A Parallel Generator of Non-Hermitian Matrices Computed from Given Spectra

Wu, Xinzhe; Petiton, Serge G.; Lu, Yutong

doi:10.1007/978-3-030-15996-2_16

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…The matrix operations on each GPU is supported by cuSPARSE, and final matrix can be obtained by gathering all sub-matrices from devices. This implementation for multi-GPUs was already presented by X. Wu et al 24 .…”

Section: Basic Implementation On Cpus and Mutil-gpusmentioning

confidence: 99%

A parallel generator of non‐Hermitian matrices computed from given spectra

Petiton

2020

Concurrency and Computation

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Summary Iterative linear algebra methods to solve linear systems and eigenvalue problems with non‐Hermitian matrices are important for both the simulation arising from diverse scientific fields and the applications related to big data, machine learning, and artificial intelligence. The spectral property of these matrices has impacts on the convergence of these solvers. Moreover, with the increase of the size of applications, iterative methods are implemented in parallel on clusters. Analysis of their behaviors with non‐Hermitian matrices on supercomputers is so complex that we need to generate large‐scale matrices with different given spectra for benchmarking. These test matrices should be non‐Hermitian and nontrivial, with high dimension. This paper highlights a scalable matrix generator that constructs large sparse matrices using the user‐defined spectrum, and the eigenvalues of generated matrices are ensured to be the same as the predefined spectrum. This generator is implemented on CPUs and multi‐GPUs platforms, with good strong and weak scaling performance on several supercomputers. We also propose a method to verify its ability to guarantee the given spectra. Finally, we give an example to evaluate the numerical properties and parallel performance of iterative methods using this matrix generator.

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Section: Basic Implementation On Cpus and Mutil-gpusmentioning

confidence: 99%

A parallel generator of non‐Hermitian matrices computed from given spectra

Petiton

2020

Concurrency and Computation

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“…In order to test m-UCGLE with matrices of high dimensions, we use the Scalable Matrix Generator with Given Spectra (SMG2S) [23,24] to generate different test matrices. SMG2S 3 is an open source package implemented and optimized using MPI and C++ templates, which allows generating efficiently large-scale sparse non-Hermitian test matrices with customized eigenvalues or spectral distribution by users to evaluate the impacts of spectra on the convergence of linear solvers.…”

Section: Test Sparse Matricesmentioning

confidence: 99%

“…In order to generate the test matrices with given dimensions and user-defined spectral distribution, three parameters p, d and h should be specified. The definition in detail of these parameters can be referred to [23]. As in shown Fig.…”

Section: Test Sparse Matricesmentioning

confidence: 99%

A distributed and parallel asynchronous unite and conquer method to solve large scale non-Hermitian linear systems with multiple right-hand sides

Petiton

2019

Parallel Computing

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Many problems in the field of science and engineering often require to solve simultaneously large-scale non-Hermitian sparse linear systems with multiple right-hand sides (RHSs). Efficiently solving such problems on extreme-scale platforms requires the minimization of global communications, reduction of synchronization points and promotion of asynchronous communications. We develop an extension of the Unite and Conquer GMRES/LS-ERAM (UCGLE) method [1] by combining it with Block GMRES method to solve non-Hermitian linear systems with multiple RHSs. UCGLE is a hybrid method consisting of three computing algorithms with asynchronous communication that allow the use of approximate eigenvalues to accelerate to solve of linear systems and to improve their fault tolerance. In this paper, the variant of UCGLE with novel components and manager engine implementations is introduced. This engine is capable of allocating multiple Block GMRES at the same time, each Block GMRES solving the linear systems with a subset of RHSs and accelerating the convergence using the eigenvalues approximated by other eigensolvers. Dividing the entire linear system with multiple RHSs into subsets and solving them simultaneously with different allocated linear solvers allow localizing calculations, reducing global communication, and improving parallel performance. Meanwhile, the asynchronous preconditioning using eigenvalues is able to speed up the convergence and improve the fault tolerance and reusability. Numerical experiments using different test matrices on supercomputer ROMEO indicate that the proposed method achieves a substantial decrease in both computation time and iterative steps with good scaling performance.

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“…The goal of the work presented by Wu et al 2 is to create non‐Hermitian matrices in parallel, to enable the comparison of solvers. More precisely, the authors presented a scalable matrix generator from given spectra (SMG2S) to benchmark the linear and eigenvalue solvers on large‐scale platforms.…”

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confidence: 99%

High‐performance computing for computational science

Gil-Costa

Senger

2020

Concurrency and Computation

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High-performance computing is the application of large-scale computer resources to solve computational problems that are either too large for standard computers or would take too long. Different parallel techniques, parallel and distributed programming libraries, and performance evaluation libraries are used to enhance the performance and to feature the execution of the algorithms. These techniques and tools are a valuable resource for anyone developing software codes for computational sciences. Moreover, all these techniques and tools have pushed the progress in several areas of science and engineering, which either demand large amounts of calculations or manipulate large volumes of data. This special issue focuses on efficient experimental solutions to problems on state-of-the-art computational systems consisting of large numbers of computational elements, including clusters, massively parallel supercomputers, and GPU-based systems. The objective is to open an opportunity for researchers to present and discuss new ideas and proposals for state-of-the art in HPC for computational science. The expected audience includes researchers and students in academic departments, government laboratories, and industrial organizations. This special issue

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A Parallel Generator of Non-Hermitian Matrices Computed from Given Spectra

Cited by 4 publications

References 10 publications

A parallel generator of non‐Hermitian matrices computed from given spectra

A parallel generator of non‐Hermitian matrices computed from given spectra

A distributed and parallel asynchronous unite and conquer method to solve large scale non-Hermitian linear systems with multiple right-hand sides

High‐performance computing for computational science

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