Iterative solvers for poromechanics : Iterative solvers for poromechanics
Abstract
This thesis concerns iterative solvers for poromechanics problems. The problems in the studies have involved linear poromechanics, non-linear poromechanics, and poromechanics under large deformation. We included high order discretizations, applied linearization techniques and splitting methods to develop new solvers. We studied the robustness and convergence of these solvers. By studying the mixed stress method as an iterative solver for poromechanics, we developed an optimized version of it. Furthermore, by extending the convergence analysis in the time domain, we developed a new version of the xed stress method that is partially parallelized. This splitting method was combined with linearization techniques to develop solvers for non-linear poromechanics. By studying the convergence of the linearisation schemes, we developed new solvers and extended the applicability to more complex phenomena, for instance poromechanics with large deformation.
Has parts
Paper A: M. Borregales, F.A. Radu, K. Kumar, and J.M. Nordbotten. Robust iterative schemes for non-linear poromechanics. Computational Geosciences, 22(4):1021-1038, 2018. The article is not available in BORA due to publisher restrictions. The published version is available at: https://doi.org/10.1007/s10596-018-9736-6.Paper B: M. Borregales and F.A. Radu. Higher Order Space-Time Elements for a Non-linear Biot Model. Numerical Mathematics and Advanced Applications ENUMATH 2017, Lecture Notes in Computational Science and Engineering 126 541-549, 2018. The article is not available in BORA due to publisher restrictions. The published version is available at: https://doi.org/10.1007/978-3-319-96415-7_49.
Paper C: M. Borregales, K. Kumar, J.M. Nordbotten and F.A. Radu. Iterative solvers for Biot model under small and large deformation. Computational Geosciences, in press, 2020. The article is available in the main thesis. The article is also available at: https://doi.org/10.1007/s10596-020-09983-0.
Paper D: M. Borregales, K. Kumar, F.A. Radu, C. Rodrigo and F.J. Gaspar. A parallel-in-time fixed-stress splitting method for Biots consolidation model. Computers and Mathematics with Applications, 77(6):1466-1478, 2019. The article is available in the main thesis. The article is also available at: https://doi.org/10.1016/j.camwa.2018.09.005.
Supplementary Paper E: J.W. Both, M. Borregales, J.M. Nordbotten, K. Kumar, and J.M. Nordbotten. Robust fixed stress splitting for Biots equations in heterogeneous media. Applied Mathematics Letters, 68 101-108, 2017. The article is available in the main thesis. The article is also available at: https://doi.org/10.1016/j.aml.2016.12.019.
Supplementary Paper F: F.A. Radu, M. Borregales, F.J. Gaspar, K. Kumar and C. Rodrigo. L-scheme and Newton based solvers for a nonlinear Biot model. Proceedings: 6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems), 7th European Conference on Computational Fluid Dynamics, ISBN: 978-84-947311-6-7 3505-3518, 2018. The article is not available in BORA.