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

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Alfio Quarteroni, Simone Deparis, Riccardo Tenderini, Stefano Pagani

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...

2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...

EPFL2022

Fast global spectral methods for three-dimensional partial differential equations

Daniel Kressner, Christoph Max Strössner

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

OXFORD UNIV PRESS2022

Analytic modelling of passive microfluidic mixers

Jean-Michel Sallese, Christophe Lallement

This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...

AMER INST MATHEMATICAL SCIENCES-AIMS2022

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Raphaël Jean Berthier

Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...

OXFORD UNIV PRESS2022

Bounds on photon scattering

Denis Karateev, Kelian Philippe Häring, Marco Meineri, Aditya Hebbar

We study 2-to-2 scattering amplitudes of massless spin one particles in

d=4

space-time dimensions, like real world photons. We define a set of non-perturbative observables (Wilson coefficients) which describe these amplitudes at low energies. We use full ...

2022

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

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

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

Luca Pegolotti

This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular imple ...

EPFL2021

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

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PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Adaptive analysis-aware defeaturing

Fast global spectral methods for three-dimensional partial differential equations

Analytic modelling of passive microfluidic mixers

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Bounds on photon scattering

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

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

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Analytic modelling of passive microfluidic mixers

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Adaptive analysis-aware defeaturing

Fast global spectral methods for three-dimensional partial differential equations

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

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

Bounds on photon scattering

A parabolic local problem with exponential decay of the resonance error for numerical homogenization