GEOMETRICAL MULTISCALE MODELING OF THE CARDIOVASCULAR SYSTEM by L. Formaggia and C. Vergara Program 1. Stand­alone models 1.1 The 3D model 1.1.1 The fluid problem 1.1.2 The structure problem 1.1.3 The coupled fluid­structure interaction problem 1.1.4 Numerical solutions of the fluid­structure interaction problem 1.2 The 1D model 1.2.1 Derivation of the 1D model for a single artery 1.2.2 Assembling a network of 1D segments 1.2.3 Numerical solution of the 1D problem 1.3 The 0D model 1.3.1 Derivation of the 0D models for a single artery 1.3.2 Assembling a network of 0D compartments 2. Numerical treatment of defective boundary condition for the 3D problem 3. The coupled heterogeneous problems 3.1 The 3D­1D problem 3.2 The 3D­0D problem 3.3 The 0D­1D problem 4. Numerical strategies for the solution of the coupled problems Bibliography ­ Cardiovascular Mathematics: Modeling and simulation of the circulatory system, edited by Luca Formaggia, Alfio Quarteroni, Alessandro Veneziani, Springer, 2009 ­ Howard C. Elman​
, David J. Silvester,​
Andrew J. Wathen,​
Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics: with Applications in Incompressible Fluid Dynamics, Oxford University Press, 2005 -
Quarteroni A., Valli A., Numerical Approximation of Partial Differential Equations, Springer, 2008 

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