@phdthesis {HjelleTUDelft2014,
	title = {A Hamilton-Jacobi Framework for Modeling Geological Folding and Deformation},
	year = {2014},
	month = {July},
	school = {Delft University of Technology},
	type = {phd},
	address = {Department of Imaging Physics, Faculty of Applied Sciences},
	keywords = {Workshop},
	isbn = {978-82-92593-15-8},
	author = {Hjelle, {\O}yvind}
}
@article {Simula.simula.2858,
	title = {Parallel Solutions of Static Hamilton-Jacobi Equations for Simulations of Geological Folds},
	journal = {Journal of Mathematics in Industry},
	volume = {4},
	number = {10},
	year = {2014},
	publisher = {Springer},
	abstract = {Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. The performance of the new methods are investigate for tow types of static Hamilton-Jacobi formulations are investigated, the isotropic eikonal equation and an anisotropic formulation used to simulate different types of geological folding. Simulations of geological folding is a key component in an industrial software used in oil and gas exploration. In particular, our experiments indicate that the new algorithms would be capable of accelerating an existing industrial simulator substantially. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds. The new methods are now being migrated to the industrial software.},
	doi = {10.1186/2190-5983-4-10},
	author = {Gillberg, Tor and Are Magnus {Bruaset} and Hjelle, {\O}yvind and Sourouri, Mohammed}
}
@article {Simula.simula.1498,
	title = {A Numerical Framework for Modelling Folds in Structural Geology},
	journal = {Mathematical Geosciences},
	volume = {45},
	number = {3},
	year = {2013},
	month = {April},
	pages = {255-276},
	publisher = {Springer},
	abstract = {A numerical framework for modelling folds in structural geology is presented. This framework is based on a novel and recently published Hamilton-Jacobi formulation by which a continuum of layer boundaries of a fold is modelled as a propagating front. All the fold classes from the classical literature (parallel folds, similar folds, and other fold types with convergent and divergent dip isogons) are modelled in 3D space as continua defined on a finite difference grid. The propagating front describing the fold geometry is governed by a static Hamilton-Jacobi equation, which is discretized by upwind finite differences and a dynamic stencil construction. This forms the basis of numerical solution by finite difference solvers such as fast marching and fast sweeping methods. A new robust and accurate scheme for initialization of finite difference solvers for the static Hamilton-Jacobi equation is also derived. The framework has been integrated in simulation software, and a numerical example is presented based on seismic data collected from the Karama Block in the North Makassar Strait outside Sulawesi.},
	keywords = {Workshop},
	author = {Hjelle, {\O}yvind and Steen A. {Petersen} and Are Magnus {Bruaset}}
}
@techreport {parallel-solvers-for-static-hamilton-jacobi-equations,
	title = {Parallel Solvers for Static Hamilton-Jacobi Equations in Three Dimensions},
	year = {2013},
	month = {September},
	publisher = {Simula Research Laboratory},
	abstract = {Three algorithms for numerical solution of static Hamilton-Jacobi equations on parallel computers are presented in this paper. The proposed algorithms are applicable to both isotropic and anisotropic problems, and are here used to simulate folded geological structures of high complexity. Our algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well on parallel architectures. In particular, these experiments indicate that the new algorithms would be capable of accelerate an existing industrial simulator to a level where detailed three-dimensional studies of complicated geological scenarios can be performed interactively. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds.},
	author = {Gillberg, Tor and Are Magnus {Bruaset} and Sourouri, Mohammed and Hjelle, {\O}yvind}
}
@article {Simula.simula.622,
	title = {Accuracy and Efficiency of Stencils for the Eikonal Equation in Earth Modelling},
