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4D Seismic History Matching Using the Ensemble Kalman Filter (EnKF): Possibilities and Challenges
(The University of Bergen, 20100527)This research endeavor presents a 4D seismic history matching work flow based on the ensemble Kalman filter (EnKF) methodology. The objective of this work is to investigate the sensitivity of different combinations of ...Doctoral thesis 
Analysis and Approximation of Coupled 1D3D Flow Models
(The University of Bergen, 20200318)In this thesis, we consider a specific instance of mixeddimensional partial differential equations (PDEs) commonly referred to as the coupled 1D3D flow model. The model itself consists of the Poisson equation defined on ...Doctoral thesis 
Analysis of multibeam sonar echos of herring schools by means of simulation
(The University of Bergen, 20130531)The synchronized behavior of large schools of fish can be a fascinating sight and has caught the attention of researchers for decades. Schools of thousands, or even millions of fish can seemingly function as a single entity, ...Doctoral thesisPeer reviewed 
Analytical Methods for Upscaling of Fractured Geological Reservoirs
(The University of Bergen, 20151016)Numerical simulations have become an essential tool for planning well operations in the subsurface, whether the application is petroleum production, geothermal energy, groundwater utilization or waste disposal and leakage. ...Doctoral thesis 
Analytical, combinatorial and topological properties of quadratic differentials and their applications
(The University of Bergen, 20171213)Quadratic differentials ﬁrst appeared in 1930s in works of Teichmuller in connection with moduli problem for Riemann surfaces. Later it was revealed that quadratic differ entials and their trajectories give solutions to ...Doctoral thesis 
An approximate hybrid method for modeling of electromagnetic scattering from an underground target
(The University of Bergen, 20101209)The detection of a potential petroleum reservoir is achieved through inversion of electromagnetic data acquired in sea floor receivers. Inversion of electromagnetic data requires a number of repeated solves of the ...Doctoral thesis 
Assessment of Sequential and Simultaneous Ensemblebased History Matching Methods for Weakly Nonlinear Problems
(The University of Bergen, 20150213)The ensemble Kalman filter (EnKF) has, since its introduction in 1994, gained much attention as a tool for sequential data assimilation in many scientific areas. In recent years, the EnKF has been utilized for estimating ...Doctoral thesis 
Bayesian and frequentist computation with application to data from the Medical Birth Registry of Norway
(The University of Bergen, 20190425)In chapter 1, the field of statistics is discussed in general terms. Then, Bayes’ theorem is presented together with the posterior distribution. Finally, we consider maximum likelihood estimation and its relation to ...Doctoral thesis 
Classical and Stochastic Slit Löwner Evolution
(The University of Bergen, 20141010)Doctoral thesis 
Compositional reservoir simulation with emphasis on the IMPSAT formulation
(The University of Bergen, 20060407)Doctoral thesis 
Computeraided proofs and algorithms in analysis
(The University of Bergen, 20130614)The computational power has increased dramatically since the appearance of the first computers, making them a vital tool in the analysis of dynamical systems. We present further applications of those two basic ideas, namely ...Doctoral thesisPeer reviewed 
Conforming Discretizations of MixedDimensional Partial Differential Equations
(The University of Bergen, 20180601)Mixeddimensional partial differential equations (PDEs) are coupled equations defined on connected manifolds of different dimensionalities. Two main examples of mixeddimensional PDEs are considered in this dissertation, ...Doctoral thesis 
Continuous Updating of a Coupled ReservoirSeismic Model Using an Ensemble Kalman Filter Technique
(The University of Bergen, 20070329)This work presents the development of a method based on the ensemble Kalman filter (EnKF) for continuous reservoir model updating with respect to the combination of production data, 3D seismic data and timelapse seismic ...Doctoral thesis 
Convective mixing in geological carbon storage
(The University of Bergen, 20111125)The industrial era has seen an exponential growth in the atmospheric concentration of carbon dioxide (CO2), resulting mainly from the burning of fossil fuels. This can cause changes in the climate that have severe impacts ...Doctoral thesis 
Derivation and numerical solution of fully nonlinear and fully dispersive water wave model equations
(The University of Bergen, 20170609)The water wave theory is a classical part of Fluid Mechanics. It has a long scientific history with a great number of mathematical results [10, 32]. The first studies in this field were done by Stokes in 1847 [34]. He ...Doctoral thesis 
Detecting Periodic Elements in Higher Topological Hochschild Homology
(The University of Bergen, 20130820)Doctoral thesisPeer reviewed 
Development and implementation of the generalized continuum model for transport in porous media
(The University of Bergen, 20180319)Fluid flow phenomena in porous media have always attracted a lot of attention of scientists and engineers. Attempts to quantify the average transport in homogeneous media with a simple partial differential equation with ...Doctoral thesis 
Efficient global minimization methods for variational problems in imaging and vision
(The University of Bergen, 20110819)Energy minimization has become one of the most important paradigms for formulating image processing and computer vision problems in a mathematical language. Energy minimization models have been developed in both the ...Doctoral thesis 
Ensemble Methods of Data Assimilation in Porous Media Flow for NonGaussian Prior Probability Density
(The University of Bergen, 20150828)Ensemblebased dataassimilation methods have gained fast growth since the ensemble Kalman filter (EnKF) was introduced into the petroleum engineering. Many techniques have been developed to overcome the inherent disadvantages ...Doctoral thesis 
Estimation and identifiability of kinetic parameters in dynamical models of biochemical reaction networks
(The University of Bergen, 20200218)This dissertation is a partial fulfillment of the requirements for the degree Doctor of Philosophy (PhD) at the Department of Mathematics, University of Bergen. The subject of the thesis is estimation of parameters in ...Doctoral thesis