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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


    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 >

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