	journal = {Computational Geosciences},
	volume = {16},
	number = {4},
	year = {2012},
	month = {September},
	pages = {933-952},
	abstract = {Motivated by the needs for creating fast and accurate models of complex geological scenarios, accuracy and efficiency of three stencils for the isotropic eikonal equation on rectangular grids are evaluated using a Fast Marching implementation. The stencils are derived by direct modelling of the wave front, resulting in new and valuable insight in terms of improved upwind and causality conditions. After intro- ducing a method for generalising first order upwind stencils to higher order, a new second order Diagonal stencil is presented. Similarly to the Multistencils Fast Marching ap- proach, the Diagonal stencil makes use of nodes in the diagonal directions, whereas the traditional Godunov stencil uses solely edge-connected neighbours. The Diagonal stencil uses nodes close to each other, reaching upwind, to get a more accurate estimate of the angle of incidence of the arriving wave front. Although the stencils are evaluated in a Fast Marching setting, they can be adapted to other efficient eikonal solvers. All first and second order stencils are evaluated in a range of tests. The first test case models a folded structure from the Zagros fold belt in Iran. The other test cases are constructed to investigate specific properties of the examined stencils. The numerical investigation considers convergence rates and CPU times for non-constant and constant speed first-arrival computations. In conclusion, the Diagonal stencil is the most efficient and accurate of the three alternatives.},
	keywords = {Workshop},
	doi = {10.1007/s10596-012-9296-0},
	author = {Gillberg, Tor and Hjelle, {\O}yvind and Are Magnus {Bruaset}}
}
@inproceedings {Simula.simula.1284,
	title = {A Data-Restoration and Model-Reconstruction Workflow for Simultaneous Seismic Interpretation and Model Building},
	journal = {EAGE 74th Conference \& Exhibition, Extended Abstracts},
	year = {2012},
	publisher = {EAGE},
	type = {Annual},
	abstract = {A workflow for simultaneous seismic interpretation and model building is presented. The workflow consists of two sequences. A first, in which a depth seismic section is gradually altered, by reverse and mainly structural processes, in order to restore the seismic section of the target at the time of deposition. In the second sequence a distribution of properties representing the target becomes subject to the normal version of the previous reverse geological processes, now ordered forward in time. The final property distribution is the reconstruction of the present day distribution. The method has many interesting advantages compared to present day workflows. It is fast and the model becomes geologically feasible. During the successive data-Restoration the impact of faults, deformation and compaction is gradually removed by invoking the inverse of these processes. The section looks \&ldquo;younger\&rdquo; and e.g. stratigraphical interfaces appears easier to interpret. Few - 10 times less than normal - and simpler surfaces are needed to represent the target no matter how much it was compartmentalised originally. Having the restoration processes and their order in place the model- Reconstruction is done very fast executing the normal processes forwardly. Additional mainly depositional and erosional processes can be added during reconstruction.},
	author = {Steen A. {Petersen} and Hjelle, {\O}yvind and Hustoft, Steinar and Houbiers, Marianne and Rasmussen, Rasmus}
}
@inproceedings {Simula.simula.1118,
	title = {A Parallel 3D Front Propagation Algorithm for Simulation of Geological Folding on GPUs},
	journal = {EAGE 74th Conference \& Exhibition, Copenhagen},
	year = {2012},
	month = {June},
	publisher = {EAGE},
	type = {Conference},
