Now showing items 1-20 of 29

• #### A Library for Computing with Trees and B-Series ﻿

(Master thesis, 2015)
Unordered rooted trees and B-series can be used to analyze the properties of many one-step methods for autonomous ordinary differential equations. This thesis describes aspects of trees and B-series necessary to use them ...
• #### Adaptive energy preserving methods for partial differential equations ﻿

(Journal article; Peer reviewed, 2017)
A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of ...
• #### Applications of splitting Methods and exponential Integrators to an electro-chemical Heart Cell Model ﻿

(Master thesis, 2007)
In this thesis we discuss how a system of ordinary differential equations (ODE) describing electro-chemical processes in a heart cell can be solved by numerical methods. The system is stiff, and explicit numerical solvers ...
• #### Community Detection in Large Social Networks ﻿

(Master thesis, 2014)
I denne masteroppgaven implementeres og testes to algoritmer for å finne gruppe- struktur i nettverk, nemlig Louvain-metoden og Diffusion and Propagation-metoden. Et nettverks gruppestruktur består av en naturlig inndeling ...
• #### Deep learning as optimal control problems: models and numerical methods ﻿

(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 ...
• #### Discrete gradient methods in image processing and partial differential equations on moving meshes ﻿

(Doctoral theses at NTNU;2018:235, Doctoral thesis, 2018)
• #### Discrete Invariant Variational Problems ﻿

(Master thesis, 2011)
This thesis studies variational problems invariant under a Lie group transformation, and invariant discretizations of these. In chapters two and three, a general method for creating symplectic integrators preserving certain ...
• #### Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows ﻿

(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 ...
• #### Energy preserving methods on Riemannian manifolds ﻿

(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 numerical methods for differential equations: Linearly implicit methods and Krylov subspace methods ﻿

(Doctoral theses at NTNU;2019:272, Doctoral thesis, 2019)
• #### Geometric and integrability properties of Kahan?s method: The preservation of certain quadratic integrals ﻿

(Peer reviewed; Journal article, 2019)
Given a quadratic vector field on possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly preserves a nearby modified ...
• #### Geometric integration of nonlinear wave equations ﻿

(Master thesis, 2007)
We give an short introduction to the Camassa-Holm equation and its travelling wave solutions. Many well-known equations in mathematical physics describe geodesic flows on appropriate Lie groups. The choice of group and ...
• #### Integral Preserving Numerical Methods on Moving Grids ﻿

(Master thesis, 2013)
Integral preservation for ordinary and partial differential equations is defined, and the integral preserving discrete gradient methods and discrete variational derivative methods on fixed grids are given, with a formal ...
• #### Kombinasjonen av eksplisitt og implisitt løser for simulering av den elektriske aktiviteten i hjertet. ﻿

(Master thesis, 2007)
Å skape realistiske simuleringer av et ECG-signal på en datamaskin kan være til stor nytte når man ønsker å forstå sammenhengen mellom det observerte ECG-signalet og hjertets tilstand. For å kunne få en realistisk simulering ...
• #### Lie Group Integrators for Cotangent Bundles of Lie Groups and Their Application to Systems of Dipolar Soft Spheres ﻿

(Master thesis, 2017)
The objective of this thesis is to study numerical integrators and their application to solving ordinary differential equations arising from mechanical systems. Many mechanical problems are naturally formulated on Lie ...
• #### Minimal Surfaces in Sub-Riemannian Geometries with Applications to Perceptual Completion ﻿

(Master thesis, 2009)
A preliminary study of the papers A Cortical Based Model of Perceptual Completion in the Roto-Translation Space'' and Minimal Surfaces in the Roto-Translation Group with Applications to a Neuro-Biological Image Completion ...
• #### A novel approach to rigid spheroid models in viscous flows using operator splitting methods ﻿

(Peer reviewed; Journal article, 2019)
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for ...
• #### Numerical Methods for Highly Oscillatory Problems ﻿

(Doktoravhandlinger ved NTNU, 1503-8181; 2010:115, Doctoral thesis, 2010)
Classical quadrature methods, i.e. methods for numerical integration,require discretizations that become more fine the more the integrandis oscillating. Conversely, asymptotic methods provide approximationsof the same ...
• #### Numerical Methods for Optical Interference Filters ﻿

(Master thesis, 2009)
We present the physics behind general optical interference filters and the design of dielectric anti-reflective filters. These can be anti-reflective at a single wavelength or in an interval. We solve the first case exactly ...
• #### Numerical Simulation of Interacting Bodies with Delays; Application to Marine Seismic Source Arrays. ﻿

(Master thesis, 2007)
This master thesis has looked at numerical simulation of interacting bodies with delays, especially the situation involving interacting airguns in seismic source arrays. The equations describing the airguns have been ...