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Multigrid Method for Fluid Dynamic Problems

Galina Muratova, Evgenia Andreeva
2014 Journal of Computational Mathematics  
This paper covers the review and some aspects of using Multigrid method for fluid dynamics problems. The main development stages of multigrid technics are presented.  ...  Thanks to this fact the main contemporary study on multigrid methods focuses on "almost" self-adjoint positivedefinite problems in linear case, and on "almost" linear problems in nonlinear case.  ...  Multigrid methods are based on the recursive use of a two-grid scheme.  ... 
doi:10.4208/jcm.1403-cr11 fatcat:muncumdabbbj5oegkr2esjkvlm

UNSTRUCTURED MULTIGRID METHOD FOR SHELLS

J. FISH, L. PAN, V. BELSKY, S. GOMAA
1996 International Journal for Numerical Methods in Engineering  
An accelerated multigrid method, which exploits shell element formulation to speed up the iterative process, is developed for inherently poor conditioned thin domain problems on unstructured grids.  ...  Numerical results show a remarkable robustness for a wide spectrum of span/thickness ratios encountered in practical applications.  ...  Tables VIII and IX investigate the influences of acceleration on the rate of convergence in the case of FST and ANS meshes, respectively.  ... 
doi:10.1002/(sici)1097-0207(19960415)39:7<1181::aid-nme899>3.0.co;2-y fatcat:4sv4hgiocvcbraesjbwpg6rw4i

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive coarsening [article]

James Brannick, Xiaozhe Hu, Carmen Rodrigo, Ludmil Zikatanov
2014 arXiv   pre-print
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace  ...  The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.  ...  Carmen Rodrigo gratefully acknowledges the hospitality of the Center for Computational Mathematics and Applications and  ... 
arXiv:1310.8385v2 fatcat:mgh4gkcxfjf7papetuka7d5odm

Многосеточные методы с косо-эрмитовыми сглаживателями для задач конвекции–диффузии с преобладающей конвекцией
Multigrid methods with skew-Hermitian based smoothers for the convection–diffusion problem with dominant convection

T.S. Martynova, G.V. Muratova, I.N. Shabas, V.V. Bavin
2022 Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie)  
The convection–diffusion equation with dominant convection is considered on a uniform grid of central difference scheme.  ...  It is demonstrated that using the proper smoothers enables to improve the convergence of the multigrid method.  ...  One of the universal methods for solving difference equations is the Fedorenko geometric multigrid method (GMG) [11] based on the use of a sequence of nested grids and transition operators from one grid  ... 
doi:10.26089/nummet.v23r104 fatcat:e7hcxyguafgm7py7ko7lykwbyy

Multigrid finite element methods on semi-structured triangular grids for planar elasticity

F. J. Gaspar, F. J. Lisbona, J. L. Gracia, C. Rodrigo
2009 Numerical Linear Algebra with Applications  
to investigate how the grid-geometry has influence on the convergence properties of multigrid methods.  ...  method on each triangular block of the coarsest grid.  ... 
doi:10.1002/nla.684 fatcat:lkr45anljrhs7kdezb72mwntxu

On The Parallel Multiblock Geometric Multigrid Algorithm

R. CIEGIS, F. GASPAR, C. RODRIGO
2008 Computational Methods in Applied Mathematics  
A new strategy for the solution of the discrete problem on the coarsest grid is proposed and the efficiency of the obtained algorithm is investigated.  ...  The application of a parallel multiblock geometric multigrid is considered. It is applied to solve a two-dimensional poroelastic model.  ...  3691 OPTCABLES and by the Lithuanian State Science and Studies Foundation as part of the project on B-03/2008 "Global optimization of complex systems using high performance computing and GRID technologies  ... 
doi:10.2478/cmam-2008-0016 fatcat:qal22snkxjd7bkrw7wv4cvtgwy

Tuning Multigrid Methods with Robust Optimization [article]

Jed Brown and Yunhui He and Scott MacLachlan and Matt Menickelly and Stefan M. Wild
2020 arXiv   pre-print
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods  ...  of a symbol representation of the algorithm.  ...  S.M. and Y.H. thank Professor Michael Overton for discussing the use of HANSO for this optimization problem during his visit to Memorial University in 2018.  ... 
arXiv:2001.00887v2 fatcat:qjp7wthza5cenodhanpwov4biu

A node-based agglomeration AMG solver for linear elasticity in thin bodies

Prasad S. Sumant, Andreas C. Cangellaris, Narayana R. Aluru
2009 Communications in Numerical Methods in Engineering  
Several case studies are taken up to validate the approach.  ...  A new, node-based agglomeration scheme is proposed for computationally efficient, aggressive and yet effective generation of coarse grids.  ...  A case study involving a two-grid approach on a square domain was used to demonstrate the validity of their method.  ... 
doi:10.1002/cnm.1116 fatcat:d7xxo3me5rc5tl6fvzuib2ig4u

