Front propagations described by static Hamilton-Jacobi equations can be used to simulate folded geological structures. Simulations of geological folds are a key ingredient in the Compound Earth Simulator (CES), an industrial software tool used in the exploration of oil and gas. In this thesis, local approximation techniques are investigated with respect to accuracy and efficiency. Several novel algorithms are also introduced, of which some are accelerated by parallel implementations on both multicore CPUs and Graphic Processing Units. These algorithms are able to simulate folds at a fraction of the time needed by the CES industry code, while retaining the same level of accuracy. Complicated tasks that previously needed several minutes to be computed can now be performed in just a matter of a few seconds, thus significantly improving the CES user experience.
List of papers. Paper IV is removed from the thesis due to publisher restrictions.
Paper I: Accuracy and efficiency of stencils for the eikonal equation in earth modelling. Tor Gillberg, Øyvind Hjelle, Are Magnus Bruaset. Published in Computational Geosciences 16, number 4 (2012), pages 933-952. doi:10.1007/s10596-012-9296-0 The final publication is available at link.springer.com.
Paper II: A semi-ordered fast iterative method (SOFI) for monotone front propagation in simulations of geological folding. Tor Gillberg Published in the proceedings of MODSIM 2011, 19th International Congress on Modelling and Simulation, pages 641-647. http://www.mssanz.org.au
Paper III: A new parallel 3D front propagation algorithm for fast simulation of geological folds. Tor Gillberg, Mohammed Sourouri, Xing Cai Published in Procedia Computer Science, 9, pages 947-955. Proceedings of the International Conference on Computational Science, ICCS 2012. doi:10.1016/j.procs.2012.04.101 This is an Elsevier Open Access article.
Paper IV: Parallel solvers for static Hamilton-Jacobi equations in three dimensions. Tor Gillberg, Are Magnus Bruaset, Mohammed Sourouri, Øyvind Hjelle. Simula Technical Report, July 2013. Under preparation for journal publication.