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10. A Survey of Parallelization Techniques for Multigrid Solvers [chapter]

Edmond Chow, Robert D. Falgout, Jonathan J. Hu, Raymond S. Tuminaro, Ulrike Meier Yang
2006 Parallel Processing for Scientific Computing  
This paper surveys the techniques that are necessary for constructing computationally efficient parallel multigrid solvers. Both geometric and algebraic methods are considered.  ...  We then cover the parallelism issues that must be addressed: parallel smoothing and coarsening, operator complexity, and parallelization of the coarsest grid solve.  ...  A Survey of Parallelization Techniques for Multigrid Solvers plane at a time in relaxation would incur a communication overhead that is too great and that depends on N .  ... 
doi:10.1137/1.9780898718133.ch10 fatcat:q72n4g5jybbtzeawtcyvjjxecy

Parallel Gradient Domain Processing of Massive Images [article]

Sujin Philip, Brian Summa, Peer-Timo Bremer, Valerio Pascucci
2011 Eurographics Symposium on Parallel Graphics and Visualization  
Specifically, we provide a parallel out-of-core method for the seamless stitching of gigapixel panoramas in a parallel MPI environment.  ...  In this paper, we provide a simple framework for the parallel gradient domain processing.  ...  This work was also performed under the auspices of the U.S.  ... 
doi:10.2312/egpgv/egpgv11/011-019 fatcat:nlqsxem4vnfg5alszdfcaqhmaa

Distributed gradient-domain processing of planar and spherical images

Michael Kazhdan, Dinoj Surendran, Hugues Hoppe
2010 ACM Transactions on Graphics  
We demonstrate our contributions on several datasets including the Digitized Sky Survey, a terapixel spherical scan of the night sky.  ...  The solver partitions images into bands, streams through these bands in parallel within a networked cluster, and schedules computation to hide the necessary synchronization latency.  ...  for sharing their image data.  ... 
doi:10.1145/1731047.1731052 fatcat:yunat5wt6re4bozfxq2wwhkiz4

Multigrid Algorithms for Optimal Engineering Computations

P.K. Jimack
2010 Computational Technology Reviews  
A discussion of some of the most significant applications of multigrid for the solution of computational engineering problems is provided and two specific case studies are considered in more detail.  ...  Multigrid methods are becoming increasingly popular within engineering software and this chapter provides a general introduction to the topic, including a short survey and selected case studies.  ...  Acknowledgements The author gratefully acknowledges the substantial contributions of his numerous research collaborators in the development and application of multigrid methods.  ... 
doi:10.4203/ctr.1.3 fatcat:nhkwfg2nxbh7fn5fgbemmjviyy

An approach for 3D multisource, multifrequency CSEM modeling

R.-E. Plessix, M. Darnet, W. A. Mulder
2007 Geophysics  
Numerical examples show the usefulness of this approach for survey design and scenario studies over complex heterogeneous structures, when the layered-earth assumption is not satisfactory.  ...  The approach consists of an efficient iterative multigridbased solver and an automatic gridding procedure.  ...  For multifrequency, multisource CSEM modeling, we parallelized over sources and frequencies, but we did not parallelize the solver.  ... 
doi:10.1190/1.2744234 fatcat:o3ykgb5odrhfviswdpw5zuvuj4

Page 489 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
An advantage of the latter approach, however, is the fact that it allows the straightforward implementation of a multigrid solver for the resulting system which is discussed, too.”  ...  Summary: “Previously a semicoarsening multigrid algorithm suitable for use on data parallel architectures was investigated.  ... 

Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU

Dominik Goddeke, Hilmar Wobker, Robert Strzodka, Jamaludin Mohd Yusof, Patrick McCormick, Stefan Turek
2009 International Journal of Computational Science and Engineering (IJCSE)  
Feast is a hardware-oriented MPI based Finite Element solver toolkit.  ...  We present accuracy experiments, a scalability test and acceleration results for different elastic objects under load.  ...  Also thanks to NVIDIA and AMD for donating hardware that was used in developing the serial version of the GPU backend.  ... 
doi:10.1504/ijcse.2009.029162 fatcat:apmjkuwxc5bufjipmr2jwnpja4

Asynchronous Parallel Solvers for Linear Systems arising in Computational Engineering

P.K. Jimack, M.A. Walkley
2011 Computational Technology Reviews  
A consequence of this is that over the next decade it will be necessary to develop and apply new numerical algorithms that are far more scalable than has historically been required.  ...  Particular emphasis is placed on the need to develop asynchronous and fault tolerant software that is built upon the most efficient underlying methods, such as multigrid and other multilevel algorithms  ...  Acknowledgements The authors acknowledge the Engineering and Physical Science Research Council (EPSRC) for their financial support for this work through grant number EP/I006737/1.  ... 
doi:10.4203/ctr.3.1 fatcat:6ho4zlpt6vdqbkubltrfnm57cq

