Santiago Badia

Fluid-structure partitioned procedures based on Robin transmission conditions

In this article we design new partitioned procedures for fluid-structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient in the Robin conditions is justified via simplified models. The strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane, as in hemodynamics applications. We analyze theoretically the new iterative procedures on a model problem, which represents a simplified blood-vessel system. In particular, the Robin-Neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures. The theoretical results are checked using numerical experimentation.

Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction

We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms based on inexact block-

On Atomistic-to-Continuum Coupling by Blending

LU

Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction

factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressure-structure velocity system at each iteration, reducing the computational cost. We investigate explicit-implicit decomposition through algebraic splitting techniques originally designed for the FSI problem. This approach leads to two different families of methods which extend to FSI the algebraic pressure correction method and the Yosida method, two schemes that were previously adopted for pure fluid problems. Furthermore, we have considered the inexact factorization of the fluid-structure system as a preconditioner. The numerical properties of these methods have been tested on a model problem representing a blood-vessel system.

Analysis of a Stabilized Finite Element Approximation of the Transient Convection-Diffusion Equation Using an ALE Framework

A mathematical framework for the coupling of atomistic and continuum models by blending them over a subdomain subject to a constraint is developed. Using the framework, four classes of atomistic-to...

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.

On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space–time discretization

In this paper we analyze a stabilized finite element method to approximate the convection-diffusion equation on moving domains using an arbitrary Lagrangian Eulerian (ALE) framework. As basic numerical strategy, we discretize the equation in time using first and second order backward differencing (BDF) schemes, whereas space is discretized using a stabilized finite element method (the orthogonal subgrid scale formulation) to deal with convection dominated flows. The semidiscrete problem (continuous in space) is first analyzed. In this situation it is easy to identify the error introduced by the ALE approach. After that, the fully discrete method is considered. We obtain optimal error estimates in both space and time in a mesh dependent norm. The analysis reveals that the ALE approach introduces an upper bound for the time step size for the results to hold. The results obtained for the fully discretized second order scheme (in time) are associated to a weaker norm than the one used for the first order method. Nevertheless, optimal convergence results have been proved. For fixed domains, we recover stability and convergence results with the strong norm for the second order scheme, stressing the aspects that make the analysis of this method much more involved.

A Highly Scalable Parallel Implementation of Balancing Domain Decomposition by Constraints

In this work, we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation is the fact that it always converges to the physical solution, even for singular ones. A detailed set of numerical experiments have been performed in order to validate our approach.

Approximation of the inductionless MHD problem using a stabilized finite element method

Abstract In this article, we analyze some residual-based stabilization techniques for the transient Stokes problem when considering anisotropic time–space discretizations. We define an anisotropic time–space discretization as a family of time–space partitions that does not satisfy the condition h 2 ⩽ C δ t with C uniform with respect to h and δt. Standard residual-based stabilization techniques are motivated by a multiscale approach, approximating the effect of the subscales onto the large scales. One of the approximations is to consider the subscales quasi-static (neglecting their time derivative). It is well known that these techniques are unstable for anisotropic time–space discretizations. We show that the use of dynamic subscales (where the subscales time derivatives are not neglected) solves the problem, and prove optimal convergence and stability results that are valid for anisotropic time–space discretizations. Also the improvements related to the use of orthogonal subscales are addressed.

Multilevel Balancing Domain Decomposition at Extreme Scales

In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then rescheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments that includes weak scalability analyses with structured and unstructured meshes for the three-dimensional Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-m...