	abstract = {A 3D front propagation algorithm for the simulation of geological folding is presented. The algorithm is implemented on multicore and GPU architectures. Numerical experiments based on OpenMP show an almost perfect scaling. Using the automatic code translator Mint, Cuda code is created from seqential C code. On a GPU the Cuda code runs 67-95 times faster than sequential code, and allows 3D grids to be computed at interactive times.},
	keywords = {Conference},
	author = {Gillberg, Tor and Hjelle, {\O}yvind and Are Magnus {Bruaset}},
	editor = {Eage, }
}
@article {Simula.simula.195,
	title = {A Hamilton-Jacobi Framework for Modeling Folds in Structural Geology},
	journal = {Mathematical Geosciences},
	volume = {43},
	number = {7},
	year = {2011},
	month = {October},
	pages = {741-761},
	publisher = {Springer},
	abstract = {A novel mathematical framework for modeling folds in structural geology is presented. All the main fold classes from the classical literature: parallel folds, similar folds, and other fold types with convergent and divergent dip isogons are modeled in 3D space by linear and non-linear first-order partial differential equations. The equations are derived from a static Hamilton-Jacobi equation in the context of isotropic and anisotropic front propagation. The proposed Hamilton-Jacobi framework represents folded geological volumes in an Eulerian context as a time of arrival field relative to a reference layer. Metric properties such as distances, gradients (dip and strike), curvature, and their spatial variations can then be easily derived and represented as three-dimensional continua covering the whole geological volume. The model also serves as a basis for distributing properties in folded geological volumes.},
	doi = {10.1007/s11004-011-9357-2},
	author = {Hjelle, {\O}yvind and Steen Agerlin {Petersen}}
}
@techreport {Simula.cg.4,
	title = {Extrapolation From a Very Low Number of Computer Experiments},
	year = {2010},
	publisher = {Simula Research Laboratory},
	author = {Lorentzen, Ralph and Hjelle, {\O}yvind and Hans Petter {Langtangen} and Are Magnus {Bruaset}}
}
@inproceedings {Simula.SC.418,
	title = {Earth Recursion, an Important Component in Sharead Earth Model Builders},
	journal = {Proceedings from the 70th EAGE Conference \& Exhibition},
	year = {2008},
	note = {The paper received Best Paper Award.},
	publisher = {Society of Petroleum Engineers and European Association of Geoscientists and Engineers},
	type = {Conference},
	address = {Rome},
	abstract = {The concept of Earth Recursion is introduced to solve critical problems of Shared Earth Model builders especially related to their capability to express the geological evolution. The recursive approach turns out to be very efficient when addressing apparently diverse questions like natural {\textquotedblleft}aging{\textquotedblright}, property depth trends, incorporation of externally defined property distributions, faults within volumes and structural restoration. The concept is implemented in the Compound Earth Model builder by StatoilHydro. It is shown how the original expression for spatial distribution of properties can be written as a recursive sequence. This revision forms the basis for the implementation of Earth Recursion in the builder and demonstrated by construction of a complex property distribution reflecting the interference of on-lapping features, normal faulting and compression.},
	author = {Steen A. {Petersen} and Hjelle, {\O}yvind}
}
@inproceedings {Simula.SC.11,
	title = {Earth Modelling Using Distance Fields Derived by Fast Marching},
	journal = {EAGE 69th Conference \& Exhibition, London},
	year = {2007},
	note = {Extended abstract},
	type = {Annual},
	abstract = {A fast methodology to distribute properties of any geological complexity in 2D and 3D space is presented. The method uses combinations of distance-fields (and other attributes) derived by Fast Marching Level Set techniques from simpler geometries in 2D and 3D to populate space with relevant physical properties. The paper presents how the methodology works for different geometries and the result of applying combined distance fields to describe realistic and complicated geological situations.},
