Publications related to Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

Parallel Algorithms for the Solution of Large-Scale Fluid-Structure Interaction Problems in Hemodynamics

This thesis addresses the development and implementation of efficient and parallel algorithms for the numerical simulation of Fluid-Structure Interaction (FSI) problems in hemodynamics. Indeed, hemodynamic conditions in large arteries are significantly aff ...

EPFL2016

Numerical Approximation of Flows in Random Porous Media

Francesco Tesei

The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...

EPFL2016

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Alfio Quarteroni, Andrea Manzoni, Federico Negri

The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...

MATHICSE2016

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

MATHICSE Technical Report : An adjoint-based method for the numerical approximation of shape optimization problems in presence of fluid-structure interaction

Andrea Manzoni

In this work, we propose both a theoretical framework and a numerical method to tackle shape op- timization problems related with uid dynamics applications in presence of uid-structure interactions. We present a general framework relying on the solution of ...

MATHICSE2016

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and ...

2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

Alfio Quarteroni, Simone Deparis, Davide Forti, Gwenol Grandperrin

Modeling Fluid-Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discre ...

Academic Press Inc Elsevier Science2016

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Daniel Kressner

A novel method for approximating structured singular values (also known as

\mu

- values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eig ...

MATHICSE2016

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Daniel Kressner, Robert Gerhard Jérôme Luce

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...

MATHICSE2016

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

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Parallel Algorithms for the Solution of Large-Scale Fluid-Structure Interaction Problems in Hemodynamics

Numerical Approximation of Flows in Random Porous Media

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

MATHICSE Technical Report : An adjoint-based method for the numerical approximation of shape optimization problems in presence of fluid-structure interaction

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Parallel Algorithms for the Solution of Large-Scale Fluid-Structure Interaction Problems in Hemodynamics

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Numerical Approximation of Flows in Random Porous Media

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

MATHICSE Technical Report : An adjoint-based method for the numerical approximation of shape optimization problems in presence of fluid-structure interaction

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity