Mustafa Emre Sahin, A. Lebedev, M. Abaļenkovs, V. Alexandrov
{"title":"Usability of Markov Chain Monte Carlo Preconditioners in Practical Problems","authors":"Mustafa Emre Sahin, A. Lebedev, M. Abaļenkovs, V. Alexandrov","doi":"10.1109/ScalA54577.2021.00011","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00011","url":null,"abstract":"In this paper, we present the results of our exploration of the applicability of preconditioners computed using the Markov Chain Monte Carlo Matrix Inversion ((MC)2MI) method to a variety of linear systems from the domain of quantum chromodynamics, plasma physics and engineering. The latter two are represented by matrices extracted from BOUT++ and Nektar++ codes with specific problem statements. Additionally, we present the scaling behaviour of our implementation for GPUs and CPUs.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122173472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Message from the Workshop Chairs","authors":"Wamca","doi":"10.1109/scala54577.2021.00004","DOIUrl":"https://doi.org/10.1109/scala54577.2021.00004","url":null,"abstract":"Since the advent of the multi-core concept, significant advances have been made on many of the related aspects. Multi-core has become a natural element in the HPC ecosystem, and its pervasiveness within the landscape of common computing devices has made it a standard. Therefore, hardware and software concerns related to multi-core are good targets for computer science investigations, with a high potential for a genuine contribution. Beside the plethora of applications for which more powerful solutions are still expected, efficient implementation techniques for many-core chip processors are of keen interest.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128212353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Takuya Ina, Y. Idomura, Toshiyuki Imamura, S. Yamashita, Naoyuki Onodera
{"title":"Iterative methods with mixed-precision preconditioning for ill-conditioned linear systems in multiphase CFD simulations","authors":"Takuya Ina, Y. Idomura, Toshiyuki Imamura, S. Yamashita, Naoyuki Onodera","doi":"10.1109/ScalA54577.2021.00006","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00006","url":null,"abstract":"A new mixed-precision preconditioner based on the iterative refinement (IR) method is developed for the preconditioned conjugate gradient (P-CG) solver and the multigrid preconditioned conjugate gradient (MGCG) solver in the multiphase thermal-hydraulic CFD code JUPITER [1]. In the IR preconditioner, linear systems are approximately solved using a block Jacobi method, which is optimized using fine block decomposition with 2D tiles to facilitate SIMD operations and software pipelining. Mixed-precision computing is designed to avoid influences of the roundoff errors in computing ill-conditioned matrices with extreme contrast of coefficients. Linear systems are normalized so that it can be computed within the dynamic range of FP16. All data is stored in FP16 to reduce memory access, while all computation is performed in FP32. The hybrid FP16/32 implementation keeps the similar convergence property as FP32, while the computational performance is close to FP16. The robustness of the FP16/32 implementation was demonstrated by scanning data formats with different bit lengths of the significand. The developed solvers are optimized on Fugaku (A64FX), and applied to ill-conditioned matrices with 90 billion DOFs in JUPITER. The P-CG and MGCG solvers with the new IR preconditioner show excellent strong scaling up to 8,000 CPUs, where 5.7 × and 3.4 × speedups are respectively achieved from the conventional solvers on Oakforest-PACS (KNL).","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122091024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proceedings of ScalA 2021: 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems [Title page]","authors":"","doi":"10.1109/scala54577.2021.00001","DOIUrl":"https://doi.org/10.1109/scala54577.2021.00001","url":null,"abstract":"","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"27 22","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132060729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimized Cascadic Multigrid Parareal Method for Explicit Time-Marching Schemes","authors":"Yen-Chen Chen, K. Nakajima","doi":"10.1109/ScalA54577.2021.00007","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00007","url":null,"abstract":"High-performance computing research is entering the exascale computing era. Large-scale simulations have more than enough parallel resources but reach a saturation point in spatial parallelization due to the communication cost and synchronization overhead. Parallel-in-time (PinT) methods are a solution to the saturation problem. To date, many efficient PinT methods have been proposed, but most experiments focus on small problems with a large number of time steps. Applications that are solved by explicit time-marching schemes, especially, are highly scalable in the spatial domain. Therefore very few researchers use PinT methods on explicit time-marching schemes. Furthermore, PinT methods often require many processors to achieve faster computation than sequential code. This work proposes a PinT method for explicit schemes that provide efficient parallelization with few working processes. The numerical experiment of advection equation and compressible viscous flow simulation shows that the proposed method could achieve better parallel efficiency than spatial parallelization.