ShiJie Luo¹, Feng Yang¹, Yingjun Wang^1,*

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 multigrid method to efficiently solve… More >

Houlin Yang¹, Bingquan Zuo^1,2,*, Zhipeng Wei^1,2, Huixin Luo^1,2, Jianguo Fei^1,2

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 used to improve the traditional… More >

Daiane Cristina Zanatta^1,*, 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 Unit (CPU) time was investigated.… More >