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Enhancing Performance and Robustness of ILU Preconditioners by Blocking and Selective Transposition

Anshul Gupta
2017 SIAM Journal on Scientific Computing  
to be computed economically, and it permits a trade-off with the restart parameter of GMRES to further improve the overall speed and robustness.  ...  Incomplete factorization is one of the most effective general-purpose preconditioning methods for Krylov subspace solvers for large sparse systems of linear equations.  ...  The author would like to thank Haim Avron, Thomas George, Rogeli Grima, Felix Kwok, and Lexing Ying. Pieces of software written by them over the years are included in WSMP's iterative solver package.  ... 
doi:10.1137/15m1053256 fatcat:sjbt4fk3pbfpjk26v4agjsf66u

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.  ...  The preconditioners used in this study are different variants of incomplete factorizations.  ...  Part of this research took place while the first author was with CERFACS and the second author was a visitor there. CERFACS's support and warm hospitality are greatly appreciated.  ... 
doi:10.1137/s1064827597326845 fatcat:jt6zzc6kpnewhhqrxvlwrnpssy

Tolerating Silent Data Corruption in Opaque Preconditioners [article]

James Elliott and Mark Hoemmen and Frank Mueller
2014 arXiv   pre-print
For a non-symmetric problem solved using GMRES and ILU, we show that at scale our fault tolerance approach incurs only 22% overhead for the worst case.  ...  We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both implemented in the Trilinos library.  ...  Should the inner solver uses a preconditioner, e.g., ILU, we then write FGmres->Gmres->ILU.  ... 
arXiv:1404.5552v1 fatcat:p7c5netlirgn3gxravleundhz4

SYMMETRIC INVERSE-BASED MULTILEVEL ILU PRECONDITIONING FOR SOLVING DENSE COMPLEX NON-HERMITIAN SYSTEMS IN ELECTROMAGNETICS

Bruno Carpentieri, Matthias Bollhöfer
2012 Electromagnetic Waves  
The results are highlighted by calculating the radar-cross-section of a full aircraft, and by a numerical comparison against other standard preconditioners.  ...  We show that the recently developed class of inverse-based multilevel incomplete LU factorization has very good potential to precondition these systems effectively.  ...  For the CFIE formulation, ILU preconditioners proved to be effective.  ... 
doi:10.2528/pier12041006 fatcat:b2ph4yfbobfyxjmxji3nzctaaq

Robust and Efficient Multilevel-ILU Preconditioning of Hybrid Newton-GMRES for Incompressible Navier-Stokes Equations [article]

Qiao Chen, Xiangmin Jiao, Oliver Yang
2021 arXiv   pre-print
convergence of the inner iterations in Newton-GMRES.  ...  We demonstrate the effectiveness of HILUNG by solving the standard 2D driven-cavity problem with Re 5000 and a 3D flow-over-cylinder problem with low viscosity.  ...  To address these challenges, we propose a new type of preconditioner for Newton-GMRES for the INS, based on a multilevel incomplete LU (MLILU) technique.  ... 
arXiv:2011.07410v3 fatcat:ktaraqrs6zalzkppirup65wju4

A Comparison of Preconditioned Krylov Subspace Methods for Large-Scale Nonsymmetric Linear Systems [article]

Aditi Ghai, Cao Lu, Xiangmin Jiao
2018 arXiv   pre-print
Our results show that GMRES tends to deliver better performance when coupled with an effective multigrid preconditioner, but it is less competitive with an ineffective preconditioner due to restarts.  ...  In this work, we present a comparison of some KSP methods, including GMRES, TFQMR, BiCGSTAB, and QMRCGSTAB, coupled with three classes of preconditioners, namely Gauss-Seidel, incomplete LU factorization  ...  of Science, Advanced Scientific Computing Research of the U.S.  ... 
arXiv:1607.00351v4 fatcat:62uskwa745gkdd7kvpooob47ly

Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels [article]

Jongmin Seo and Daniele E. Schiavazzi and Alison L. Marsden
2019 arXiv   pre-print
We focus on three approaches: the problem agnostic generalized minimum residual (GMRES) and stabilized bi-conjugate gradient (BICGS) methods, and a recently proposed, problem specific, bi-partitioned (  ...  In this study, we focus on the numerical simulation of cardiovascular hemodynamics with rigid and deformable walls, discretized in space and time through the variational multi-scale finite element method  ...  The authors would like to thank the two anonymous reviewers whose comments greatly contributed to improve the completeness of the present study.  ... 
arXiv:1901.07539v1 fatcat:pbpesguw3ng2pdpylixzmylszy

HILUCSI: Simple, Robust, and Fast Multilevel ILU for Large-Scale Saddle-Point Problems from PDEs [article]

Qiao Chen, Aditi Ghai, Xiangmin Jiao
2021 arXiv   pre-print
As a multilevel preconditioner, HILUCSI statically and dynamically permutes individual rows and columns to the next level for deferred factorization.  ...  We demonstrate the effectiveness of HILUCSI for dozens of benchmark problems, including those from the mixed formulation of the Poisson equation, Stokes equations, and Navier-Stokes equations.  ...  Matthias Bollhöfer for helpful discussions on ILUPACK and for sharing ILUPACK with us.  ... 
arXiv:1911.10139v4 fatcat:jthkh42hwnhgnattkniqv4xxra

