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Page 1254 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
How- ever, GMRES preconditioned with ILU and multigrid can take advantage of Jacobian freezing to produce an efficient scheme that is relatively independent of grid size and grid quality.”  ...  ; Austin, TX) A higher-order Godunov scheme coupled with dynamic local grid refinement for flow in a porous medium.  ... 

Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods [article]

Will Pazner
2020 arXiv   pre-print
We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing.  ...  The system is preconditioned using a spectrally equivalent low-order (p=1) finite element operator discretization on a refined mesh.  ...  Figure 2 . 2 Line and ILU smoothing: multigrid-preconditioned conjugate gradient iteration counts (residual reduction of 10 12 ) for a Poisson problem on a Cartesian grid.  ... 
arXiv:1908.07071v2 fatcat:squxophlcnfcfbc6qtirr7g64i

Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems

Michele Benzi, Daniel B. Szyld, Arno van Duin
1999 SIAM Journal on Scientific Computing  
Numerical experiments are presented whereby the effect of reorderings on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems is shown.  ...  It is shown that certain reorderings for direct methods, such as reverse Cuthill-McKee, can be very beneficial.  ...  Hwajeong Choi and Jacko Koster provided some of the codes which were used for the numerical experiments.  ... 
doi:10.1137/s1064827597326845 fatcat:jt6zzc6kpnewhhqrxvlwrnpssy

Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics

Mark F. Adams
2004 Numerical Linear Algebra with Applications  
We discuss constraint coarsening strategies for constructing multigrid coarse grid spaces and several classes of multigrid smoothers for these systems.  ...  This paper develops a general framework for applying algebraic multigrid techniques to constrained systems of linear algebraic equations that arise in applications with discretized PDEs.  ...  The ILU preconditioner is the processor local, level fill, ILU method in PETSc with a level fill of one.  ... 
doi:10.1002/nla.374 fatcat:korhfe34ibdblkchoikb5h7t2e

Solvers for the cardiac bidomain equations

E.J. Vigmond, R. Weber dos Santos, A.J. Prassl, M. Deo, G. Plank
2008 Progress in Biophysics and Molecular Biology  
The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue.  ...  Due to the highly nonlinear nature of the ODEs, fully implicit solutions are extremely difficult. A sophisticated approach is found in Ref.  ...  Preconditioned Conjugate Gradient with ILU preconditioning (PCG-ILU) has been implemented on both types of platforms.  ... 
doi:10.1016/j.pbiomolbio.2007.07.012 pmid:17900668 pmcid:PMC2881536 fatcat:4zwhqsv4cvcltmac3slbbokday

Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

W.Kyle Anderson, Russ D. Rausch, Daryl L. Bonhaus
1996 Journal of Computational Physics  
An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described.  ...  The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized  ...  Acknowledgments The authors would like to thank Shahyar Pirzadeh for generating the mesh for the wing with the partial-span flap as well as Jim Ross and Bruce Storms at the NASA Ames Research center for  ... 
doi:10.1006/jcph.1996.0219 fatcat:rjnsy4ojqfblbk7u3dmjkkousi

Application of implicit–explicit high order Runge–Kutta methods to discontinuous-Galerkin schemes

Alex Kanevsky, Mark H. Carpenter, David Gottlieb, Jan S. Hesthaven
2007 Journal of Computational Physics  
We demonstrate in a number of numerical test problems that IMEX methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid-induced  ...  Despite the popularity of high-order explicit Runge-Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very  ...  fully unstructured meshes.  ... 
doi:10.1016/j.jcp.2007.02.021 fatcat:lsv7rfnmhbf3rdweegpzwguyzu

Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods

J.N. Shadid, R.P. Pawlowski, J.W. Banks, L. Chacón, P.T. Lin, R.S. Tuminaro
2010 Journal of Computational Physics  
This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD.  ...  The nonlinear solver strategy employs Newton-Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners.  ...  An ILU preconditioned Newton-Krylov type solver is used for the flow equations and a direct sparse solver is used for the linear magnetics equation.  ... 
doi:10.1016/j.jcp.2010.06.018 fatcat:qubwtc354ba33k25bfqwayzdgq

