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 >

Xinyao Liu¹, Baojiang Cui^1,*, Lantao Xing²

Intelligent Automation & Soft Computing, Vol.34, No.1, pp. 295-305, 2022, DOI:10.32604/iasc.2022.020032

Abstract With the rise of mobile network, user location information plays an increasingly important role in various mobile services. The analysis of mobile users’ trajectories can help develop many novel services or applications, such as targeted advertising recommendations, location-based social networks, and intelligent navigation. However, privacy issues limit the sharing of such data. The release of location data resulted in disclosing users’ privacy, such as home addresses, medical records, and other living habits. That promotes the development of trajectory generators, which create synthetic trajectory data by simulating moving objects. At current, there are some disadvantages in the process of generation. The… More >

Xinqing Li¹, Qinghai Zhao^1,*, Hongxin Zhang¹, Tiezhu Zhang², Jianliang Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 683-704, 2021, DOI:10.32604/cmes.2021.015685

Abstract This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties. To characterize the random-field uncertainties with a reduced set of random variables, the Karhunen-Loève (K-L) expansion is adopted. The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization. Under dividing the design domain, the volume fraction of each preset gradient layer is extracted. Based on the ordered solid isotropic microstructure with penalization (Ordered-SIMP), a functionally graded multi-material interpolation model is formulated by individually optimizing each preset… 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 >

Huawen Shu, Minghai Xu, Xinyue Duan^*, Yongtong Li, Yu Sun, Ruitian Li, Peng Ding

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 509-523, 2020, DOI:10.32604/cmes.2020.08806

Abstract A finite volume method based unstructured grid is presented to solve the two dimensional viscous and incompressible flow. The method is based on the pressure-correction concept and solved by using a semi-staggered grid technique. The computational procedure can handle cells of arbitrary shapes, although solutions presented in this paper were only involved with triangular and quadrilateral cells. The pressure or pressure-correction value was stored on the vertex of cells. The mass conservation equation was discretized on the dual cells surrounding the vertex of primary cells, while the velocity components and other scale variables were saved on the central of primary… More >

S. Itoh¹, K. Taguchi¹, Y. Umemoto¹, H. Serizawa¹, H. Murakawa¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 47-54, 2008, DOI:10.3970/icces.2008.005.047

Abstract The authors have proposed Fractal and Hierarchical Multi-Grid Methods for solving ultra large FE problems [1, 2]. In these methods, the domain to be analyzed is subdivided into multi-grid which has fractal or hierarchical structure and the solution is obtained by solving equations for small cells or nodes at each hierarchy successively. In this research, potential capability of a Hierarchical Multi-Grid method is examined through simple example problems. More >

George A. Gravvanis¹, Christos K. Filelis-Papadopoulos¹, Paschalis I.Matskanidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.4, pp. 323-345, 2014, DOI:10.3970/cmes.2014.100.323

Abstract Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving the coarsening and the convergence behavior of the method. In this paper, an AMG method is introduced that utilizes a new generic approximate inverse algorithm as a smoother in conjunction with common coarsening techniques, such as classical Ruge-Stüben coarsening, CLJP and PMIS coarsening. The proposed approximate inverse scheme, namely Generic Approximate Banded Inverse (GenAbI), is a banded approximate inverse based on Incomplete LU factorization with zero fill–in (ILU(0)). The new class of Generic Approximate Banded Inverse can be computed for… More >

Christos K. Filelis-Papadopoulos¹, George A. Gravvanis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 233-253, 2013, DOI:10.3970/cmes.2013.090.232

Abstract During the last decades, multigrid methods have been extensively used in order to solve large scale linear systems derived from the discretization of partial differential equations using the finite difference method. Approximate Inverses in conjunction with Richardon’s iterative method could be used as smoothers in the multigrid method. Thus, a new class of smoothers based on approximate inverses could be derived. Effectiveness of explicit approximate inverses relies in the fact that they are close approximants to the inverse of the coefficient matrix and are fast to compute in parallel. Furthermore, the class of finite difference approximate inverses proposed in conjunction… More >

B. M. Pasquim¹, V. C. Mariani²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 113-132, 2008, DOI:10.3970/cmes.2008.035.113

Abstract This study presents a Cartesian grid method and its application to solve a steady flow in a lid-driven triangular two-dimensional cavity. The evolution of stream function and vorticity inside a triangular lid-driven cavity, when the Reynolds number changes from 1 to 6000, is presented. For space discretization on the interior of triangular cavity orthogonal Cartesian grid is used. Then, using this grid, trapezoidal volumes appear in the interface between solid and fluid. For a suitable treatment of these volumes the Eulerian-Lagrangian methodology is used. The Navier-Stokes equations are solved numerically using finite-volume method. On the basis of the numerical studies… More >