Fast Preconditioned Krylov Methods for Boundary Integral Equations in Electromagnetic Scattering [chapter]

Bruno Carpentieri
2012 Trends in Electromagnetism - From Fundamentals to Applications  
In our experiments, the CORS method is the fastest non-Hermitian solver with respect to CPU time on most selected examples except GMRES with large restart.  ...  Comparison of standard preconditioners To illustrate the difficulty of finding a good preconditioner for this problem class, in Table 2 we report one experiments with the GMRES solver and various algebraic  ... 
doi:10.5772/32848 fatcat:ptw3r2zyunerrjejg4eelqqqm4

A comparison of GMRES and CGSTAB accelerations for incompressible Navier-Stokes problems

P. Chin, P.A. Forsyth
1993 Journal of Computational and Applied Mathematics  
Recently, incomplete LU preconditioned conjugate-gradient-type matrix solvers have been used in conjunction with Newton or Newton-like methods to solve the fully-coupled incompressible Navier-Stokes equations  ...  In this work, we compare GMRES and CGSTAB, a "stabilized" variant of CGS.  ...  Recently, Incomplete LU (ILU) preconditioned Conjugate-Gradient-type (CG) iterative solvers have been used effectively for these problems [ 3, 5, 13, 15, 18, 19, 25] and for other applications such as  ... 
doi:10.1016/0377-0427(93)90037-c fatcat:f4yftax2r5g7dp5u5viq3fgwc4

Linear systems solvers — recent developments and implications for lattice computations

A. Frommer
1997 Nuclear Physics B - Proceedings Supplements  
Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix.  ...  example of the Wilson fermion matrix.  ...  One therefore has to stop GMRES after a certain number (k, say) of iterations and restart the process with the current iterate x k as a new initial guess.  ... 
doi:10.1016/s0920-5632(96)00605-6 fatcat:vk63dblwpbbytandsv5zmoodkm

Algebraic preconditioners for the Fast Multipole Method in electromagnetic scattering analysis from large structures: trends and problems

Bruno Carpentieri
2009 Electronic Journal of Boundary Elements  
<div>The Fast Multipole Method was introduced by Greengard and Rokhlin in a seminal paper appeared in 1987 for studying large systems of particle interactions with reduced algorithmic and memory complexity  ...  Thanks to the use of iterative techniques and efficient parallel preconditioners, fast integral solvers involving tens of million unknowns are nowadays feasible and can be integrated in the design processes  ...  Convergence of GMRES preconditioned by the Frobenius-norm minimization approximate inverse is achieved only with large values of restart.  ... 
doi:10.14713/ejbe.v7i1.952 fatcat:wr272axot5arzplh5aqqdi7oaq

Factorization-Based Sparse Solvers and Preconditioners [chapter]

Xiaoye Sherry Li
2015 Series in Contemporary Applied Mathematics  
We present our recent work in using the direct solver SuperLU code base to develop a new supernode-based ILU preconditioner and a domain-decomposition hybrid solver.  ...  Efficient solution of large-scale, ill-conditioned and highly-indefinite algebraic equations often relies on high quality preconditioners together with iterative solvers.  ...  Acknowledgments This research was supported in part by the Director, Office of Science, Office of Advanced Scientific Computing Research, of the U.S. Department of Energy under Contract No.  ... 
doi:10.1142/9789814675772_0005 fatcat:gnzsqn34rjetxgag4kvopj4ili

Factorization-based sparse solvers and preconditioners

X S Li, M Shao, I Yamazaki, E G Ng
2009 Journal of Physics, Conference Series  
We present our recent work in using the direct solver SuperLU code base to develop a new supernode-based ILU preconditioner and a domain-decomposition hybrid solver.  ...  Efficient solution of large-scale, ill-conditioned and highly-indefinite algebraic equations often relies on high quality preconditioners together with iterative solvers.  ...  Acknowledgments This research was supported in part by the Director, Office of Science, Office of Advanced Scientific Computing Research, of the U.S. Department of Energy under Contract No.  ... 
doi:10.1088/1742-6596/180/1/012015 fatcat:z2zdblxjyrcfdpmhziydgrwhim

An efficient GPU version of the preconditioned GMRES method

José I. Aliaga, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí
2018 Journal of Supercomputing  
In a previous effort, we developed a GPU-aware version of the GMRES method included in ILUPACK, a package of solvers distinguished by its inverse-based multilevel ILU preconditioner.  ...  This situation has motivated the study and development of several iterative solvers, among which preconditioned Krylov subspace methods occupy a place of privilege.  ...  As a consequence, the transference overhead is more significant when the solver converges in only a few steps and does not approach the restart point of GMRES, which is set at 30 iterations in our experiments  ... 
doi:10.1007/s11227-018-2658-1 fatcat:iob4da2yabbollbvcleojyz55i
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