Laís de Oliveira1,*, Marcio Augusto Villela Pinto2, Simone de Fátima Tomazzoni Gonçalves2, Grazielli Vassoler Rutz3

    CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.2, pp. 251-270, 2018, DOI:10.31614/cmes.2018.04237

    Abstract Studies of problems involving physical anisotropy are applied in sciences and engineering, for instance, when the thermal conductivity depends on the direction. In this study, the multigrid method was used in order to accelerate the convergence of the iterative methods used to solve this type of problem. The asymptotic convergence factor of the multigrid was determined empirically (computer aided) and also by employing local Fourier analysis (LFA). The mathematical model studied was the 2D anisotropic diffusion equation, in which ε > 0 was the coefficient of a nisotropy. The equation was discretized by the Finite… More >

  • Open Access


    An Evaluation of Multigrid Acceleration for the Simulation of an Edge FLame in a Mixing Layer

    M. Wasserman1,2, Y. Mor-Yossef1,2, J.B. Greenberg1

    CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.3, pp. 203-228, 2015, DOI:10.3970/cmes.2015.106.203

    Abstract A test problem of a laminar edge flame formed in the mixing layer of two initially separated streams of fuel and oxidant is employed to evaluate the performance of multigrid acceleration of the iterative solution of the central difference finite difference scheme approximating the governing energy and species mass fraction conservation equations. The multigrid method was found to be extremely efficient and significantly improved the iterative convergence relative to that of a single grid method. For low to moderate chemical Damkohler numbers, acceleration factors of up to six (6!) times were recorded in the computational… More >

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