2015
DOI: 10.1007/s00791-016-0260-8
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Multigrid method for nonlinear poroelasticity equations

Abstract: In this study, a nonlinear multigrid method is applied for solving the system of incompressible poroelasticity equations considering nonlinear hydraulic conductivity. For the unsteady problem, an additional artificial term is utilized to stabilize the solutions when the equations are discretized on collocated grids. We employ two nonlinear multigrid methods, i.e. the "full approximation scheme" and "Newton multigrid" for solving the corresponding system of equations arising after discretization. For the steady… Show more

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Cited by 12 publications
(5 citation statements)
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“…In the multigrid framework, the choice of the smoother is a key point to ensure the convergence and the performance of the method. Several strategies have proposed such as Vanka-type smoothers for three-field non-linear poroelasticity, Uzawa-type smoothers obtained by splitting the discrete operators or also parameter dependent smoothers based on a fixed-stress scheme [17][18][19]. An efficient distributive smoother for staggered grids is proposed and analyzed in [20,21].…”
Section: Previous Workmentioning
confidence: 99%
“…In the multigrid framework, the choice of the smoother is a key point to ensure the convergence and the performance of the method. Several strategies have proposed such as Vanka-type smoothers for three-field non-linear poroelasticity, Uzawa-type smoothers obtained by splitting the discrete operators or also parameter dependent smoothers based on a fixed-stress scheme [17][18][19]. An efficient distributive smoother for staggered grids is proposed and analyzed in [20,21].…”
Section: Previous Workmentioning
confidence: 99%
“…Here we extend the latter formulations to include other morphogens and additional nonlinearities, and focus on a stronger twoway coupling required for the case of primordia patterns. The development of efficient preconditioners for chemotaxis has not yet been addressed in literature, whereas nonlinear poromechanics has already been studied [31,32] albeit only in a small deformations regime. In this work we provide efficient and scalable for both chemotaxis and large deformations poroelasticity.…”
Section: Introductionmentioning
confidence: 99%
“…Poroelasticity problems have been attracting attention from the scientific computing community [21,47] (and references therein). Another class of numerical methods that are used to solve the poroelasticity equations are the finite volume method combined with a nonlinear multigrid method as adopted by Luo et al [25]. In addition, stabilised finite difference methods using central differences on staggered grids are used by Gaspar et al [16,17] to solve Biot's model.…”
Section: Introductionmentioning
confidence: 99%