Parameter-robust discretization and preconditioning of Biot's\n consolidation model

2015/07/12 by Jeonghun J. Lee, Lee, Jeonghun J., Kent‐André Mardal +3 · 12 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1507.03199

Abstract

Biot's consolidation model in poroelasticity has a number of applications in\nscience, medicine, and engineering. The model depends on various parameters,\nand in practical applications these parameters ranges over several orders of\nmagnitude. A current challenge is to design discretization techniques and\nsolution algorithms that are well behaved with respect to these variations. The\npurpose of this paper is to study finite element discretizations of this model\nand construct block diagonal preconditioners for the discrete Biot systems. The\napproach taken here is to consider the stability of the problem in non-standard\nor weighted Hilbert spaces and employ the operator preconditioning approach. We\nderive preconditioners that are robust with respect to both the variations of\nthe parameters and the mesh refinement. The parameters of interest are small\ntime-step sizes, large bulk and shear moduli, and small hydraulic conductivity.\n

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• Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
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• An inherent regularization approach to parameter-free preconditioning for nearly incompressible linear poroelasticity and elasticity
• Time-continuous strongly conservative space-time finite element methods for the dynamic Biot model

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