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

Saxena, Gaurav; Jimack, Peter K.; Walkley, Mark A.

doi:10.1002/cpe.4328

Cited by 4 publications

(6 citation statements)

References 33 publications

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“…In [7] and [20] we formulated a strategy for minimizing the cache-misses of a sub-domain and showed the superiority of such partitions by experimenting on single grids and Geometric Multigrid, respectively . Overlap of communication with computation formed a significant part of our analytical derivation for cache-minimizing topologies.…”

Section: Discussionmentioning

confidence: 99%

“…In this work we tested our high level model for predicting optimal domain partitions on uniform structured 3-D grids developed in [7] and [20] for the more general cases of an AMR solver. The model in [7] demonstrated that communication minimization is not the sole criterion upon which mesh partitioning should be based and that it is essential to take into account the cache-misses for optimality.…”

Section: Discussionmentioning

confidence: 99%

“…Due to the combinatorial explosion of the possible topology space, optimality in the current work implies the best topology of those considered. We undertook our assessment based upon the model in [7], [20] and the use of the open source BoxLib library which we described briefly in the current work.…”

Section: Discussionmentioning

confidence: 99%

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A Cache-Aware Approach to Adaptive Mesh Refinement in Parallel Stencil-Based Solvers

Saxena

Jimack

Walkley

2017

2017 IEEE 19th International Conference on High Performance Computing and Communications; IEEE 15th International Conference On

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In prior-research the authors have demonstrated that, for stencil-based numerical solvers for Partial Differential Equations (PDEs), the parallel performance can be significantly improved by selecting sub-domains that are not cubic in shape (Saxena et. al., HPCS 2016, pp. 875-885). This is achieved through accounting for cache utilization in both the message passing and the computational kernel, where it is demonstrated that the optimal domain decompositions not only depend on the communication and load balance but also on the cache-misses, amongst other factors. In this work we demonstrate that those conclusions may also be extended to more advanced numerical discretizations, based upon Adaptive Mesh Refinement (AMR). In particular, we show that when basing our AMR strategy on the local refinement of patches of the mesh, the optimal patch shape is not typically cubic. We provide specific examples, with accompanying explanation, to show that communication minimizing strategies are not necessarily the best choice when applying AMR in parallel. All numerical tests undertaken in this work are based upon the open source BoxLib library.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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A Cache-Aware Approach to Adaptive Mesh Refinement in Parallel Stencil-Based Solvers

Saxena

Jimack

Walkley

2017

2017 IEEE 19th International Conference on High Performance Computing and Communications; IEEE 15th International Conference On

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“…We initialize MPI with the MPI THREAD FUNNELED thread support level and after domain partitioning [27,28], assign the sub-domains to individual MPI processes. Our implementation as of now supports only a 1-D x-decomposition (see Appendix A).…”

Section: Internal Design and Domain Partitioningmentioning

confidence: 99%

BioFVM-X: An MPI+OpenMP 3-D Simulator for Biological Systems

Saxena

León

Montagud

et al. 2021

Computational Methods in Systems Biology

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Multi-scale simulations require parallelization to address large-scale problems, such as real-sized tumor simulations. BioFVM is a software package that solves diffusive transport Partial Differential Equations for 3-D biological simulations successfully applied to tissue and cancer biology problems. Currently, BioFVM is only shared-memory parallelized using OpenMP, greatly limiting the execution of large-scale jobs in HPC clusters. We present BioFVM-X: an enhanced version of BioFVM capable of running on multiple nodes. BioFVM-X uses MPI+OpenMP to parallelize the generic core kernels of BioFVM and shows promising scalability in large 3-D problems with several hundreds diffusible substrates and $$\approx $$ ≈ 0.5 billion voxels. The BioFVM-X source code, examples and documentation, are available under the BSD 3-Clause license at https://gitlab.bsc.es/gsaxena/biofvm_x.

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“…Saxena et al provided a cost model that includes the traditional load‐balance between processors, the communication volume but also the cache misses to decompose optimally a matrix that may be 2D or 3D. The paper addresses a multi‐level decomposition, so that the model can take into account hybrid computers like a cluster of multi‐core computers.…”

Section: Hpc and Co: This Special Issuementioning

confidence: 99%

HPC & Co strike back: Where are distributed paradigms heading toward?

Limet

Merlo

Spalazzi

2018

Concurrency and Computation

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From the dawn of parallelization, the diffusion of High-Performance Computing (HPC) has grown exponentially until nowadays, thereby leading to the birth and development of a huge research community in this field. During the last decades, the important research results have led to extend the domain of HPC into three different dimensions, namely Architectures, Research Topics, and Application Domains. ArchitecturesTraditional HPC architectures have been sided with several wide-area distributed paradigms such as Peer-to-Peer (P2P), Grid, Cloud, Fog and PervasiveComputing. 1-3 Each of them aims new specific objectives along with the original goal of improving performance and reliability. In this paper, the different declinations of the traditional HPC are grouped into three macro-categories, namely SIMD, Multi- * , and Cluster.• SIMD. It stands for "single instruction, multiple data" according to the Flynn taxonomy. 4 This refers to computing systems where a single instruction stream operates on multiple data streams in order to perform operations that may be naturally parallelized (eg, array processors, GPUs, GPGPUs, etc). This category also includes many specialized processing units, as vector extensions of modern processors like Streaming SIMD Extensions (SSE) 5 or Advanced Vector Extensions (AVX). 6• Multi- * . It refers to many-core, multi-core, and multi-processor architectures. They are all architectures characterized by the presence of multiple instruction streams operating on multiple data streams. What distinguishes this type of architectures from other MIMD architectures ("multiple instructions, multiple data" always according to the Flynn taxonomy 4 ) is the sharing of the central memory.• Cluster. It refers to Cluster Computing, namely a group of cost-effective linked commercial off-the-shelf computers working together so closely that they act as a single machine. What distinguishes this type of architecture from other MIMD-like architectures is the absence of central memory sharing (each processing unit has its own private memory) but the presence of mass memory sharing. As a matter of fact, the current Top500 supercomputers 7 are mostly clusters.Regarding wide-area distributed paradigms, all of them are included in the MIMD category (according to the Flynn's taxonomy). What distinguishes this type of architecture from other MIMD architectures is the lack of sharing of both the central memory and the mass memory. This paper takes into consideration the main four distributed paradigms that arose from traditional HPC, namely Grid Computing, Ubiquitous Computing, Peer-to-Peer Computing, Cloud, and the emerging Fog Computing. In brief:• Grid Computing 8-10 denotes a distributed architecture that enables coordinated resource sharing for problem-solving within dynamic organizations consisting of individuals, institutions, and resources.• Ubiquitous Computing (also known as Pervasive Computing or UbiComp) 11,12 refers to making available to users computational resources, which provide information and servi...

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

Cited by 4 publications

References 33 publications

A Cache-Aware Approach to Adaptive Mesh Refinement in Parallel Stencil-Based Solvers

A Cache-Aware Approach to Adaptive Mesh Refinement in Parallel Stencil-Based Solvers

BioFVM-X: An MPI+OpenMP 3-D Simulator for Biological Systems

HPC & Co strike back: Where are distributed paradigms heading toward?

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