Summary
A 3D elasto‐plastic rate‐dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium “Beyond 2000 in Computational Geotechnics,” pages 249‐261, 1999). An original strain‐driven algorithm with an Inexact Newton iterative scheme is used to compute the state variables for a given strain increment.The model is validated against laboratory measurements, checked on a simplified test case, and used to simulate land subsidence due to groundwater and hydrocarbon production. The numerical results prove computationally effective and robust, thus allowing for the use of the model on real complex geological settings.
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.
The numerical simulation of physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large-scale simulations are concerned, one of the most computationally expensive tasks is the solution of linear systems of equations arising from the discretization of the partial differential equations governing physical processes. This work presents Chronos, a collection of linear algebra functions specifically designed for the solution of large, sparse linear systems on massively parallel computers. Its emphasis is on modern, effective, and scalable Algebraic Multigrid (AMG) preconditioners for high performance computing (HPC). This work describes the numerical algorithms and the main structures of this software suite, especially from an implementation standpoint. Several numerical results arising from practical mechanics and fluid dynamics applications with hundreds of millions of unknowns are addressed and compared with other state-of-the-art linear solvers, proving Chronos's efficiency and robustness.
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