Blar i NTNU Open på forfatter "Holden, Helge"
-
A Lipschitz metric for the Camassa--Holm equation
Antonio Carrillo, José; Grunert, Katrin; Holden, Helge (Peer reviewed; Journal article, 2020)We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving ... -
Microbial Enhanced Oil Recovery - Modeling and Numerical Simulations
Amundsen, Aleksander (Master thesis, 2015)This thesis examines the process by which microbes are used to enhance oil recovery from subsurface reservoirs. A brief introduction to reservoirs is given and the possible effects of microbes are explained. A model is ... -
Modelling of Electromagnetic Fields in Conductive Media and development of a Full Vectorial Contrast Source Inversion Method
Wiik, Torgeir (Master thesis, 2008)Seismic surveys are well established in hydrocarbon prospecting, and technology for processing seismic data has been developed through decades. The first electromagnetic survey for hydrocarbon prospecting however, was ... -
Models for dense multilane vehicular traffic
Risebro, Nils Henrik; Holden, Helge (Journal article; Peer reviewed, 2019)We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill--Whitham--Richards model where the velocity in each lane depends only on the density in the ... -
Multiscale Finite Volume Methods: Extension to Unstructured Grids with Applications in Reservoir Simulation
Møyner, Olav (Master thesis, 2012)In reservoir simulations, one of the biggest challenges is solving large modelswith complex geological properties. Because reservoirs can be several kilome-ters long, and still be geologically inhomogeneous over centimeters, ... -
Multiscale Modelling of Elastic Parameters
Børset, Kari (Master thesis, 2008)Petrophysical properties in general and elasticity in particular have heterogeneous variations over many length scales. In a reservoir model, on which one for example can simulate fluid flow, seismic responses and resisitivity, ... -
Multiscale-Streamline Inversion for High-Resolution Reservoir Models
Stenerud, Vegard (Doktoravhandlinger ved NTNU, 1503-8181; 2007:211, Doctoral thesis, 2007)The topic of this thesis is streamline-based integration of dynamic data for porous media systems, particularly in petroleum reservoirs. In the petroleum industry the integration of dynamic data is usually referred to as ... -
Next Generation Multiscale Methods for Reservoir Simulation
Møyner, Olav (Doctoral theses at NTNU;2016:374, Doctoral thesis, 2016)In this thesis, we discuss multiscale simulation techniques for flow and transport in porous media, discretized on unstructured grids. The model equations considered are taken from the field of reservoir simulation, where ... -
Noise-driven bifurcations in a neural field system modelling networks of grid cells
Carrillo, José A.; Holden, Helge; Solem, Susanne (Peer reviewed; Journal article, 2022)The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns ... -
Numerical Aspects of Flow Based Local Upscaling
Odsæter, Lars Vingli (Master thesis, 2013)We start this thesis by giving an introduction to reservoir simulation and upscaling in particular. The most common upscaling techniques, including power averaging methods and flow based local and global methods [10], are ... -
Numerical Methods for the Benjamin-Ono Equation
Fiksdal, Geir Midgard (Master thesis, 2013)In this thesis, we compare four numerical methods for solving the Benjamin-Ono equation. The numerical methods are presented in detail, and we compare them for different test problems. We derive the Hirota bilinear form ... -
Numerical Solutions of Traffic Flow on Networks: Using the LWR-Model and the Godunov Scheme
Bergersen, Bjørnar Dolva (Master thesis, 2014)This paper shows how to create a simulationtool for traffic flow in a network using the Lighthill--Witham--Richards model and the Godunov scheme. First some basic rules about conservation laws are described and how to solve ... -
On angular measures in axiomatic Euclidean planar geometry
Grötschel, Martin; Hanche-Olsen, Harald; Holden, Helge; Krystek, Michael P. (Peer reviewed; Journal article, 2022)We address the issue of angular measure, which is a contested issue for the International System of Units (SI).We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional ... -
On Mimetic Finite Difference Methods for Grids with Curved Faces
Bø, Ruben Kristoffer Thomasse (Master thesis, 2012)In this thesis the mimetic finite difference method for grids with curved faces is presented, implemented and tested with an emphasis on applications in reservoir simulation. The thesis gives a brief introduction to reservoir ... -
On Operator Splitting for the Viscous Burgers' and the Korteweg-de Vries Equations
Nilsen, Espen Birger (Master thesis, 2011)We discuss numerical quadratures in one and two dimensions, which is followed by a discussion regarding the differentiation of general operators in Banach spaces. In addition, we discuss the standard and fractional Sobolev ... -
On the accuracy of the finite volume approximations to nonlocal conservation laws
Aggarwal, Aekta; Holden, Helge; Vaidya, Ganesh Kiran (Peer reviewed; Journal article, 2023) -
On the Braess Paradox with Nonlinear Dynamics and Control Theory
Colombo, Rinaldo; Holden, Helge (Journal article; Peer reviewed, 2016)We show the existence of the Braess paradox for a traffic network with nonlinear dynamics described by the Lighthill–Whitham–Richards model for traffic flow. Furthermore, we show how one can employ control theory to avoid ... -
On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System
Grunert, Katrin; Holden, Helge; Grasmair, Markus (Chapter, 2018)The Camassa–Holm equation and its two-component Camassa–Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the ... -
On the Hunter-Saxton equation
Nordli, Anders Samuelsen (Master thesis, 2012)The Cauchy problem for a two-component Hunter-Saxton equation, begin{align*}(u_t+uu_x)_x&=frac{1}{2}u_x^2+frac{1}{2}rho^2,rho_t+(urho)_x) &= 0,end{align*}on $mathbb{R}times[0,infty)$ is studied. Conservative and dissipative ... -
On the index of meromorphic operator-valued functions and some applications
Berndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger (Chapter, 2017)We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert ...