Publications related to Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Optimal control for Partial Differential Equations

In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...

2013

Parallel algorithms and efficient implementation techniques for finite element approximations

Radu Popescu

In this thesis we study the efficient implementation of the finite element method for the numerical solution of partial differential equations (PDE) on modern parallel computer archi- tectures, such as Cray and IBM supercomputers. The domain-decomposition ...

EPFL2013

Isogeometric numerical simulation of solute dynamics in blood flows

Andrea Di Blasio

Solutes and drugs are transported in the circulatory system by the blood for which absorption processes occur at the arterial walls. The comprehension, modeling, and numerical simulation of these phenomena, both in physiological and pathological conditions ...

2013

Multiscale Modeling of Thermo-Mechanical Coupling Between Atomistic and Continuum Domains

Srinivasa Babu Ramisetti

The motivation to study multiscale problems such as friction and crack propagation/nucleation has triggered the development of multiscale models. The state-of-the-art multiscale models that have been developed until today are successfully applied to a vari ...

EPFL2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Isogeometric Analysis of the Advective Cahn-Hilliard Equation: Spinodal Decomposition Under Shear Flow

Luca Dede'

We present a numerical study of the spinodal decomposition of a binary fluid undergoing shear flow using the advective Cahn-Hilliard equation, a stiff, nonlinear, parabolic equation characterized by the presence of fourth-order spatial derivatives. Our num ...

Elsevier2013

Local discontinuous Galerkin methods for fractional diffusion equations

Jan Sickmann Hesthaven

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems in one space dimension, characterized by having fractional derivatives, parameterized by beta in [1,2]. After demonstrating that a classic ap ...

EDP Sciences2013

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Alfio Quarteroni, Christian Vergara, Luca Formaggia

In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the ...

Academic Press Inc Elsevier Science2013

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

Alfio Quarteroni, Simone Deparis, Adelmo Cristiano Innocenza Malossi, Paolo Crosetto

Simulating arterial trees in the cardiovascular system can be made by the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are ...

Society for Industrial and Applied Mathematics2013

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir-capillaries interface

Alfio Quarteroni, Carlo D'Angelo

In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interf ...

Taylor & Francis Ltd2013

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

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Optimal control for Partial Differential Equations

Parallel algorithms and efficient implementation techniques for finite element approximations

Isogeometric numerical simulation of solute dynamics in blood flows

Multiscale Modeling of Thermo-Mechanical Coupling Between Atomistic and Continuum Domains

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Isogeometric Analysis of the Advective Cahn-Hilliard Equation: Spinodal Decomposition Under Shear Flow

Local discontinuous Galerkin methods for fractional diffusion equations

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir-capillaries interface

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Parallel algorithms and efficient implementation techniques for finite element approximations

Local discontinuous Galerkin methods for fractional diffusion equations

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

Isogeometric numerical simulation of solute dynamics in blood flows

Optimal control for Partial Differential Equations

Isogeometric Analysis of the Advective Cahn-Hilliard Equation: Spinodal Decomposition Under Shear Flow

Multiscale Modeling of Thermo-Mechanical Coupling Between Atomistic and Continuum Domains

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir-capillaries interface