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Design Considerations for a Flexible Multigrid Preconditioning Library

Jérémie Gaidamour, Jonathan Hu, Chris Siefert, Ray Tuminaro
2012 Scientific Programming  
MueLu is a library within the Trilinos software project [An overview of Trilinos, Technical Report SAND2003-2927, Sandia National Laboratories, 2003] and provides a framework for parallel multigrid preconditioning  ...  This article gives an overview of design considerations for the MueLu package: user interfaces, internal design, data management, usage of modern software constructs, leveraging Trilinos capabilities,  ...  Conclusion In this paper we have presented a flexible design for a multigrid preconditioning library, MueLu.  ... 
doi:10.1155/2012/310508 fatcat:p5g4rq4oyvd5blluoia7tx4zy4

AMGCL: an Efficient, Flexible, and Extensible Algebraic Multigrid Implementation [article]

Denis Demidov
2018 arXiv   pre-print
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of  ...  The design principles behind AMGCL are discussed and it is shown that the code performance is on par with alternative implementations.  ...  For example, the CUSP library provides implementation of smoothed aggregation multigrid [5, 12] , but only supports NVIDIA hardware.  ... 
arXiv:1811.05704v1 fatcat:mm7g2qegjfgz3c5n3pyj5uifym

On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level Schwarz

R. S. Tuminaro, C. H. Tong, J. N. Shadid, K. D. Devine, D.M. Day
2002 Communications in Numerical Methods in Engineering  
To facilitate use, a multilevel preconditioner software module, ML, has been constructed.  ...  This report discusses the implementation of one method in the module: a two-level Krylov-Schwarz preconditioner.  ...  CONCLUSIONS Multigrid technology has received considerable attention in recent years due to its fast convergence rates compared to classical preconditioning methods.  ... 
doi:10.1002/cnm.478 fatcat:wlwjefuecrccxib4wdufj3nxwu

Tusas: A fully implicit parallel approach for coupled phase-field equations [article]

Supriyo Ghosh, Christopher K. Newman, Marianne M. Francois
2021 arXiv   pre-print
with a preconditioned Jacobian-free Newton-Krylov method.  ...  We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations.  ...  Department of Energy's Office of Science and National Nuclear Security Administration, responsible for delivering a capable exascale ecosystem, including software, applications, and hardware technology  ... 
arXiv:2006.16764v2 fatcat:xowucvwwyfc4jpujrueyl6a4yq

A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Georg May, Francesca Iacono, Antony Jameson
2010 Journal of Computational Physics  
We use such tools as efficient numerical libraries and automatic differentiation (AD) to obtain a flexible platform for high-order CFD computations. This is discussed in Section 4.  ...  Alternatively this may be viewed as a preconditioning procedure for the nonlinear Newton method.  ...  The US Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon.  ... 
doi:10.1016/ fatcat:itfmvrzmz5gubfcboz6vywkrj4

SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods [article]

Sashikumaar Ganesan, Manan Shah
2020 arXiv   pre-print
Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented.  ...  Combining the hybrid AMG framework as a preconditioner with Krylov Subspace solvers like Conjugate Gradient, BiCG methods provides a solver stack to solve a large class of problems.  ...  = b -Ax 0 , z 0 = M −1 r 0 Perform one AMG cycle on Az 0 = r 0 4: p 0 = z 0 5: for j = 0,1,.... till || r j ||> tol do 6: Algorithm 3. 2 2 Preconditioned Flexible BiCG Algorithm 1: INPUT: A: n × n sparse  ... 
arXiv:2007.00056v1 fatcat:mgk2apk6tfevjnhx2iguxemq4q

Extreme-scale Multigrid Components within PETSc [article]

Dave A. May, Patrick Sanan, Karl Rupp, Matthew G. Knepley, Barry F. Smith
2016 arXiv   pre-print
Lastly, we demonstrate via numerical experiments employing geometric multigrid with structured meshes, the flexibility and performance gains possible using our MPI-rank agglomeration implementation.  ...  Multilevel preconditioners represent a family of scalable techniques for solving discrete PDEs of this type and thus are the method of choice for high-resolution simulations.  ...  Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public  ... 
arXiv:1604.07163v1 fatcat:gpnszozdfzhepjv7xrkqmdvj7y

FLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solver

M. Rasquin, H. Deconinck, G. Degrez
2010 International Journal for Numerical Methods in Engineering  
A new library called FLEXMG has been developed for a spectral/finite-element incompressible flow solver called SFELES.  ...  FLEXMG allows to use various types of iterative solvers preconditioned by algebraic multigrid methods.  ...  Fabien Delalondre (Rensselaer Polytechnic Institute) is also warmly acknowledged for his suggestions about some possible smoothing strategies for the aggregation-type multigrid.  ... 
doi:10.1002/nme.2808 fatcat:uji3q2jwxjdazh36jigsdh4pfq

