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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.
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.
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
Laurence Halpern Présidente
, 2015
"... methods for incompressible fluidstructure interaction ..."
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