Open and completed master projects

Open master projects

This is a list of open master projects in Section 4. If you are interested in a project, please contact the project supervisor given in the left column.

Supervisor	Open projects
S. H. Christiansen	Theory of finite elements
G. Dahl	Combinatorial matrices
U. S. Fjordholm	• Stability of the ENO method • Numerical methods for nonlocal conservation laws
E. Hiltunen	• Lattice-summation methods for band-gap evanescent waves • Homogenization theory for high-contrast time-dependent particles • Perturbation theory for dispersion relations of spacetime-periodic materials
H. Hoel	• Numerical methods for the stochastic Allen–Cahn equation • Hitting times for diffusion processes
K. Karlsen	• Neural Networks and PDEs in Modern Function Spaces: Sobolev and Barron Spaces • Well-Posedness of Fractional Bidomain Models for Cardiac Electrophysiology • Weak Convergence Methods for Stochastic Conservation Laws • Numerical Methods for Stochastic Perturbations of the Shallow Water Camassa-Holm Equation • Well-Posedness and Time-Discretization of Stochastic Bidomain Models for Cardiac Electrophysiology • Compactness estimates for approximate solutions of stochastic conservation laws • Compactness estimates for difference approximations of conservation laws • Discontinous Galerkin methods for stochastic Degasperis-Procesi equations

Completed master projects

This is a list of master projects supervised by members of Section 4 (Computational Mathematics and Partial Differential Equations) since 2011. The columns show year of graduation, title of the thesis, and supervisor.

Year	Title	Sup.
2024	Graphs and matchings	ØR
2024	Synthetic data generation for an inverse scattering problem	USF
2023	Pseudo-Hamiltonian System Identification	ØR
2023	Optimizing Coordination on Road Construction Sites with a Reinforcement Learning Framework	ØR
2022	Computing Spectra with Error Control	ØR
2022	Algorithms in compressed sensing	ØR
2021	Compressed Sensing and Deep Learning - Investigation of stability properties for linear inverse problems	ØR
2021	On recent advances in compressed sensing	ØR
2021	Computational barriers in statistical estimation and reconstruction - Can solutions to the LASSO be computed?	ØR
2021	Finite-volume methods with dense neural networks	USF
2011	Interpolatory surface subdivision	MF
2013	Boundary conditions for interpolatory subdivison	MF
2017	Nonlinear interpolatory curve subdivision schemes	MF
2017	Transfinite surface interpolation over irregular n-sided domains	MF
2011	Modellering av diffusjon av nevrotransmittere i den ekstracellulære vesken	SC
2015	Stability of upwind mixed discretizations of convection diffusion equations	SC
2015	Plane Wave Semi-Continuous Galerkin method for the Helmholtz equation	SC
2014	Applications of compressed sensing in computational physics	ØR
2016	Coherence estimates between Hadamard matrices and Daubechies wavelets	ØR
2016	Sparse Matrix Storage Schemes with OpenCL for a Linear System arising from a Discrete Model of Elasticity	ØR
2018	Recommender systems analysis by compressed sensing	ØR
2018	Iterative Algorithms in Compressive Sensing	ØR
2018	Compressed Sensing and the Quadratic Bottleneck Problem: A Combinatorics Approach	ØR
2019	Krylovmetodar for strukturerte lineære system	ØR
2019	Parseval Reconstruction Networks	ØR
2019	Stability of Adaptive Neural Networks for Image Reconstruction	ØR
2020	Can everything be learned? Recovery of highly sparse images using deep neural networks	ØR
2021	Computational barriers in statistical estimation and reconstruction	ØR
2018	Take a look at the wild side	NHR
2020	Løyse PDE ved hjelp av nevrale nettverk	NHR
2011	Convergence of a Relaxation Scheme for a 2x2 Triangular System of Conservation Laws	NHR
	Portfolio optimization with Conditional Value-at-Risk constraints	GD
	Risk - reward optimization; illustrated with Conditional Value-at-Risk	GD
	Dobbeltstokastiske matriser, Skalering og Rangering	GD
	Applications of Directed Algebraic Topology in Optimization Theory	GD
	Ranking and Hillside Form
	Numerical Methods for Solving the Fastest Mixing Markov Chain Problem	GD
	Trafikktilordning og Optimering	GD
	Optimization in l1- norm for Sparse Recovery	GD
	Optimale randbetingelser for det diskrete Laplace-problemet	GD
	Optimising airside operations of an airport for punctuality and stability	GD
	The northern European gas market as a linear programming model	GD
	Arrival, departure and surface management of flights by exploiting the network simplex algorithm	GD
	The Fastest Mixing Markov Chain	GD
	Doubly Stochastic Matrices and the Assignment Problem	GD
	On solving the inverse problem of intensity modulated radiation therapy	GD
	Numerical methods for the Camassa Holm equation	KHK
	Portfolio Optimization in a Jump-Diffusion Market with Durability and Local Substitution: A Penalty Approximation of a Singular Control Problem	KHK
	Pricing the American Put Option by the Method of Zhu	KHK
	The bidomain equations of cardiac electrophysiology: Homogenization and stochastic forcing	KHK
	Partial Differential Equation Models of Active Transport in Neuronal Axons	KHK
	Nonlinear Compactness Effects of Scalar Conservation Law	KHK
	Analysis of the power penalty method for American options using viscosity solutions	KHK
	Pricing Perpetual American Options with Linear Programming	KHK
	Convergence of penalty methods for American options. Variational solutions and the compactness method	KHK

Published Aug. 13, 2021 11:59 AM - Last modified June 29, 2025 4:53 PM