Modeling the Performance of an Algebraic Multigrid Cycle Using Hybrid MPI/OpenMP

Gahvari, Hormozd; Gropp, William; Jordan, Kirk E.; Schulz, Martin; Yang, Ulrike Meier

doi:10.1109/icpp.2012.41

Cited by 22 publications

(12 citation statements)

References 17 publications

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“…Most striking is the performance degradation on coarse grids when there is only one MPI task per node. The conventional wisdom from our past work is that introducing OpenMP improves coarse grid performance at the cost of fine grid performance [8]. The predictions of the performance model reflect this.…”

Section: Resultsmentioning

confidence: 84%

“…The model is based on a model we previously developed [7], [8], with an addition to take into account the simultaneous multithreading on Blue Gene/Q. We first present the original model, followed by the modifications to take SMT into account.…”

Section: Performance Modelmentioning

confidence: 99%

“…However, we do not use these in our model for Blue Gene/Q, as we do not expect there to be issues arising from this based on our experiences with other machines with strong interconnects, such as the Blue Gene/P [7] and Cray XK6 [8] machines we evaluated in our past work. To cover hybrid MPI/OpenMP, we penalize t i to take into account limited memory bandwidth resulting from threads contending when accessing memory shared by multiple cores.…”

Section: Instead Of Multiplying Bymentioning

confidence: 99%

“…If b j is the memory bandwidth per thread when running j OpenMP threads, then we multiply t i by b1 bj . In [8], there was also a penalty to take into account threads migrating to cores on different sockets; we do not apply this penalty on Blue Gene/Q as each node has only one processor.…”

Section: Instead Of Multiplying Bymentioning

confidence: 99%

“…To aid us in adapting AMG to Blue Gene/Q, we develop in this paper a performance model for the AMG solve cycle on Blue Gene/Q, and use it to analyze observed performance on a prototype system, highlighting issues that need to be addressed when adapting AMG to Blue Gene/Q. Our model builds upon our past work that featured performance models for AMG programmed entirely in a distributed memory model [7] and for AMG programmed in hybrid MPI/OpenMP [8], extending it to cover simultaneous multithreading.…”

Section: Introductionmentioning

confidence: 99%

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Performance Modeling of Algebraic Multigrid on Blue Gene/Q: Lessons Learned

Gahvari

Gropp

Jordan

et al. 2012

2012 SC Companion: High Performance Computing, Networking Storage and Analysis

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Abstract-The IBM Blue Gene/Q represents a large step in the evolution of massively parallel machines. It features 16-core compute nodes, with additional parallelism in the form of four simultaneous hardware threads per core, connected together by a five-dimensional torus network. Machines are being built with core counts in the hundreds of thousands, with the largest, Sequoia, featuring over 1.5 million cores. In this paper, we develop a performance model for the solve cycle of algebraic multigrid on Blue Gene/Q to help us understand the issues this popular linear solver for large, sparse linear systems faces on this architecture. We validate the model on a Blue Gene/Q at IBM, and conclude with a discussion of the implications of our results.

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Section: Resultsmentioning

confidence: 84%

Section: Performance Modelmentioning

confidence: 99%

Section: Instead Of Multiplying Bymentioning

confidence: 99%

Section: Instead Of Multiplying Bymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance Modeling of Algebraic Multigrid on Blue Gene/Q: Lessons Learned

Gahvari

Gropp

Jordan

et al. 2012

2012 SC Companion: High Performance Computing, Networking Storage and Analysis

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A quasi‐cache‐aware model for optimal domain partitioning in parallel geometric multigrid

Saxena

Jimack

Walkley

2017

Concurrency and Computation

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Summary Stencil computations form the heart of numerical simulations to solve Partial Differential Equations using Finite Difference, Finite Element, and Finite Volume methods. Geometric Multigrid is an optimal scriptOfalse(Nfalse), hierarchical tool employing stencil computations in its chief constituents, namely, smoothing, restriction, and interpolation. When Multigrid is parallelized over distributed‐shared memory architectures, traditionally, the domain partitioning creates cubic partitions of the mesh to minimize overall communication. Thus, the orthodox approach considers only load‐balancing and communication minimization for completely determining the domain partitioning. In this article, we show that these two factors are not sufficient to obtain optimal partitions for Parallel Geometric Multigrid. To this effect, we develop and validate a high level analytical model to show that “close to 2‐D” partitions for Geometric Multigrid can give higher performance than the partitions returned by the MPI_Dims_create() function which minimizes the communication volume by default. We quantify sub‐domain level cache‐misses in Parallel Geometric Multigrid and obtain families of optimal domain partitions. We conclude that the sub‐domain level cache‐misses for the application‐specific stencil computational kernel and communicated planes should be taken into account in addition to communication minimization/load‐balance to obtain optimal partitions for Parallel Geometric Multigrid.

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Improving Performance of the Hypre Iterative Solver for Uintah Combustion Codes on Manycore Architectures Using MPI Endpoints and Kernel Consolidation

Sahasrabudhe

Berzins

2020

Lecture Notes in Computer Science

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Modeling the Performance of an Algebraic Multigrid Cycle Using Hybrid MPI/OpenMP

Cited by 22 publications

References 17 publications

Performance Modeling of Algebraic Multigrid on Blue Gene/Q: Lessons Learned

Performance Modeling of Algebraic Multigrid on Blue Gene/Q: Lessons Learned

A quasi‐cache‐aware model for optimal domain partitioning in parallel geometric multigrid

Improving Performance of the Hypre Iterative Solver for Uintah Combustion Codes on Manycore Architectures Using MPI Endpoints and Kernel Consolidation

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