Abstract
Frequency domain Biot equation in quasi-static state can be applied to model low-frequency loading of fluid-filled poroelastic materials and estimate effective frequency-dependent strain-stress relations. We propose an algorithm of solving the system of linear algebraic equations (SLAE) obtained from finite-difference approximation of Biot equations. The algorithm involves the Biconjugate Gradient Stabilized (BICGSTAB) iterative solver with a field-split preconditioner technique. In this paper, we estimate the number of floating-point operations required for both the proposed algorithm and direct approach. Performed numerical experiments demonstrate the fast convergence of the iterative process and confirm performance and memory usage benefits of the suggested approach compared to the direct method.
S.S. developed the algorithm and M.N. did the numerical simulations using the supercomputer facilities of Siberian Supercomputer Center (Cluster NKS-30T) under the support of RSCF grant no. 19-77-20004. V.L. performed the analysis of the results under the support of FNI project FWZZ-2022-0022.
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Solovyev, S., Novikov, M., Lisitsa, V. (2023). Field-Split Iterative Solver for Quasi-Static Biot Equation. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14106. Springer, Cham. https://doi.org/10.1007/978-3-031-37111-0_4
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