Publications related to Discretization

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Fabio Zoccolan, Gianluigi Rozza

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation

Alfio Quarteroni, Francesco Regazzoni

When generating in-silico clinical electrophysiological outputs, such as electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical models have relied on single physics, i.e. of the cardiac electrophysiology (EP), neglecting the role o ...

Elsevier Science Sa2024

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Marco Picasso, Samuel Dubuis

A space-time adaptive algorithm is presented to solve the incompressible Navier-Stokes equations. Time discretization is performed with the BDF2 method while continuous, piecewise linear anisotropic finite elements are used for the space discretization. Th ...

San Diego2023

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Alfio Quarteroni, Francesca Bonizzoni

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Lausanne2023

lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Alfio Quarteroni, Luca Dede', Marco Fedele

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the ...

Amsterdam2023

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Liang Xu

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Isabel Haasler, Axel Ringh, Yiqiang Chen

In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...

2023

Efficient lattice Green's function method for bounded domain problems

William Curtin, Ankit Gupta, Max Ludwig Hodapp

The lattice Green's function method (LGFM) is the discrete counterpart of the continuum boundary element method and is a natural approach for solving intrinsically discrete solid mechanics problems that arise in atomistic-continuum coupling methods. Here, ...

WILEY2022

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Discretization

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Efficient lattice Green's function method for bounded domain problems

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Graph Chatbot

Chat with Graph Search

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Efficient lattice Green's function method for bounded domain problems

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution