Blar i NTNU Open på forfatter "Celledoni, Elena"
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Accurate discretizations of torqued rigid body dynamics
Gustafsson, Einar (Master thesis, 2010)This paper investigates the solution of the free rigid body equations of motion, as well as of the equations governing the torqued rigid body. We will consider two semi-exact methods for the solution of the free rigid body ... -
An introduction to Lie group methods for rigid body systems
Becker, Cathrine Thorsen (Bachelor thesis, 2021)Denne oppgaven er en kort introduksjon til Lie-gruppe-metoder. Relevant bakgrunnmateriale om Lie-gruppe-teori presenteres og vi gir en introduksjon til Lie-Euler, Runge-Kutta Munthe-Kaas og kommutatorfrie metoder. To ... -
B-stability of numerical integrators on Riemannian manifolds
Arnold, Martin; Celledoni, Elena; Cokaj, Ergys; Owren, Brynjulf Rustad; Tumiotto, Denise (Peer reviewed; Journal article, 2024)We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce ... -
B-stability of numerical integrators on Riemannian manifolds
Arnold, Martin; Celledoni, Elena; Cokaj, Ergys; Owren, Brynjulf Rustad; Tumiotto, Denise (Peer reviewed; Journal article, 2024)We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce ... -
Bruk av kunstige nevrale nettverk til å predikere bøyemomenter til stigerør
Gustad, Halvor Snersrud (Master thesis, 2019)Tretthet var inntil nylig ikke ansett som en utfordring for stigerør- og brønnhodesystemer. Belastning på strukturene ble derfor ikke tatt med i design kravene. Siden har utvikling av numeriske modeller og overvåkningssystemer ... -
Computational geometric methods for preferential clustering of particle suspensions
Tapley, Benjamin Kwanen; Andersson, Helge Ingolf; Celledoni, Elena; Owren, Brynjulf (Peer reviewed; Journal article, 2022)A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the ... -
Computing Metrics on Riemannian Shape Manifolds: Geometric shape analysis made practical
Fonn, Eivind (Master thesis, 2009)Shape analysis and recognition is a field ripe with creative solutions and innovative algorithms. We give a quick introduction to several different approaches, before basing our work on a representation introduced by Klassen ... -
Data-driven and geometric numerical methods for mechanical systems
Leone, Andrea (Doctoral theses at NTNU;2024:240, Doctoral thesis, 2024) -
Deep learning as optimal control problems: models and numerical methods
Benning, Martin; Celledoni, Elena; Ehrhardt, Matthias J.; Owren, Brynjulf; Schönlieb, Carola-Bibiane (Journal article; Peer reviewed, 2019)We consider recent work of [11] and [6], where deep learning neuralnetworks have been interpreted as discretisations of an optimal control problemsubject to an ordinary differential equation constraint. We review the first ... -
Deep neural networks on diffeomorphism groups for optimal shape reparametrization
Celledoni, Elena; Glöckner, Helge; Riseth, Jørgen Nilsen; Schmeding, Alexander (Journal article; Peer reviewed, 2023)One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally ... -
DETECTING AND DETERMINING PRESERVED MEASURES AND INTEGRALS OF BIRATIONAL MAPS
Celledoni, Elena; Evripidou, Charalambos; McLaren, David I.; Owren, Brynjulf; Quispel, G.R.W.; Tapley, Benjamin Kwanen (Peer reviewed; Journal article, 2022)In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use ... -
Discrete conservation laws for finite element discretisation of multisymplectic PDEs
Celledoni, Elena; Jackaman, James (Peer reviewed; Journal article, 2021)In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and ... -
Discrete gradient methods in image processing and partial differential equations on moving meshes
Ringholm, Torbjørn (Doctoral theses at NTNU;2018:235, Doctoral thesis, 2018) -
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article; Peer reviewed, 2018)This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This ... -
DYNAMICAL SYSTEMS - BASED NEURAL NETWORKS
Celledoni, Elena; Murari, Davide; Owren, Brynjulf Rustad; Schonlieb, Carola-Bibiane; Sherry, Ferdia (Peer reviewed; Journal article, 2023) -
Dynamics of the N-fold Pendulum in the Framework of Lie Group Integrators
Celledoni, Elena; Cokaj, Ergys; Leone, Andrea; Murari, Davide; Owren, Brynjulf Rustad (Peer reviewed; Journal article, 2022)Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist, and in this work we focus on Runge-Kutta-Munthe-Kaas methods. First, ... -
Energy preserving methods on Riemannian manifolds
Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article, 2018)The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. ... -
Energy-Preserving Integrators Applied to Nonholonomic Systems
Celledoni, Elena; Farre Puiggali, Marta; Høiseth, Eirik Hoel; Martin de Diego, David (Peer reviewed; Journal article, 2019)We introduce energy-preserving integrators for nonholonomic mechanical systems. We will see that the nonholonomic dynamics is completely determined by a triple ({{\mathcal {D}}}^*, \varPi , \mathcal {H}), where {{\mathcal ... -
Energy-preserving numerical methods for differential equations: Linearly implicit methods and Krylov subspace methods
Li, Lu (Doctoral theses at NTNU;2019:272, Doctoral thesis, 2019) -
Equivariant neural networks for inverse problems
Celledoni, Elena; Ehrhardt, Matthias J.; Etmann, Christian; Owren, Brynjulf; Schönlieb, Carola-Bibiane; Sherry, Ferdia (Peer reviewed; Journal article, 2021)In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of ...