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128698761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"[Copyright notice]","authors":"","doi":"10.1109/scala54577.2021.00002","DOIUrl":"https://doi.org/10.1109/scala54577.2021.00002","url":null,"abstract":"","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130704371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Passel: Improved Scalability and Efficiency of Distributed SVM using a Cacheless PGAS Migrating Thread Architecture","authors":"Brian A. Page, P. Kogge","doi":"10.1109/ScalA54577.2021.00009","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00009","url":null,"abstract":"Stochastic Gradient Descent (SGD) is a valuable algorithm for large-scale machine learning, but has proven difficult to parallelize on conventional architectures because of communication and memory access issues. The HogWild series of mixed logically distributed and physically multi-threaded algorithms overcomes these issues for problems with sparse characteristics by using multiple local model vectors with asynchronous atomic updates. While this approach has proven effective for several reported examples, there are others, especially very sparse cases, that do not scale as well. This paper discusses an SGD Support Vector Machine (SVM) on a cacheless migrating thread architecture using the Hogwild algorithms as a framework. Our implementations on this novel architecture achieved superior hardware efficiency and scalability over that of a conventional cluster using MPI. Furthermore these improvements were gained using naive data partitioning techniques and hardware with substantially less compute capability than that present in conventional systems.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123705593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gonzalo Berger, Manuel Freire, Renzo Marini, Ernesto Dufrechu, P. Ezzatti
{"title":"Unleashing the performance of bmSparse for the sparse matrix multiplication in GPUs","authors":"Gonzalo Berger, Manuel Freire, Renzo Marini, Ernesto Dufrechu, P. Ezzatti","doi":"10.1109/ScalA54577.2021.00008","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00008","url":null,"abstract":"The evolution of data science and machine learning has increased the applicability of the sparse matrix multiplication (SPGEMM) kernel. Unlike more well-known operations such as the SPMV, in the SPGEMM the nonzero pattern of the result is determined by the interaction between the nonzero patterns of the inputs, which impose serious challenges to the development of high-performance implementations for accelerators. Recent efforts in this subject aim to mitigate this irregularity through the use of block-based sparse storage formats, obtaining promissing results on accelerators such as GPUs. In this work we study the format bmSparse [1] and propose optimizations to attack the principal bottlenecks of the original SPGEMM implementation for Nvidia GPUs. We evaluate the proposal using nine sparse matrices of different sizes, showing remarkable speedups with respect to CUSPARSE's CSR variant.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124497133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Isha Aggarwal, Aditya Kashi, Pratik Nayak, C. Balos, C. Woodward, H. Anzt
{"title":"Batched Sparse Iterative Solvers for Computational Chemistry Simulations on GPUs","authors":"Isha Aggarwal, Aditya Kashi, Pratik Nayak, C. Balos, C. Woodward, H. Anzt","doi":"10.1109/ScalA54577.2021.00010","DOIUrl":"https://doi.org/10.1109/ScalA54577.2021.00010","url":null,"abstract":"This paper presents batched iterative solvers for GPU architectures. We elaborate on the design of the batched functionality aiming for optimal performance while still giving the user some flexibility in terms of choosing a sparse matrix format, a preconditioner optimized for the distinct items of the batch, and an application-specific stopping criterion that is evaluated for each problem in the batch, individually. Performance results for benchmark problems coming from PeleLM simulations reveal the potential of the batched iterative solvers for computational chemistry simulations, and their advantage compared to the current vendor-provided batched solutions.","PeriodicalId":147849,"journal":{"name":"2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115227032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}