Matrix Reordering Using Multilevel Graph Coarsening for ILU Preconditioning

Daniel Osei-Kuffuor, Ruipeng Li, Yousef Saad
2015 SIAM Journal on Scientific Computing  
However, for certain problems, ILU factorizations can yield factors that are unstable, and in some cases quite dense.  ...  Incomplete LU factorization (ILU) techniques are a well-known class of preconditioners, often used in conjunction with Krylov accelerators for the iterative solution of linear systems of equations.  ...  Schroeder for providing us with the data for the anisotropic examples presented in the experiments.  ... 
doi:10.1137/130936610 fatcat:2rxjx5klazed3gdrv3wfzwwsfm

Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

Jurjen Duintjer Tebbens, Miroslav Tůma
2007 SIAM Journal on Scientific Computing  
For example, it is successful in significantly decreasing the number of iterations of a preconditioned iterative method for solving subsequent systems of a sequence when compared with freezing the preconditioner  ...  We present a new approach for approximate updates of factorized nonsymmetric preconditioners for solving sequences of linear algebraic systems.  ...  The authors thank Philipp Birken and Ladislav Lukšan for providing the software for solving the nonlinear problems and for useful instructions to work with it.  ... 
doi:10.1137/06066151x fatcat:5bk4fknbzfdzhijjkzfukjpcvm

Approximate and Incomplete Factorizations [chapter]

Tony F. Chan, Henk A. Van der Vorst
1997 ICASE/LaRC Interdisciplinary Series in Science and Engineering  
However, there is still a practical need for preconditioning techniques that can be applied to a general matrix. Incomplete factorization preconditioners are among the candidates for this.  ...  Meijerink and Van der Vorst 75 considered these methods as incomplete factorizations and they proved the existence of ILU preconditioners for M-matrices.  ...  However, unlike for ILU, existence is not guaranteed for general M-matrices. Moreover, it is highly dependent on the ordering of the unknowns 57, 55 .  ... 
doi:10.1007/978-94-011-5412-3_6 fatcat:kxpalofz7vb35htjg7pvixeeoq

A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization

N. Umetani, S. P. MacLachlan, C. W. Oosterlee
2009 Numerical Linear Algebra with Applications  
Although our method extends to solving problems on unstructured grids, we focus here on heterogeneous Helmholtz problems on Cartesian grids.  ...  In particular, we compare preconditioners based on a point-wise Jacobi smoother with those using an ILU(0) smoother, we compare using the prolongation operator developed by de Zeeuw in [37] with interpolation  ...  This convergence is highly satisfactory for this real-life setting.  ... 
doi:10.1002/nla.634 fatcat:d37dissxy5bjhfbhlvbc5n7c4q

A parallel block multi-level preconditioner for the 3D incompressible Navier–Stokes equations

Howard C Elman, Victoria E Howle, John N Shadid, Ray S Tuminaro
2003 Journal of Computational Physics  
Previous work has focused on demonstrating the optimality of these preconditioners with respect to mesh size on serial, two-dimensional, steady-state computations employing geometric multi-grid methods  ...  Our results display nearly optimal convergence rates for steady-state solutions as well as for transient solutions over a wide range of CFL numbers on the two-dimensional and three-dimensional lid-driven  ...  For ILU, one ILU sweep is performed before and after the coarse grid correction on each V-cycle level.  ... 
doi:10.1016/s0021-9991(03)00121-9 fatcat:3jclab4abfg7jjdnj5qynq2zpa

Preconditioning Techniques for Large Linear Systems: A Survey

Michele Benzi
2002 Journal of Computational Physics  
For these reasons, there is a need for preconditioning techniques that are universally applicable.  ...  With a good preconditioner, the computing time for the preconditioned iteration should be significantly less than that for the unpreconditioned one.  ...  This had been pointed out by Dutto, who studied the effect of ordering on GMRES with ILU(0) preconditioning in the context of solving the compressible Navier-Stokes equations on unstructured grids [127  ... 
doi:10.1006/jcph.2002.7176 fatcat:5yzgrk7dn5cmjezhnweicab3tq

Multigrid Methods for the Stokes Equations using Distributive Gauss–Seidel Relaxations based on the Least Squares Commutator

Ming Wang, Long Chen
2013 Journal of Scientific Computing  
Based on that, an efficient multigrid method is developed for finite element discretizations of the Stokes equations on both structured grids and unstructured grids.  ...  It is much more efficient and robust than inexact Uzawa smoothers [4, 6, 60], especially on the unstructured grids.  ...  The authors also would like to thank two referees for their thorough review. The quality of the paper is improved by addressing their constructive comments and suggestions.  ... 
doi:10.1007/s10915-013-9684-1 fatcat:yxepbog2bbfzrf2q574eeda5uq
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