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- Santiago Badia, Fabio Nobile, Christian Vergara
- J. Comput. Physics
- 2008

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… (More)

- Santiago Badia, Annalisa Quaini, Alfio Quarteroni
- SIAM J. Scientific Computing
- 2008

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-LU factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is… (More)

- Santiago Badia, Alba Hierro
- SIAM J. Scientific Computing
- 2014

The aim of this work is to design monotonicity-preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear (shock-capturing) stabilization. As linear stabilization, we consider and analyze a novel symmetric projection stabilization technique based on a local Scott-Zhang projector. Next, we design a weighting of… (More)

- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2009

In this paper we propose stabilized finite element methods for both Stokes’ and Darcy’s problems that accommodate any interpolation of velocities and pressures. Apart from the interest of this fact, the important issue is that we are able to deal with both problems at the same time, in a completely unified manner, in spite of the fact that the functional… (More)

- Santiago Badia, Pavel B. Bochev, +4 authors Michael L. Parks
- 2007

A method for coupling atomistic and continuum models across a subdomain, or bridge region, is presented. Coupling is effected through a force-based blending model. The method properly accounts for the the atomistic and continuum contributions to the force balance at points in the bridge region. Simple patch tests and computational experiments are used to… (More)

- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2006

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… (More)

In this work we propose a Robin-Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid-structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [Badia, Nobile and Vergara, J. Comput. Phys. 227 (2008) 7027 –7051]. We… (More)

- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2012

A new mixed finite element approximation of Maxwell’s problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the… (More)

- Santiago Badia, Alberto F. Martín, Javier Principe
- SIAM J. Scientific Computing
- 2014

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 coarsegrid 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… (More)

- Santiago Badia, Ramon Codina
- Applied Mathematics and Computation
- 2009

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 ≤ Cδt with C uniform with respect to h and δt. Standard residual-based… (More)