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 >

Arash Mehraban¹, Henry Tufo¹, Stein Sture², Richard Regueiro^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1283-1303, 2021, DOI:10.32604/cmes.2021.017476 - 25 November 2021

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 >

Luciano Pereira da Silva^1,*, 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 - 22 July 2021

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 >

Jingfa Li¹, Daobing Wang¹, Bo Yu^1,*, 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 >

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 >

Michely Laís de Oliveira^1,*, 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 >

M. Wasserman^1,2, Y. Mor-Yossef^1,2, 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 >

Jason F. Hammond¹, Elizabeth J. Stewart², John G. Younger³, Michael J.Solomon², David M. Bortz^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.3, pp. 295-340, 2014, DOI:10.32604/cmes.2014.098.295

Abstract The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion… 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 >