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25
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.
A quasiNewton algorithm based on a reduced model for fluidstructure interaction problems in blood flows
 M2AN Math. Model. Numer. Anal
"... Abstract. We propose a quasiNewton algorithm for solving fluidstructure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the socalled added mass effect. Various test cases show that the method allow ..."
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Cited by 46 (6 self)
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Abstract. We propose a quasiNewton algorithm for solving fluidstructure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the socalled added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluidstructure simulations performed either with a simple 1D structure model or with shells in large displacements. Mathematics Subject Classification. 65M60, 74K25, 76D05, 76Z05. 1.
Splitting methods based on algebraic factorization for fluidstructure interaction
 SIAM J. Scientific Computing
"... Abstract. We discuss in this paper the numerical approximation of fluidstructure interaction (FSI) problems dealing with strong addedmass effect. We propose new semiimplicit algorithms based on inexact blockLU factorization of the linear system obtained after the spacetime discretization and li ..."
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Cited by 41 (11 self)
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Abstract. We discuss in this paper the numerical approximation of fluidstructure interaction (FSI) problems dealing with strong addedmass effect. We propose new semiimplicit algorithms based on inexact blockLU factorization of the linear system obtained after the spacetime discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressurestructure velocity system at each iteration, reducing the computational cost. We investigate explicitimplicit 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 fluidstructure system as a preconditioner. The numerical properties of these methods have been tested on a model problem representing a bloodvessel system.
Stabilized explicit coupling for fluidstructure interaction using Nitsche’s method
 C. R. Math. Acad. Sci. Paris
"... apport de recherche ISSN 02496399 ISRN INRIA/RR6445FR+ENGinria00247409, version 4 23 Oct 2008Stabilization of explicit coupling in fluidstructure interaction involving fluid incompressibility ..."
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Cited by 32 (6 self)
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apport de recherche ISSN 02496399 ISRN INRIA/RR6445FR+ENGinria00247409, version 4 23 Oct 2008Stabilization of explicit coupling in fluidstructure interaction involving fluid incompressibility
Modular vs. nonmodular preconditioners for fluidstructure systems with large addedmass effect
 Computer Methods in Applied Mechanics and Engineering, in press
, 2008
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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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Heterogeneous domain decomposition methods for fluidstructure interaction problems
, 2005
"... Summary. In this note, we propose SteklovPoincaré iterative algorithms (mutuated from the analogy with heterogeneous domain decomposition) to solve fluidstructure interaction problems. Although our framework is very general, the driving application is concerned with the interaction of blood flow an ..."
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Cited by 5 (1 self)
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Summary. In this note, we propose SteklovPoincaré iterative algorithms (mutuated from the analogy with heterogeneous domain decomposition) to solve fluidstructure interaction problems. Although our framework is very general, the driving application is concerned with the interaction of blood flow and vessel wall in large arteries. 1
The Development Of MultiPhysics Analysis Software (contributed
"... analysis tools for coupled fluidstructure interaction analysis In order to develop the capabilities of CIMNE’s software in the FluidStructure Interaction (FSI) domain, research and development activities have been focused in three different fronts: • Advances in fluid solver technology. • Developm ..."
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analysis tools for coupled fluidstructure interaction analysis In order to develop the capabilities of CIMNE’s software in the FluidStructure Interaction (FSI) domain, research and development activities have been focused in three different fronts: • Advances in fluid solver technology. • Development of a unified software platform (KRATOS) to allow integration of singlefield codes into a coupled multiphysics solver. • Development of new coupling algorithms. Each of these aspects is summarized in the reports included in this document.
Accepted Manuscript An unconditionally stable semiimplicit FSI finite element method
"... unconditionally stable semiimplicit FSI finite element method, Comput. Methods Appl. Mech. ..."
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unconditionally stable semiimplicit FSI finite element method, Comput. Methods Appl. Mech.