Research Interests

Heterogeneous computing using accelerator units

Modern graphics cards (GPUs) have an unrivaled ability for parallel processing of floating-point vectors, as documented extensively on the GPGPU webpage. Around 2004, a few colleageus and I started to use inexpensive commodity graphics cards as a platform for high-performance computing. We were the first group to study high-resolution methods for conservation and balance laws, for which we obtained (more than) an order of magnitude speedup. Later, several other researchers have followed in our footsteps.

I have supervised several students on GPGPU and heterogeneous computing, and together with Tor Dokken, I founded a new research group at SINTEF.

High-resolution methods for conservation laws

In my PhD and during my first years as a researcher I worked a lot on high-resolution methods for hyperbolic conservation laws. In particular, I worked on

The primary applications were within:

The last ten years or so, my focus has shifted more towards applications in porous media, where I still work on the use of front-tracking methods in combination with streamline simulation. As a result of this shift in interest, I am no longer responsible for the Conservation Laws Preprint Server, which I started in 1996. However, I am still reading literature and using high-resolution schemes as an example when investigating HPC on graphics hardware.

Analysis of operator splitting methods

My first scientific activity was mathematical analysis of numerical methods for nonlinear PDEs. I was concerned with questions concerning existence, uniqueness, and stability. Together with Holden, Kalsen, and Risebro, I developed a nice theory for convergence of general operator splitting methods that is written up in recent book, which is accompanied by software routines.

Miscellaneous

Apart from the above, I am generally interested in numerical solution of (nonlinear) PDEs, scientific computing, and visualization.

Numerical methods for flow in porous media

My research group at SINTEF works on fast, efficient and accurate numerical methods for flow in porous media. In particular, we aim to develop numerical methods that facilitate direct simulation of high-resolution, industry-standard geomodels of highly heterogeneous and fractured porous media containing multimillion cells. To this end, we work on algorithmic development of:

Open-source tools for reservoir modeling

The MATLAB Reservoir Simulation Toolbox: As part of this research we have developed a comprehensive set of routines and data structures for reading, representing, processing, and visualizing unstructured grids, with particular emphasis on the corner-point formate used within the petroleum industry. To enable other researchers to benefit from our efforts, we have compiled a MATLAB toolbox, which is released under the GNU General Public License (GPL). The toolbox consists of two main parts: a core offering basic functionality and single and two-phase solvers, and a set of add-on modules offering more advanced models, viewers and solvers. MRST is mainly intended as a toolbox for rapid prototyping and demonstration of new simulation methods and modeling concepts on unstructured grids. Despite this, many of the tools are quite efficient and can be applied to surprisingly large and complex models.
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The OPM initiative: I am currently part of an collaborative effort to develop an open-source (GPL) simulation suite for flow and transport in porous media. The OPM suite will target reservoir simulation and CO2 sequestration as well as modelling of biological systems and engineered media. In particular, OPM will contain support for industry-standard grid formats (corner-point grids, etc).
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Geological Storage of CO2

I work on mathematical modelling and risk analysis for geological storage of CO2, where my primary interest is in developing fast simulation tools for estimating structural, residual, and solubility trapping. I have also worked with assessing the impact that top-surface morphology has on the migration of CO2. I am also quite interested in formulating benchmarks and comparative solution projects as a means to study the uncertainties involved in modelling and simulation of C02 deposition.

PDE-based image processing

I have been interested in image processing since my days as an undergraduate student. A few years ago, SINTEF started a new activity on PDE-based methods for image processing. I was scientific advisor for this activity, but apart from this, my only contribution to PDE-based image processing has been to organize a few conferences/workshops and edit two conference proceedings.