On the robustness of the multigrid method combining ILU and Partial Weight applied in an orthotropic diffusion problem

G. Vassoler Rutz, M. Augusto Villela Pinto, S. de FátimaTomazzoni Gonçalves
2019 Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería  
Local Fourier Analysis (LFA) is carried out in order to increase the efficiency of the multigrid method. Pure diffusion with orthotropy aligned to the coordinate axis x is the model considered.  ...  Equations are discretized by Finite Difference Method with uniform grid and second-order numerical scheme.  ...  Acknowledgements The authors would like to acknowledge the Graduate Program in Numerical Methods for Engineering (PPGMNE) of the Federal University of Parana (UFPR).  ... 
doi:10.23967/j.rimni.2019.03.001 fatcat:zyr5h2no6bfp7jp3ruomuzcgq4

The ILU method for finite-element discretizations

Stefan Sauter
1991 Journal of Computational and Applied Mathematics  
In Section 3 we shall study the influence of the grid for the stability of the ILU iteration and give a somewhat surprising example, which makes us optimistic with regard to a generalization of the theoretical  ...  But up to now a restricting fact of the method was that, apparently, the algorithm can only be applied efficiently to finite-difference discretizations on rectangular grids.  ...  I am deeply indepted to Gabriel Wittum, from whom I learned much about the ILU decomposition, and who suggested to transfer the method to finite elements.  ... 
doi:10.1016/0377-0427(91)90228-c fatcat:vasf7yro7fg2xoxdhsy5bcclsa

Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media [article]

Andrés Arrarás, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
2018 arXiv   pre-print
to a mixed-dimensional multigrid method.  ...  Several numerical experiments are presented to demonstrate the robustness of the monolithic mixed-dimensional multigrid method with respect to the permeability of the fractures, the grid size and the number  ...  Smoother The performance of a multigrid method is essentially influenced by the smoothing algorithm.  ... 
arXiv:1811.01264v1 fatcat:ff7si4k6ebdifearg4qtzlqawy

An agglomeration-based adaptive discontinuous Galerkin method for compressible flows

G. Zenoni, T. Leicht, A. Colombo, L. Botti
2017 International Journal for Numerical Methods in Fluids  
In this work we exploit the possibility to devise Discontinuous Galerkin discretizations over polytopic grids to perform grid adaptation strategies based on agglomeration coarsening of a fine grid obtained  ...  test cases.  ...  In these works, for a model equation, a detailed study of the gains in terms of quadrature points number and, for some cases, CPU time is reported.  ... 
doi:10.1002/fld.4390 fatcat:ntbptlkgsvdu5ayt7wcxbg4p3a

Performance of Geometric Multigrid Method forTwo-Dimensional Burgers' Equations with Non-Orthogonal, Structured Curvilinear Grids

Daiane Cristina Zanatta, Luciano Kiyoshi Arak, Marcio Augusto Villela Pinto, Diego FernandoMoro
2020 CMES - Computer Modeling in Engineering & Sciences  
Therefore, several parameters of multigrid method and solvers were tested for the problem, with the use of nonorthogonal structured curvilinear grids and multigrid method, resulting in an algorithm with  ...  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  ...  Acknowledgement: The first author would like to thank the State University of Centro-Oeste (UNICENTRO) for granting a financial support and full leave of absence from teaching activities.  ... 
doi:10.32604/cmes.2020.012634 fatcat:eei72fwzxnduzhhgcwtdqnzt2m

Parallel multilevel methods with adaptivity on unstructured grids

Xing Cai, Klas Samuelsson
2000 Computing and Visualization in Science  
As the foundation of the methods we propose an algorithm for generating and partitioning a hierarchy of adaptively refined unstructured grids, so that adaptivity can be incorporated up to a certain grid  ...  We present two parallel multilevel methods for solving large-scale discretized partial differential equations on unstructured 2D/3D grids.  ...  This work has received support from The Research Council of Norway (Programme for Supercomputing) through a grant of computing time.  ... 
doi:10.1007/pl00013543 fatcat:uea7o2bwkvhyvkf55oc53xry4e

Higher-order finite element discretizations in a benchmark problem for incompressible flows

Volker John, Gunar Matthies
2001 International Journal for Numerical Methods in Fluids  
The discrete systems obtained with higher-order discretizations are solved with a modified coupled multigrid method whose behaviour within the benchmark problem is also studied numerically. 886 capabilities  ...  The discrete problems obtained with higher-order discretizations are solved by a modified coupled multigrid method with Vanka-type smoothers.  ...  ACKNOWLEDGMENTS The work of the second author was supported by the Deutsche Forschungsgemeinschaft (DFG) by grant En278/2-1. Figure 2 was plotted using the software package GRAPE.  ... 
doi:10.1002/fld.195 fatcat:5ppyy564kbarbe3qwmzf7t2nka
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