Design of Parallel BEM Analyses Framework for SIMD Processors

Journal of Information Processing

Ida

et al. 2022

A hierarchical matrix (H-matrix) is an approximated form that represents N × N correlations of N objects. H-matrix construction is achieved by dividing a matrix into submatrices (partitioning), followed by calculating these submatrices' element values (filling). Matrix partitioning consists of two steps: cluster tree (CT) construction, where objects are divided into clusters hierarchically; and block cluster tree (BCT) construction, which involves observing all cluster pairs at the same CT level that satisfies the admissibility condition. This study proposes two parallel implementation methods of partitioning operations on distributed memory systems (DMSs): distributed cluster tree construction (DCTC) and redundant cluster tree construction (RCTC). In DCTC, both CT and BCT constructions are parallelized using workers in all computing nodes. In RCTC, CT is constructed in every computing node redundantly by employing only intra-node work stealing. The BCT is then constructed in parallel using workers in all computing nodes. RCTC cannot achieve speedup using multiple computing nodes, but can eliminate the data exchange cost incurred by DCTC. We used the task-parallel language Tascell, which employs both intra-and inter-node work stealing, to handle arbitrary unbalanced tree construction and traversal on DMSs. Our RCTC implementations achieved a 1.11-1.20-fold speedup using up to 8 nodes × 36 workers in numerical experiments with 3D electric field analyses and N 10 8 .

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Section: Introductionmentioning

confidence: 99%

Parallelization of Matrix Partitioning in Hierarchical Matrix Construction on Distributed Memory Systems

Journal of Information Processing

Ida

et al. 2022

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“…H-matrix construction is achieved by dividing a matrix into submatrices (partitioning), followed by calculating the element values of these submatrices (filling). We can find many proposals [4], [5], [6], [7], [8], [9] to parallelize the filling operation and they are applied to H-matrix libraries such as Hlib [3] and HACApK [7], but the partitioning operation still remains sequential. This is partly because the cost of the partitioning operation is much lower compared to the filling operation, approximately one thousandth when N 10 6 .…”

Section: Introductionmentioning

confidence: 99%

“…This is partly because the cost of the partitioning operation is much lower compared to the filling operation, approximately one thousandth when N 10 6 . However, this cost is becoming considerable because hundreds of speedups have been achieved for the filling operation using MPI, GPU, and SIMD vectorization [4], [5], [9]. For example, Ref.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of Matrix Partitioning in Construction of Hierarchical Matrices using Task Parallel Languages

Journal of Information Processing

Nakashima

et al. 2019

Self Cite

A hierarchical matrix (H-matrix) is an approximated form that represents N × N correlations of N objects. H-matrix construction is achieved by partitioning a matrix into submatrices, followed by calculating the element values of these submatrices. This paper proposes implementations of matrix partitioning using task parallel languages, Cilk Plus and Tascell. Matrix partitioning is divided into two steps: cluster tree construction by dividing objects into clusters hierarchically, and block cluster tree construction by observing all cluster pairs at the same level of the cluster tree that satisfy an admissibility condition. As the two types of trees constructed and traversed in these steps are unpredictably unbalanced, it is expected that we can efficiently parallelize both these steps using task parallel languages. To obtain sufficient parallelism in the cluster tree construction, we not only execute recursive calls in parallel but also parallelize the inside of each recursive step. For the block cluster tree construction, we assigned each worker its own space so that the workers can store the cluster pairs without using locks. As a result, compared to a sequential implementation in C, we achieved up to an 11.5-fold speedup using Cilk Plus and a 12.6-fold speedup by Tascell for the cluster tree construction. For the block cluster tree construction, up to a 37.7-fold speedup by Cilk Plus and a 38.8-fold speedup using Tascell are achieved. In regard to the entire process of matrix partitioning, we achieved up to a 12.2-fold speedup by Cilk Plus and a 14.5-fold speedup using Tascell. All experiments were executed on two 18-core Xeon processors with real datasets to generate coefficient matrices used in the surface charge method.

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Construction of Hierarchical Matrix on Distributed Memory Systems using a Task Parallel Language

2022 Tenth International Symposium on Computing and Networking Workshops (CANDARW)

Ida

et al. 2022