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Numerical mathematics
, 2000
"... Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a ..."
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Cited by 99 (12 self)
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Abstract. In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physiopathology. Mathematics Subject Classification (2000). 92C50,96C10,76Z05,74F10,65N30,65M60. Keywords. Cardiovascular mathematics; mathematical modeling; fluid dynamics; Navier– Stokes equations; numerical approximation; finite element method; differential equations. 1.
Acceleration of a fixed point algorithm for fluidstructure interaction using transpiration conditions
 in Second MIT Conference on Computational Fluid and Solid Mechanics, Elsevier
, 2003
"... Abstract. In this work, we address the numerical solution of fluidstructure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schem ..."
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Cited by 16 (2 self)
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Abstract. In this work, we address the numerical solution of fluidstructure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly nonlinear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standard strategies for solving this nonlinear problems, are fixed point based methods such as BlockGaussSeidel (BGS) iterations. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixedpoint algorithm which combines the standard BGS iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method. Mathematics Subject Classification. 65M60, 65B99, 74F10. 1.
A domain decomposition framework for fluidstruture interation problems
 In Proceedings of the Third International Conference on Computational Fluid Dynamics (ICCFD3
, 2004
"... interaction problems ..."
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DOMAIN DECOMPOSITION SOLVERS FOR THE FLUIDSTRUCTURE INTERACTION PROBLEMS WITH ANISOTROPIC ELASTICITY MODELS
"... Abstract. In this work, a twolayer coupled fluidstructurestructure interaction model is considered, which incorporates an anisotropic structure model into the fluidstructure interaction problems. We propose two domain decomposition solvers for such a class of coupled problems: a RobinRobin prec ..."
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Cited by 1 (1 self)
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Abstract. In this work, a twolayer coupled fluidstructurestructure interaction model is considered, which incorporates an anisotropic structure model into the fluidstructure interaction problems. We propose two domain decomposition solvers for such a class of coupled problems: a RobinRobin preconditioned GMRES solver combined with an inner DirichletNeumann iterative solver, and a RobinRobin preconditioned GMRES solver combined with an inner monolithic algebraic multigrid solver capable of handling an anisotropic compressible and nearly incompressible subproblem. 1.
ARTICLE IN PRESS
, 2009
"... Journal of Computational Physics journal homepage: www.elsevier.com/locate/jcp 2 Stable looselycoupledtype algorithm for fluid–structure interaction ..."
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Journal of Computational Physics journal homepage: www.elsevier.com/locate/jcp 2 Stable looselycoupledtype algorithm for fluid–structure interaction
A Modular, Operator Splitting Scheme for FluidStructure Interaction Problems with Thick Structures
, 2013
"... We present an operatorsplitting scheme for fluidstructure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the NavierStokes ..."
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We present an operatorsplitting scheme for fluidstructure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the NavierStokes equations for an incompressible viscous fluid are used to model the fluid. The operator splitting scheme, based on Lie splitting, separates the elastodynamics structure problem, from a fluid problem in which structure inertia is included to achieve unconditional stability. We prove energy estimates associated with unconditional stability of this modular scheme for the full nonlinear FSI problem defined on a moving domain, without requiring any subiterations within time steps. Two numerical examples are presented, showing excellent agreement with the results of monolithic schemes. Firstorder convergence in time is shown numerically. Modularity, unconditional stability without temporal subiterations, and simple implementation are the features that make this operatorsplitting scheme particularly appealing for multiphysics problems involving fluidstructure interaction.