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… 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 - 15 April 2022

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… 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 - 19 April 2021

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 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 - 19 February 2021

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 >

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 - 15 December 2020

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 >

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 - 01 May 2020

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 More >

N. Ma^1,2, K. Sato³, K. Takada⁴

CMC-Computers, Materials & Continua, Vol.46, No.3, pp. 195-219, 2015, DOI:10.3970/cmc.2015.046.195

Abstract The local mechanical behaviors of advanced high strength steels undergoing a very large strain from uniform plastic deformation to fracture were investigated with the aid of a measured displacement field and a measurement based FEM. As a measurement method, a digital image grid method (DIGM) was developed and the three-direction transient displacement field on uniaxial tensile test pieces was measured. Combining the measured transient displacement field with the finite element method, a measurement based FEM (M-FEM) was developed for the computation of distribution of the local strains, local stresses and ductile damage accumulation in a 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… 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 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 >