Fault-tolerant finite-element multigrid algorithms with hierarchically compressed asynchronous checkpointing

Dominik Göddeke, Mirco Altenbernd, Dirk Ribbrock
2015 Parallel Computing  
We examine novel fault tolerance schemes for data loss in multigrid solvers which essentially combine ideas of checkpoint-restart with algorithm-based fault tolerance.  ...  A performance model gives further insight into the benefits and applicability of our techniques.  ...  We would like to thank Sven Buijssen, Stefan Turek and Peter Zajac for helpful discussions.  ... 
doi:10.1016/j.parco.2015.07.003 fatcat:u3wjo6rlyje73f3g5bimuajos4

FEAST-realization of hardware-oriented numerics for HPC simulations with finite elements

Stefan Turek, Dominik Göddeke, Christian Becker, Sven H. M. Buijssen, Hilmar Wobker
2010 Concurrency and Computation  
FEAST (Finite Element Analysis & Solutions Tools) is a Finite Element based solver toolkit for the simulation of PDE problems on parallel HPC systems which implements the concept of 'hardware-oriented  ...  numerics', a holistic approach aiming at optimal performance for modern numerics.  ...  Thanks to NVIDIA for donating hardware that was used in the development of Feast's GPU backend.  ... 
doi:10.1002/cpe.1584 fatcat:6omy4woanrbn7dqigs3q4ql5hq

Using GPUs to improve multigrid solver performance on a cluster

Dominik Goddeke, Robert Strzodka, Jamaludin Mohd Yusof, Patrick McCormick, Hilmar Wobker, Christian Becker, Stefan Turek
2008 International Journal of Computational Science and Engineering (IJCSE)  
This article explores the coupling of coarse and fine-grained parallelism for Finite Element simulations based on efficient parallel multigrid solvers.  ...  From a software perspective, we integrate the GPU solvers into the existing MPI-based Finite Element package by implementing the same interfaces as the CPU solvers, so that for the application programmer  ...  In the context of a (parallel) multigrid solver, this assigns the GPU the task of a local smoother.  ... 
doi:10.1504/ijcse.2008.021111 fatcat:dneg67kvhnc5hjjeocpaji3oxi

Page 5344 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Computa- tional complexity of multigrid waveform relaxation, which shows that the complexity of these techniques is comparable to that of the best sequential solvers for initial-boundary value problems  ...  ISBN 3-519-02717-8 The multigrid waveform relaxation method is a technique devel- oped in the last decade in order to allow an optimal use of the pos- sibilities of the recent parallel systems in solving  ... 

GPU acceleration of an unmodified parallel finite element Navier-Stokes solver

Dominik Goddeke, Sven H.M. Buijssen, Hilmar Wobker, Stefan Turek
2009 2009 International Conference on High Performance Computing & Simulation  
In this paper we explore the limitations of our approach by accelerating a Navier-Stokes solver.  ...  We have previously suggested a minimally invasive approach to include hardware accelerators into an existing large-scale parallel finite element PDE solver toolkit, and implemented it into our software  ...  Thanks to NVIDIA for donating hardware.  ... 
doi:10.1109/hpcsim.2009.5191718 dblp:conf/ieeehpcs/GoddekeBWT09 fatcat:mm4tch3fjnc3vgmh7hxkdnrq6u

Parallel 3d shape optimization for cellular composites on large distributed-memory clusters [article]

Jose Pinzon and Martin Siebenborn and Andreas Vogel
2020 arXiv   pre-print
This article aims at applying shape optimization to compute cell size and arrangement for elastic energy minimization of a cellular composite material model for the upper layer of the human skin.  ...  A scaling study is presented for up to 12,288 cores and 3 billion DoFs.  ...  The authors gratefully acknowledge the HLRS for supporting this project by providing computing time on the GCS Supercomputer Hazel Hen and their kind support.  ... 
arXiv:2003.09683v1 fatcat:v6e2fwccvvawbjscgefzfojryq

Parallel 3d shape optimization for cellular composites on large distributed-memory clusters

Jose Pinzon, Martin Siebenborn, Andreas Vogel
2020 Journal of Advanced Simulation in Science and Engineering  
This article aims at applying shape optimization to compute cell size and arrangement for elastic energy minimization of a cellular composite material model for the upper layer of the human skin.  ...  A scaling study is presented for up to 12,288 cores and 3 billion DoFs.  ...  The authors gratefully acknowledge the HLRS for supporting this project by providing computing time on the GCS Supercomputer Hazel Hen and their kind support.  ... 
doi:10.15748/jasse.7.117 fatcat:4dnlnlgmjffzhfcqk4h2w47tgi
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