Related papers: Robust Block Preconditioners for Biot's Model
Hybridizable discretizations allow for the elimination of local degrees-of-freedom leading to reduced linear systems. In this paper, we determine and analyse an approach to construct parameter-robust preconditioners for these reduced…
Poroelasticity problems play an important role in various engineering, geophysical, and biological applications. Their full discretization results in a large-scale saddle-point system at each time step that is becoming singular for locking…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system for…
This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…
In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast…
We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified…
For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field…
We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze…
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time…
In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we…
Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid…
In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…
We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and…
We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by…
We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…