	doi = {10.3997/2214-4609.201401555},
	author = {Steen Agerlin {Petersen} and Hjelle, {\O}yvind and Susanne Lund {Jensen}},
	editor = {Eage, }
}
@inproceedings {Simula.SC.8,
	title = {Fast Marching Level Set Methods Applied to Geomodelling},
	journal = {69th EAGE Conference \& Exhibition},
	year = {2007},
	type = {Conference},
	abstract = {Numerical schemes based on Fast Marching Level Set techniques are used for calculating distance fields and related scalar and vector fields for distributing physical properties in geological bodies in 2d and 3d space. The scalar fields are generated by solving partial differential equations (PDEs) by finite difference schemes over 2d and 3d Cartesian grids. To compute the distance field, the PDE is the well-known Eikonal equation. The speed and the numerical stability of Fast Marching make it a powerful tool in geo-applications. We demonstrate how distance fields, gradient fields and parameter distribution fields, representing object-space relations, can be calculated fast and consistently on 2d and 3d Cartesian grids. In particular we have been using Fast Marching in Norsk Hydro{\textquoteright}s Compound Modelling environment, where simple geometries and univariate functions are combined to form complex 3d geological models.},
	author = {Hjelle, {\O}yvind and Steen Agerlin {Petersen}}
}
@book {Hjelle.2006.1,
	title = {Triangulations and Applications},
	year = {2006},
	publisher = {Springer},
	organization = {Springer},
	address = {Berlin},
	isbn = {ISBN: 3-540-33260-X},
	author = {Hjelle, {\O}yvind and D{\ae}hlen, Morten}
}
@article {Hjelle.2005.1,
	title = {Multilevel Least Squares Approximation of Scattered Data Over Binary Triangulations},
	journal = {Computing and Visualization in Science},
	volume = {8},
	number = {2},
	year = {2005},
	month = {April},
	pages = {81-92},
	abstract = {An adaptive method for approximating huge scattered data sets is presented. The approximation scheme generates multilevel triangulations obtained using a subdivision scheme known as longest edge bisection. Nested function spaces are defined over the multilevel triangulations. The approximation problem is solved by successive refinement of the triangulation while iterative methods are used for solving a system of linear equations at intermediate levels of the multi-level scheme. Regularization terms are coupled with a standard least squares formulation to guarantee uniqueness and control smoothness of the solution.},
	author = {Hjelle, {\O}yvind and D{\ae}hlen, Morten}
}
@misc {Hjelle.2005.2,
	title = {Triangulations and Applications},
	howpublished = {Lecture Notes, University of Oslo},
	year = {2005},
	note = {Lecture notes, University of Oslo, 227 pages},
	author = {Hjelle, {\O}yvind and D{\ae}hlen, Morten}
}
@inbook {Sulebak.2003.1,
	title = {Multiresolution Spline Models and Their Applications in Geomorphology},
	booktitle = {Concepts and Modelling in Geomorphology: International Perspectives},
	year = {2003},
	pages = {221-237},
	publisher = {Terrapub},
	organization = {Terrapub},
	address = {Tokyo},
	author = {Jan Rasmus {Sulebak} and Hjelle, {\O}yvind},
	editor = {I. S. {Evans} and Dikau, R. and Tokunaga, E. and Ohmori, H. and Hirano, M.}
}
@techreport {Hjelle.2001.1,
	title = {Approximation of Scattered Data With Multilevel B-Splines},
	number = {STF42 A01011},
	year = {2001},
	publisher = {SINTEF},
	address = {Oslo},
	author = {Hjelle, {\O}yvind}
}
@inbook {SC.5.Daehlen.2001,
	title = {A Triangle-Based Carrier for Geographical Data},
	booktitle = {Spatial Information and the Environment},
	year = {2001},
	pages = {105-120},
	publisher = {Taylor \& Francis Books Ltd},
	organization = {Taylor \& Francis Books Ltd},
	author = {D{\ae}hlen, Morten and Fimland, M. and Hjelle, {\O}yvind},
	editor = {Halls, Peter}
}
@techreport {SC.7.Daehlen.2000,
	title = {A Hierarchical Framework for Triangle-Based Surface and Polygonal Networks},
	year = {2000},
	publisher = {University of Oslo},
	author = {D{\ae}hlen, Morten and Hjelle, {\O}yvind}
}
@techreport {Hjelle.2000.1,
