Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

Iwashita, Takeshi; Nakashima, Hiroshi; Takahashi, Yasuhito

doi:10.1109/ipdps.2012.51

Cited by 38 publications

(41 citation statements)

References 38 publications

(39 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm is selected to obtain the desired degree of parallelism and load balance on each color to ensure the effectiveness of MS-BMC-GS. This algorithm combines a greedy approach with algebraic block multi-coloring [10]. Two parameters need to be specified for block multi-coloring: the size of the block and the number of colors.…”

Section: Coloring Algorithm For Ms-bmc-gsmentioning

confidence: 99%

“…Various parallelized GS smoothers, such as the hybrid method [9,19], MC-GS [1,7,13,17], and BMC-GS [2,10] have been developed. The hybrid smoother uses the weighted Jacobi to remove the data dependencies of the GS smoother among the separated units.…”

Section: Related Workmentioning

confidence: 99%

“…Multi-color Gauss-Seidel (MC-GS) [1] [13][17] is a method designed to exploit the parallelism of the GS method, it leads to inferior data locality, which decreases the cache hit rate. The block multi-color Gauss-Seidel (BMC-GS) [2] [10] improves the data locality such that it equals that of sequential GS.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods

Kawai

Ida

Matsuba

et al. 2020

Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region

View full text Add to dashboard Cite

In this paper, we propose a multiplicative Schwartz-type block multicolor Gauss-Seidel (MS-BMC-GS) smoother for algebraic multigrid (AMG) methods. AMG is an excellent solver and one of the most effective preconditioners for Krylov subspace methods such as the conjugate gradient method. The achievable degree of parallelism, convergence ratio, and computational cost of AMG strongly depend on the chosen smoother. As multiple unknowns are relaxed simultaneously, the MS-BMC-GS smoother realizes higher convergence than the existing parallel Gauss-Seidel smoother. Although this increases the amount of computation, the increase in the computational time is mitigated by the high cache hit ratio owing to the novel blocking technique. Numerical experiments demonstrate that MS-BMC-GS outperforms the block multi-color GS smoother by 18%.

show abstract

Section: Coloring Algorithm For Ms-bmc-gsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods

Kawai

Ida

Matsuba

et al. 2020

Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region

View full text Add to dashboard Cite

show abstract

“…We have shown how we significantly outperform their implementation. Iwashita et al [12] proposed an approach that uses blocked coloring scheme to accelerate ICCG solver for multi-threaded execution. Their work was specific for ICCG and does not involve SIMD parallelism.…”

Section: Related Workmentioning

confidence: 99%

Exploiting recent SIMD architectural advances for irregular applications

Chen

Jiang

Agrawal

2016

Proceedings of the 2016 International Symposium on Code Generation and Optimization

View full text Add to dashboard Cite

A broad class of applications involve indirect or datadependent memory accesses and are referred to as irregular applications. Recent developments in SIMD architectures-specifically, the emergence of wider SIMD lanes, combination of SIMD parallelism with many-core MIMD parallelism, and more flexible programming APIs-are providing new opportunities as well as challenges for this class of applications. In this paper, we propose a general optimization methodology, to effectively optimize different subclasses of irregular applications. Based on the observation that all applications with indirect memory accesses can be viewed as sparse matrix computations, we design an optimization methodology, which includes three sub-steps: 1) locality enhancement through tiling, 2) data access pattern identification, and 3) write conflict removal at both SIMD and MIMD levels. This method has been applied to unstructured grids, molecular dynamics, and graph applications, in addition to sparse matrix computations. The speedups achieved by our single threaded vectorized code over serial code is up to 9.05, whereas the overall speedup while utilizing both SIMD and MIMD (61 cores in Intel Xeon Phi) with our approach is up to 467.1. Further optimization using matrix reordering on irregular reductions and graph algorithms is able to achieve an incremental speedup of up to 1.69, though at a relatively high preprocessing cost. Moreover, SpMM using our approach outperforms routines from a highly optimized commercial library by up to 2.81x.

show abstract

“…Since the changes which directly take advantage of the regular structure of the grid are not allowed in the optimization phase, algebraic block multicolor ordering [8] is used for the SymGS part. Table I shows the operations performed in one CG iteration.…”

Section: B Implementation Of Hpcg On Pezy-scmentioning

confidence: 99%

Implementation and Evaluation of Data-Compression Algorithms for Irregular-Grid Iterative Methods on the PEZY-SC Processor

Yoshifuji¹,

Sakamoto²,

Nitadori

et al. 2016

2016 6th Workshop on Irregular Applications: Architecture and Algorithms (IA3)

View full text Add to dashboard Cite

Abstract-Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with relatively low computational cost. However, the direction of the evolution of high-performance processors in the last two decades have caused serious degradation of the computational efficiency of iterative methods on irregular grids, because of relatively low memory bandwidth. Data compression can in principle reduce the necessary memory memory bandwidth of iterative methods and thus improve the efficiency. We have implemented several data compression algorithms on the PEZY-SC processor, using the matrix generated for the HPCG benchmark as an example. For the SpMV (Sparse Matrix-Vector multiplication) part of the HPCG benchmark, the best implementation without data compression achieved 11.6Gflops/chip, close to the theoretical limit due to the memory bandwidth. Our implementation with data compression has achieved 32.4Gflops. This is of course rather extreme case, since the grid used in HPCG is geometrically regular and thus its compression efficiency is very high. However, in real applications, it is in many cases possible to make a large part of the grid to have regular geometry, in particular when the resolution is high. Note that we do not need to change the structure of the program, except for the addition of the data compression/decompression subroutines. Thus, we believe the data compression will be very useful way to improve the performance of many applications which rely on the use of irregular grids.

show abstract

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

Cited by 38 publications

References 38 publications

Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods

Multiplicative Schwartz-Type Block Multi-Color Gauss-Seidel Smoother for Algebraic Multigrid Methods

Exploiting recent SIMD architectural advances for irregular applications

Implementation and Evaluation of Data-Compression Algorithms for Irregular-Grid Iterative Methods on the PEZY-SC Processor

Contact Info

Product

Resources

About