Browsing NTNU Open by Author "Holden, Helge"
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A Convergent CrankNicolson Galerkin Scheme for the BenjaminOno Equation
Galtung, Sondre Tesdal (Master thesis, 2016)In this thesis we prove the convergence of a CrankNicolson type Galerkin finite element scheme for the initial value problem associated to the BenjaminOno equation. The proof is based on a recent result for a similar ... 
A CUDA BackEnd for the Equelle Compiler.
Holm, Håvard Heitlo (Master thesis, 2014)As parallel and heterogeneous computing becomes more and more a necessity for implementing high performance simulators, it becomes increasingly harder for scientists and engineers without experience in high performance ... 
A GPU Accelerated Simulator for CO2 Storage
Prestegård, Elisabeth K (Master thesis, 2014)The goal of this thesis has been to develop a fast simulator for largescale migration of CO2 in saline aquifers. We have also focused on being able to let the CO2 storage atlas from the Norwegian Petroleum Directorate ... 
A Lipschitz metric for the HunterSaxton equation
Carrillo, José A; Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2019)We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ... 
A Lipschitz metric for the Hunter–Saxton equation
Antonio Carrillo, Jose; Grunert, Katrin; Holden, Helge (Journal article; Peer reviewed, 2019)We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ... 
A Modular Implementation of the Traffic Equation Using the Cell Transmission Model
Lahmeyer, Ludwig (Master thesis, 2019)Evnen til å simulere og modifisere et veinett i en virtuell simulering er et uvurderlig verktøy for å spare ressurser og tid for å identifisere den beste løsningen på et gitt problem. Målet med dette prosjektet var å skape ... 
A Parallel Multiscale Mixed FiniteElement Method for the Matlab Reservoir Simulation Toolbox
Hoff, Anders (Master thesis, 2012)We start by giving a brief introduction to reservoirs and reservoir modelling at different scales. We introduce a mathematical model for the twophase flow, before we look at numerical discretizations. In particular we ... 
A ThreeDimensional Finite Element Poisson Solver for Monte Carlo Particle Simulators
Fatnes, Siri Narvestad (Master thesis, 2018)A finite element Poisson solver for the calculation of the threedimensional electric field in selfconsistent particle simulations has been implemented in Fortran and integrated into an existing Monte Carlo simulator for ... 
Addendum to “The KolmogorovRiesz compactness theorem” [Expo. Math. 28 (2010) 385–394]
HancheOlsen, Harald; Holden, Helge (Journal article; Peer reviewed, 2016)We show how to improve on Theorem 10 in HancheOlsen and Holden (2010), describing when subsets in W1,p(Rn) are totally bounded subsets of Lq(Rn) for p 
An improvement of the KolmogorovRiesz compactness theorem
HancheOlsen, Harald; Holden, Helge; Malinnikova, Eugenia (Journal article; Peer reviewed, 2018)The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces. 
An Investigation Into Braess' Paradox and Selfish Routing in Traffic Flow  Solving the nonlinear traffic program with linear cost functions on traffic networks
Sørensen, Anette Østbø (Master thesis, 2014)The aim of this master thesis was to investigate Braess' Paradox in traffic flow and to look at the effect of selfish routing in optimization of flow distribution on traffic networks. Braess' Paradox is a well known ... 
An Investigation Into Braess' Paradox and Selfish Routing in Traffic Flow: Solving the nonlinear traffic program with linear cost functions on traffic networks
Sørensen, Anette Østbø (Master thesis, 2014)The aim of this master thesis was to investigate Braess' Paradox in traffic flow and to look at the effect of selfish routing in optimization of flow distribution on traffic networks. Braess' Paradox is a well known ... 
Applying hybrid methods to reduce nonphysical cycles in the flux field
Haugland, Christine Marie Øvrebø (Master thesis, 2012)In this thesis we present the theoretical background for the twopoint fluxapproximation method; (TPFA), mimetic discretisation methods, and the multipoint flux approximation method; (MPFA). Theoretical arguments concerning ... 
Asymptotic Approximations of Gravity Waves in Water
Jansen, Arne Kristian (Master thesis, 2009)The governing equations for waves propagating in water are derived by use of conservation laws. The equations are then cast onto dimensionless form and two important parameters are obtained. Approximations by use of ... 
A continuous interpolation between conservative and dissipative solutions
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denoted dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the twocomponent Camassa–Holm system ... 
A continuous interpolation between conservative and dissipative solutions for the twocomponent CamassaHolm system
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denotedαdissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the twocomponent Camassa–Holm system ... 
Continuum limit of FollowtheLeader models – a short proof
Holden, Helge; Risebro, Nils Henrik (Journal article, 2018)We offer a simple and selfcontained proof that the FollowtheLeader model converges to the LighthillWhithamRichards model for traffic flow. 
Convergence and convergence rates of numerical methods for conservation laws
Solem, Susanne (Doctoral theses at NTNU;2019:11, Doctoral thesis, 2019) 
Convergence of a fully discrete finite difference scheme for the Kortewegde Vries equation
Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik (Journal article, 2015)We prove convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data ut=0 = u0 is of high ... 
Development of an immersed boundary method for simulating contaminated fluid interfaces in twophase flow
Lysgaard, Morten Olsen (Master thesis, 2015)This thesis covers the theory and implementation, verification and validation of an immersed boundary method for simulating the effect of an elastic membrane covering water drops in crude oil. First an introduction to ...