Browsing NTNU Open by Author "Holden, Helge"
Now showing items 1-20 of 72
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A Convergent Crank-Nicolson Galerkin Scheme for the Benjamin-Ono Equation
Galtung, Sondre Tesdal (Master thesis, 2016)In this thesis we prove the convergence of a Crank--Nicolson type Galerkin finite element scheme for the initial value problem associated to the Benjamin--Ono equation. The proof is based on a recent result for a similar ... -
A CUDA Back-End 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 large-scale 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 kink-model for gas simulation
Mustad, Ruben (Master thesis, 2020)I denne masteroppgaven er vi interessert i Eulerligningene for kompressibel gass. En vanlig modell for å simulere gassflyt i rør er de isotermiske Eulerligningene. I denne oppgaven vil vi se på en modell som beskriver ... -
A Lipschitz metric for the Hunter-Saxton 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 Finite-Element 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 two-phase flow, before we look at numerical discretizations. In particular we ... -
A Three-Dimensional 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 three-dimensional electric field in self-consistent particle simulations has been implemented in Fortran and integrated into an existing Monte Carlo simulator for ... -
Addendum to “The Kolmogorov-Riesz compactness theorem” [Expo. Math. 28 (2010) 385–394]
Hanche-Olsen, Harald; Holden, Helge (Journal article; Peer reviewed, 2016)We show how to improve on Theorem 10 in Hanche-Olsen and Holden (2010), describing when subsets in W1,p(Rn) are totally bounded subsets of Lq(Rn) for p -
An improvement of the Kolmogorov-Riesz compactness theorem
Hanche-Olsen, 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 non-linear 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 non-linear 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 two-point flux-approximation 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 two-component Camassa–Holm system ... -
A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system
Grunert, Katrin; Holden, Helge; Raynaud, Xavier (Peer reviewed; Journal article, 2015)We introduce a novel solution concept, denotedα-dissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ... -
Continuum limit of Follow-the-Leader models – a short proof
Holden, Helge; Risebro, Nils Henrik (Journal article, 2018)We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards 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 Korteweg-de 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 u|t=0 = u0 is of high ...