2020 - SIAM Fellow For contributions to the advancement of mathematics within the geosciences, multiscale and operator-splitting numerical methods, and open-source software tools.
His work in Graphics covers topics such as Computer graphics (images) which are related to areas like Computer graphics. He combines Computer graphics and Computer graphics (images) in his studies. In his study, Grid is strongly linked to Geodesy, which falls under the umbrella field of Benchmark (surveying). His Grid study frequently draws connections between adjacent fields such as Geodesy. He applies the principles of Solver, Process (computing) and MATLAB in his work under Programming language. His Process (computing) study frequently links to related topics such as Programming language. In most of his Epistemology studies, his work intersects topics such as Ideal (ethics) and Simple (philosophy). Simple (philosophy) is frequently linked to Epistemology in his study. While working in this field, Knut-Andreas Lie studies both Applied mathematics and Mathematical optimization.
His study on Geometry is mostly dedicated to connecting different topics, such as Grid, Flow (mathematics) and Basis (linear algebra). Many of his studies on Basis (linear algebra) apply to Geometry as well. Mechanics is intertwined with Flow (mathematics) and Finite volume method in his research. His Finite volume method study often links to related topics such as Mechanics. His study on Quantum mechanics is mostly dedicated to connecting different topics, such as Scale (ratio) and Nonlinear system. His Nonlinear system study frequently intersects with other fields, such as Quantum mechanics. In his articles, he combines various disciplines, including Applied mathematics and Mathematical optimization. His study deals with a combination of Mathematical optimization and Solver. His Discretization research extends to the thematically linked field of Mathematical analysis.
His Iterative method research is covered under the topics of Gauss–Seidel method and Preconditioner. Knut-Andreas Lie merges Gauss–Seidel method with Iterative method in his study. Preconditioner is frequently linked to Algorithm in his study. Algorithm and Discretization are two areas of study in which he engages in interdisciplinary work. In his papers, he integrates diverse fields, such as Discretization and Nonlinear system. He merges many fields, such as Nonlinear system and Linearization, in his writings. His Software study combines Open platform, Open source software and Open source studies. Knut-Andreas Lie applies the principles of Topology (electrical circuits) and Block (permutation group theory) in his work under Combinatorics. Topology (electrical circuits) is closely attributed to Combinatorics in his research.
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Open-source MATLAB implementation of consistent discretisations on complex grids
Knut–Andreas Lie;Knut–Andreas Lie;Stein Krogstad;Ingeborg Skjelkvåle Ligaarden;Jostein Roald Natvig.
Computational Geosciences (2012)
Scale Space and Variational Methods in Computer Vision
Xue-Cheng Tai;Knut Mørken;Marius Lysaker;Knut-Andreas Lie.
Lecture Notes in Computer Science (2009)
An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)
Published in <b>2019</b> (2019)
A Hierarchical Multiscale Method for Two-Phase Flow Based upon Mixed Finite Elements and Nonuniform Coarse Grids
Jorg E. Aarnes;Stein Krogstad;Knut-Andreas Lie.
Multiscale Modeling & Simulation (2006)
Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs
Helge Holden;Kenneth Hvistendahl Karlsen;Knut-Andreas Lie;Nils Henrik Risebro.
A comparison of multiscale methods for elliptic problems in porous media flow
Vegard Kippe;Jørg E. Aarnes;Knut-Andreas Lie.
Computational Geosciences (2008)
Multiscale mixed/mimetic methods on corner-point grids
Jørg E. Aarnes;Stein Krogstad;Knut-Andreas Lie.
Computational Geosciences (2008)
Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels
Jørg E. Aarnes;Vegard Kippe;Knut-Andreas Lie.
Advances in Water Resources (2005)
An Introduction to the Numerics of Flow in Porous Media using Matlab
Jørg E. Aarnes;Tore Gimse;Knut-Andreas Lie.
Geometric Modelling, Numerical Simulation, and Optimization (2007)
MRST-AD - an Open-Source Framework for Rapid Prototyping and Evaluation of Reservoir Simulation Problems
Stein Krogstad;Knut–Andreas Lie;Olav Møyner;Halvor Møll Nilsen.
annual simulation symposium (2015)
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