From low-rank retractions to dynamical low-rank approximation and back
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The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...
The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...
Purpose: This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approac ...
The exploration of electronically excited states and the study of diverse photochemical and photophysical processes are the main goals of molecular electronic spectroscopy. Exact quantum-mechanical simulation of such experiments is, however, beyond current ...
The method of moments (MOM), as introduced by R. F. Harrington more than 50 years ago, is reviewed in the context of the classic potential integral equation (PIE) formulations applied to both electrostatic (part 1) and electrodynamic, or full-wave, problem ...
The method of moments (MOM), as introduced by Roger F. Harrington more than 50 years ago, is reviewed in the context of the classic potential integral equation (IE) formulations applied to both electrostatic (part 1) and electrodynamic or full-wave problem ...
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...
We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...
We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...
