Publications related to Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Truncated low-rank methods for solving general linear matrix equations

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Pierre Robert Maurice Millien

We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz force induced tis ...

Elsevier2015

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Jan Sickmann Hesthaven, Paolo Gatto

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

Springer Verlag2015

Boundary elements method for microfluidic two-phase flows in shallow channels

François Gallaire, Mathias Nagel

In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-On-A-Chip devices and ch ...

Elsevier2015

A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

Pierre Robert Maurice Millien

We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can ...

Elsevier2015

MATHICSE Technical Report: Numerical homogenization methods for parabolic monotone problems

Assyr Abdulle

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. ...

MATHICSE2015

Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits

Sébastien Basterrechea

This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form [ \mathcal Lu + \mathcal Q(u) = f.] The main result of thi ...

EPFL2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

Idiap2015

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

Paul Isaac Denis Louis Marie Cazeaux

We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam-like elastic material containing millions of air-filled alveoli connected by a ...

World Scientific Publ Co Pte Ltd2015

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

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Truncated low-rank methods for solving general linear matrix equations

A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Boundary elements method for microfluidic two-phase flows in shallow channels

A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

MATHICSE Technical Report: Numerical homogenization methods for parabolic monotone problems

Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

Truncated low-rank methods for solving general linear matrix equations

A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography

Boundary elements method for microfluidic two-phase flows in shallow channels

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

MATHICSE Technical Report: Numerical homogenization methods for parabolic monotone problems

Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits