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Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model

1
Department of Communication Engineering and Informatics, The University of Electro-Communications, Tokyo 182-8585, Japan
2
Department of Mathematical Engineering, Musashino University, Tokyo 135-8181, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Junseok Kim
Mathematics 2021, 9(18), 2248; https://doi.org/10.3390/math9182248
Received: 31 July 2021 / Revised: 2 September 2021 / Accepted: 10 September 2021 / Published: 13 September 2021
(This article belongs to the Special Issue Modern Applications of Numerical Linear Algebra)
We aim to accelerate the linear equation solver for crack growth simulation based on the phase field model. As a first step, we analyze the properties of the coefficient matrices and prove that they are symmetric positive definite. This justifies the use of the conjugate gradient method with the efficient incomplete Cholesky preconditioner. We then parallelize this preconditioner using so-called block multi-color ordering and evaluate its performance on multicore processors. The experimental results show that our solver scales well and achieves an acceleration of several times over the original solver based on the diagonally scaled CG method. View Full-Text
Keywords: crack growth simulation; phase field model; conjugate gradient method; incomplete Cholesky factorization; parallelization; block red-black ordering; performance evaluation crack growth simulation; phase field model; conjugate gradient method; incomplete Cholesky factorization; parallelization; block red-black ordering; performance evaluation
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MDPI and ACS Style

Ishii, G.; Yamamoto, Y.; Takaishi, T. Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model. Mathematics 2021, 9, 2248. https://doi.org/10.3390/math9182248

AMA Style

Ishii G, Yamamoto Y, Takaishi T. Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model. Mathematics. 2021; 9(18):2248. https://doi.org/10.3390/math9182248

Chicago/Turabian Style

Ishii, Gaku, Yusaku Yamamoto, and Takeshi Takaishi. 2021. "Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model" Mathematics 9, no. 18: 2248. https://doi.org/10.3390/math9182248

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