	title = {A Triangulation Template Library (TTL): Generic Design of Triangulation Software},
	number = {STF42 A00015},
	year = {2000},
	publisher = {SINTEF},
	address = {Oslo},
	author = {Hjelle, {\O}yvind}
}
@inbook {Halbwachs.1999.1,
	title = {Generalized Maps in Geological Modeling: Object-Oriented Design of Topological Kernels},
	booktitle = {Advances in Software Tools for Scientific Computing},
	year = {1999},
	pages = {339 - 356},
	publisher = {Springer},
	organization = {Springer},
	author = {Halbwachs, Yvon and Hjelle, {\O}yvind},
	editor = {Hans Petter {Langtangen} and Are Magnus {Bruaset} and Quak, E.}
}
@inproceedings {Floater.1998.1,
	title = {OMEGA: a CAD-Based Approach to Geological Modelling},
	journal = {GOCAD ENSG Conference, 3D Modeling of Natural Objects : A Challenge for the 2000{\textquoteright}s, Nancy},
	year = {1998},
	month = {June},
	publisher = {ENSG},
	type = {1},
	address = {Nancy},
	author = {Floater, Michael and Halbwachs, Yvon and Hjelle, {\O}yvind and Reimers, Martin}
}
@inproceedings {SC.5.Arge.1997.b,
	title = {Mathematical Software for Terrain Modelling},
	journal = {The 5th Scandinavian Conference on Geographical Information systems},
	year = {1997},
	pages = {297-309,},
	type = {1},
	author = {Arge, Erlend and D{\ae}hlen, Morten and Hjelle, {\O}yvind},
	editor = {Bj{\o}rke, J.T.}
}
@inbook {Arge.1997.1,
	title = {Object-Oriented Scattered Data Modelling With Siscat.},
	booktitle = {Modern Software Tools for Scientific Computing},
	year = {1997},
	pages = {289-308},
	publisher = {Birkh{\"a}user},
	organization = {Birkh{\"a}user},
	author = {Stein Erlend {Arge} and Hjelle, {\O}yvind},
	editor = {Arge, Erlend and Are Magnus {Bruaset} and Hans Petter {Langtangen}}
}
@inbook {Arge.1997.2,
	title = {Software Tools for Modelling Scattered Data},
	booktitle = {Numerical Methods and Software Tools in Industrial Mathematics},
	year = {1997},
	pages = {47-62},
	publisher = {Birkh{\"a}user},
	organization = {Birkh{\"a}user},
	author = {Arge, Erlend and Hjelle, {\O}yvind},
	editor = {D{\ae}hlen, M. and Tveito, Aslak}
}
@inbook {Fremming.1997.1,
	title = {Surface Modelling From Scattered Geological Data},
	booktitle = {Numerical Methods and Software Tools in Industrial Mathematics},
	year = {1997},
	pages = {305-320},
	publisher = {Birkh{\"a}user},
	organization = {Birkh{\"a}user},
	author = {Nils Petter {Fremming} and Hjelle, {\O}yvind and Tarrou, Christian},
	editor = {D{\ae}hlen, M. and Tveito, Aslak}
}
@techreport {Hjelle.1996.3,
	title = {C++ Programming and Functionality Standard},
	number = {STF42 A96009},
	year = {1996},
	publisher = {SINTEF},
	address = {Oslo},
	author = {Hjelle, {\O}yvind}
}
@techreport {Hjelle.1996.2,
	title = {Data Structures in Siscat},
	number = {STF42 A96007},
	year = {1996},
	publisher = {SINTEF},
	address = {Oslo},
	author = {Hjelle, {\O}yvind}
}
@techreport {Hjelle.1996.1,
	title = {Explicit Surfaces in Siscat},
	year = {1996},
	publisher = {SINTEF},
	address = {Oslo},
	author = {Hjelle, {\O}yvind}
}
@techreport {SC.7.Daehlen.1993.d,
	title = {Compact Representation of Seismic Sections},
	year = {1993},
	publisher = {SINTEF},
	author = {D{\ae}hlen, Morten and Hjelle, {\O}yvind}
}
@techreport {SC.7.Steinlein.1992,
	title = {Compact Digital Representation of Seismic Sections},
	year = {1992},
	note = {(Poster session at the conference "Petroleum Exploration and Exploitation in Norway", Stavanger 1991)},
	publisher = {SINTEF},
	author = {O. A. {Steinlein} and Hjelle, {\O}yvind and D{\ae}hlen, Morten}
}
@inproceedings {Hjelle.1992.1,
	title = {Compact Digital Representation of Seismic Sections},
	journal = {62nd Annual International SEG meeting},
	year = {1992},
	month = {October},
	publisher = {.},
	type = {1},
	address = {New Orleans},
	author = {Hjelle, {\O}yvind and Steinlein, Odd}
}
@article {SC.7.Daehlen.1989,
	title = {Datareduksjon Av H{\o}gdekurver P{\r a} Digitale Kart},
	journal = {Kart og plan},
	volume = {49},
	number = {5},
	year = {1989},
	pages = {469-471,},
	author = {D{\ae}hlen, Morten and Hjelle, {\O}yvind}
}
