My main research field is in the numerical analysis of differential equations, in particular I am interested in the development of numerical methods that preserve underlying geometrical structures of the equations (geometric integration), like symplecticity or volume preservation.

I am also interested in the application of mathematics to interdisciplinary projects, especially towards medicine. I have established project collaborations with medicine on image processing and image analysis projects, modelling of physiological processes, use of machine learning in image analysis and as a diagnostic tool.

MAT101

MAT121(Lineær algebra/Linear algebra)

MNF130(Diskrete strukturar/Discrete mathematics)

MAT160(Beregningsalgoritmer/Numerical analysis 1)

MAT213(Funkskjonsteori/Complex analysis)

MAT251(Klassisk og beregningsorientert mekanikk/ Classical and computational mechanics)

MAT261(Numerisk lineæralgebra/Numerial linear algebra)

MAT262(Bildebehandling/Image processing)

MNF262(Innføringskurs i bildebehandling og visualisering)

Master students:

• Sjur Kvammen (2006) Geometric Integration Methods for Denoising Tensor-valued Images , University of Bergen
• Kristin Eik (2008) Om fluidregistrering for medisinske bilete , University of Bergen
• Eyram Schwinger (2009) Renal Function Estimation using Magnetic Resonance Images, University of Bergen
• Gleb Berdnikov (2011) Image registration with volume constraints, University of Bergen
• Jon Nyfløtt, (2011) "Comparison of distance measures in multimodal image registration", University of Bergen 
• Anna Katharina Trull (2013) "Estimation of parameter stability in some compartment modeling in DCE-MRI", University of Lübeck.
• Milo Viviani (2015), "Geometric integration of the point vortex equation on a rotating sphere", Universita' degli studi di Pavia.
• Andrea Raffo (2016), "Comparmental analysis of 4D MRI data. Application to renal physiology", Universita' degli studi di Genova.
• Will Haugland (2017), "Real-time image based stabilization for Dynamic Contrast Enhanced Ultrasound", Universitetet i Bergen
• Thorstein Rykkje (2018), "Lie groups and the principle of virtual work applied to systems of linked rigid bodies", University of Bergen
• Nikolai Sætran (2018), "Lagrangian dynamics for solid multi-body systems with the Moving Frame formalism", University of Bergen
• Håkon Gimse, (2019), Convolutional Neural Networks for Malaria Detection, University of Bergen
• Fredrick Pfeil, (2019), A higher order IMEX for highly oscillatory differential equations, University of Bergen

PhD Student:

• Are Losnegård (2009- ), co-supervisor
• Xue Huyian (2009-2013), "Volume preserving integrators for ordinary differential equations". UiB
• Eyram Schwinger (2011-2015) Mathematical methods for ship detection from Terra-SAR imaging. University of Ghana, Legon
• Tiril Pedersen Gurholt (2013) "Image processing, filtering and segmentation of data-sets for reservoir simulations", co-supervisor, UiB.
• Ulin Nuha Abdul Qohar (2017-2023) "Modeling and simulation of blood circulation and perfusion", UiB
• Geir K. Nilsen (2018-2022) "Epistemic Uncertainty Quantification in Deep Learning by the Delta Method", UiB
• I-Hao Chen (2022-), UiB, NORCE

Research associates:

• Åsmund Kjørstad, image segmentation of the kidney
• Erik Hanson, medical image processing
• Aurora Campo, image processing for biology, stereological methods.

Postdocs:

• Ilan Degani (2006-2009), quantum control.
• Erlend Hodneland (2010-2011), image registration.

MAT292projects:

• 2009: Erik Natvig, On the optimal control of quantum systems
• 2009: Børge Garpestad, Applications of differential geometry in computer graphics
• 2010: Steinar Børge, Pharmacokinetic and compartment modelling

Retrieve full list from MathSciNet (requires subscription).

NFR Frinatek no. 262203 “Flow based interpretation of Dynamic Contrast-Enhanced imaging” (2017-2021)

Ended projects:

Cody: Computational Dynamics (2006-2009)

NFR no. 191178/V30, GeNuIn: Geometric Numeric Integration in Applications. (NFR, 2009-2012)

MedViz: From Vision to Decision

CRiSP (EU, 2011-2013)

NFR no. 208081 DAADppp Bergen-Lübeck, "Explicit Modelling in DCE-MRI" (2011-2012)

UiB-Meltzer  "Imagina -- Multimodal image alignment" (2011-2012)

UiB-SPIRE "Modelling and Quantification in DCE-MRI" (2013-2014)