Analysis and Practical Use of Flexible BiCGStab

Jie Chen, Lois C. McInnes, Hong Zhang
2016 Journal of Scientific Computing  
A flexible version of the BiCGStab algorithm for solving a linear system of equations is analyzed.  ...  Hence, in order to maintain a similar convergence behavior to BiCGStab while reducing the preconditioning cost, the flexible version can be used with a moderate tolerance in the preconditioning Krylov  ...  Acknowledgements We thank Satish Balay, Jed Brown and Barry Smith for insightful discussions and assistance with experiments.  ... 
doi:10.1007/s10915-015-0159-4 fatcat:22xmk7qvd5ffxpvbhaiwm6lefm

Accelerating linear solvers for Stokes problems with C++ metaprogramming [article]

Denis Demidov, Lin Mu, Bin Wang
2020 arXiv   pre-print
The approach is based on the policy-based design pattern and partial template specialization, and is implemented in the open source AMGCL library.  ...  We evaluate both monolithic and composite preconditioning strategies for the 3 benchmark problems.  ...  To illustrate this, listing 1 defines a GMRES iterative solver preconditioned with the algebraic multigrid (AMG).  ... 
arXiv:2006.06052v3 fatcat:ykn2yblg7fgnfivr4adi4ja2bq

Tolerating Silent Data Corruption in Opaque Preconditioners [article]

James Elliott and Mark Hoemmen and Frank Mueller
2014 arXiv   pre-print
We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both implemented in the Trilinos library.  ...  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.  ...  Algebraic Multigrid Preconditioning Next, we consider solving the SPD Poisson problem. This problem is suitable for CG or GMRES, and MueLu is a very effective preconditioner.  ... 
arXiv:1404.5552v1 fatcat:p7c5netlirgn3gxravleundhz4

Scalable computation of thermomechanical turbomachinery problems [article]

Chris N. Richardson, Nathan Sime, Garth N. Wells
2018 arXiv   pre-print
We seek to dispel this notion by presenting performance data for a collection of realistic, large-scale thermomechanical simulations.  ...  A commonly held view in the turbomachinery community is that finite element methods are not well-suited for very large-scale thermomechanical simulations.  ...  Acknowledgements We thank Dr Mark Adams of Lawrence Berkeley National Laboratory for his advice on the use of smoothed aggregation AMG.  ... 
arXiv:1804.10060v1 fatcat:2c4sbmv7nne37iyabqunx2u62a

Mantle Convection Modeling with Viscoelastic/Brittle Lithosphere: Numerical and Computational Methodology [chapter]

Louis Moresi, David May, Justin Freeman, Bill Appelbe
2003 Lecture Notes in Computer Science  
The specialized code shows better scaling for a single processor. The parallel scaling of the general code is very flat for "realistic" problem sizes indicating efficient use of multiple processors.  ...  A Lagrangian Integration point finite element method is discussed which can simulate very large deformation viscoelasticity with a strain-dependent yield stress.  ...  In the parallel code (SNARK ), we sought a more general implementation which would be suitable for a broader range of problems, with a more flexible code design (See the paper by Appelbe et al in this  ... 
doi:10.1007/3-540-44863-2_76 fatcat:auvdawr3rnapndpeiu7fl5b3ti

Preparing sparse solvers for exascale computing

Hartwig Anzt, Erik Boman, Rob Falgout, Pieter Ghysels, Michael Heroux, Xiaoye Li, Lois Curfman McInnes, Richard Tran Mills, Sivasankaran Rajamanickam, Karl Rupp, Barry Smith, Ichitaro Yamazaki (+1 others)
2020 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Sparse solvers provide essential functionality for a wide variety of scientific applications.  ...  This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.  ...  This lack of a unified approach poses a considerable challenge on the software stack in general.  ... 
doi:10.1098/rsta.2019.0053 pmid:31955673 fatcat:bqw6xqixbrabddmxglmtcbw2wa

Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc

A. V. Knyazev, M. E. Argentati, I. Lashuk, E. E. Ovtchinnikov
2007 SIAM Journal on Scientific Computing  
BLOPEX is available as a stand-alone serial library, as an external package to PETSc ("Portable, Extensible Toolkit for Scientific Computation", a general purpose suite of tools for the scalable solution  ...  , and IBM BlueGene/L supercomputer, using PETSc domain decomposition and hypre multigrid preconditioning.  ...  We thank Jose Roman, a member of SLEPc team, for writing the SLEPc interface to our hypre LOBPCG.  ... 
doi:10.1137/060661624 fatcat:juhy2srxi5gxjafyc232q2ofym
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