Multiscale solver for subsurface poromechanical problems
- Solution of linear systems is often the bottleneck in large-scale subsurface modeling, especially when tightly coupled multiphysics systems are considered. Iterative linear solvers that are employed critically depend on efficient and scalable preconditioners to achieve robust convergence. The objective of this work is the development of scalable and efficient multilevel multiscale preconditioners targeting problems of geomechanics, single-phase flow and poromechanics on general polyhedral grids in one unified framework. We have developed a flexible unstructured coarsening framework that constructs a multilevel hierarchy of topological grid representations suitable for both nodal (finite-element) and cell-centered (finite-volume) discretizations. At every level, interpolation and restriction operators are defined by computing numerical basis functions using the Multiscale Restriction-Smoothed Basis (MsRSB) method, which has been additionally extended with a matrix filtering strategy designed to guarantee convergence of the smoothing iterations for problems that do not produce an M-matrix. We also develop a multiscale preconditioner for coupled poromechanical problems based on a combination of pressure and displacement basis functions and a block-triangular smoothing operator. Robustness and algorithmic scalability of the method are verified using a series of two and three-dimensional test cases including single-physics and coupled problems. In addition, this work describes an optimized parallel implementation of the proposed multiscale methods, its main computational kernels and data structures for representing the mesh hierarchy and multiscale operators. We investigate the performance and scalability of the developed multiscale solver and compare it to a state-of-the-art algebraic multigrid solver using a series of structured and unstructured grid test problems. Good weak and strong scaling is observed on up to 16 shared memory cores and 32 distributed memory nodes for a range of problems from 1 million to 140 million grid cells.
|Type of resource
|electronic resource; remote; computer; online resource
|1 online resource.
|Degree committee member
|Degree committee member
|Stanford University, Department of Energy Resources Engineering
|Statement of responsibility
|Submitted to the Department of Energy Resources Engineering.
|Thesis Ph.D. Stanford University 2022.
- © 2022 by Sergey Klevtsov
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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