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

Gaku Ishii, Yusaku Yamamoto and Takeshi Takaishi
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Gaku Ishii: Department of Communication Engineering and Informatics, The University of Electro-Communications, Tokyo 182-8585, Japan
Yusaku Yamamoto: Department of Communication Engineering and Informatics, The University of Electro-Communications, Tokyo 182-8585, Japan
Takeshi Takaishi: Department of Mathematical Engineering, Musashino University, Tokyo 135-8181, Japan

Mathematics, 2021, vol. 9, issue 18, 1-21

Abstract: 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.

Keywords: crack growth simulation; phase field model; conjugate gradient method; incomplete Cholesky factorization; parallelization; block red-black ordering; performance evaluation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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