Eigenvalue solution of sparse matrix based on MPETSc

Rong Gu

doi:10.1117/12.3006741

26 September 2023 Eigenvalue solution of sparse matrix based on MPETSc

Rong Gu

Proceedings Volume 12793, International Conference on Mechatronics and Intelligent Control (ICMIC 2023); 127931J (2023) https://doi.org/10.1117/12.3006741
Event: International Conference on Mechatronics and Intelligent Control (ICMIC2023), 2023, Wuhan, China

Abstract

Parallel computing plays an increasingly important role in the field of numerical computing, with technological developments permitting an ever-increasing range of potential applications. However, the design of parallel numerical programs is far more difficult than serial programs, especially in the face of complex application problems, the development and performance optimization of massive parallel numerical programs are very challenging. High-performance numerical software often requires a comprehensive and long exploration process from design to implementation. With the help of existing parallel algorithm packages, this paper develops efficient finite element parallel programs without accounting for complex data distribution and communication. In doing so, this method greatly reduces the difficulty and cost of finite element parallel computing and shortens the development cycle. This paper makes a series of optimizations for algorithms and computational processes to improve their stability, computational efficiency, and parallel scalability. Subsequently, the algorithm is made suitable for solving the eigenvalues of a large-scale sparse matrix in a parallel computing environment. The software package formed in this paper depends neither on the specific structure of the matrix nor on the vector, meaning it can be applied to arbitrary matrix-vector structures. The test results for several typical matrices show that the algorithm and software package have not only good numerical stability and scalability, but also a greater improvement in efficiency when compared with other parallel solvers.

(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Rong Gu "Eigenvalue solution of sparse matrix based on MPETSc", Proc. SPIE 12793, International Conference on Mechatronics and Intelligent Control (ICMIC 2023), 127931J (26 September 2023); https://doi.org/10.1117/12.3006741

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KEYWORDS

Matrices

Chemical elements

Parallel computing

Design and modelling

Algorithm development

Data communications

Iterative methods

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