Iterative splitting schemes for a soft material poromechanics model

Both, Jakub Wiktor; A., Barnafi, Nicolás; Radu, F.; Zunino, Paolo; Quarteroni, Alfio

doi:10.1016/j.cma.2021.114183

Cited by 8 publications

(9 citation statements)

References 45 publications

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“…each iteration is a linearization iteration decoupling different physical sub-problems by a suitable choice of the inexact Jacobian. The decoupling strategies are closely related to previous developments for the corresponding linearized problem [3].…”

Section: Monolithic and Block-partitioned Numerical Solversmentioning

confidence: 92%

“…We employ ideas previously developed for the linearized problem [3] justified by a similar coupling character of the exact Jacobian, cf. Sec.…”

Section: Two-way Splittingmentioning

confidence: 99%

“…The model combines thermodynamically-consistent linearization [7] of a fullynonlinear model [10], but with a nonlinear constitutive stress-strain relation [13]; the final model consists in a nonlinear coupled system of three physics. Quasi-Newton solvers are proposed integrating stabilized two-way and three-way decoupling, inspired by splitting schemes derived for the linearized model [3] which guarantee linear convergence. Our numerical results show that our iterative splitting quasi-Newton schemes outperform the widely used monolithic Newton method, with a reduction in computer times of up to a 50% for the three-way and an 85% for the two-way, making them an attractive choice for the fully-nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

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Iterative Quasi-Newton Solvers for Poromechanics Applied to Heart Perfusion

Both

Nicolas

2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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Sequential block-partitioned solvers have in the recent past been quite popular for multi-physics and in particular poroelasticity models. Such enable tailored solver technology for the respective single-physics problems via iterative coupling, as well as suggest suitable block-preconditioners for monolithic solvers.In this talk, we focus on a thermodynamically consistent poroelasticity model recently proposed. It extends the classical quasi-static Biot equations by incoporating inertia contributions in both solid and fluid equations, aiming at biomedical applications; for instance, the perfusion of the heart.Following ideas and techniques from previous works, we present block-partitioned solvers for the fully dynamic poroelasticity model supported by theoretical convergence analysis.

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Section: Monolithic and Block-partitioned Numerical Solversmentioning

confidence: 92%

“…We employ ideas previously developed for the linearized problem [3] justified by a similar coupling character of the exact Jacobian, cf. Sec.…”

Section: Two-way Splittingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Iterative Quasi-Newton Solvers for Poromechanics Applied to Heart Perfusion

Both

Nicolas

2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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“…Even if many numerical methods for the approximation of linear poroelasticity and their convergence analysis can be found in the recent literature (see [12,[17][18][19]55] and the references therein), much less attention has been given to formulations addressing large-strain poromechanics. In this regard, recent works include an enriched Galerkin framework [27], stabilised finite elements [15,84] and hybrid finite elements as well [83].…”

Section: Introductionmentioning

confidence: 99%

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Gómez-Vargas

Lourenço

et al. 2022

J Sci Comput

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In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes.

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“…In this result of well-posedness, (1.1) is rewritten as a first-order system in time which also done below for its discretization. In order to enhance physical realism in poroelasticity, generalizations of the system (1.1) are presented in, e.g., [16,42].…”

Section: Introductionmentioning

confidence: 99%

Convergence of a continuous Galerkin method for hyperbolic-parabolic systems

Bause¹,

Köcher²,

Radu³

2022

Preprint

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We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro-and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pairs of finite elements for the spatial approximation of the unknowns are investigated. Optimal order error estimates of energy-type are proven. Superconvergence at the time nodes is addressed briefly. The error analysis can be extended to discontinuous and enriched Galerkin space discretizations. The error estimates are confirmed by numerical experiments.

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Iterative splitting schemes for a soft material poromechanics model

Cited by 8 publications

References 45 publications

Iterative Quasi-Newton Solvers for Poromechanics Applied to Heart Perfusion

Iterative Quasi-Newton Solvers for Poromechanics Applied to Heart Perfusion

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Convergence of a continuous Galerkin method for hyperbolic-parabolic systems

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