Franz Georg Fuchs

• Fuchs, Franz Georg; Lye, Kjetil Olsen; Nilsen, Halvor Møll; Stasik, Alexander Johannes & Sartor, Giorgio (2022). Constraint Preserving Mixers for the Quantum Approximate Optimization Algorithm. Algorithms. ISSN 1999-4893. 15(6). doi: 10.3390/a15060202. Fulltekst i vitenarkiv Vis sammendrag

  The quantum approximate optimization algorithm/quantum alternating operator ansatz (QAOA) is a heuristic to find approximate solutions of combinatorial optimization problems. Most of the literature is limited to quadratic problems without constraints. However, many practically relevant optimization problems do have (hard) constraints that need to be fulfilled. In this article, we present a framework for constructing mixing operators that restrict the evolution to a subspace of the full Hilbert space given by these constraints. We generalize the “XY”-mixer designed to preserve the subspace of “one-hot” states to the general case of subspaces given by a number of computational basis states. We expose the underlying mathematical structure which reveals more of how mixers work and how one can minimize their cost in terms of the number of CX gates, particularly when Trotterization is taken into account. Our analysis also leads to valid Trotterizations for an “XY”-mixer with fewer CX gates than is known to date. In view of practical implementations, we also describe algorithms for efficient decomposition into basis gates. Several examples of more general cases are presented and analyzed.

• Fuchs, Franz Georg; Kolden, Herman Øie; Aase, Niels Henrik & Sartor, Giorgio (2021). Efficient Encoding of the Weighted MAX k-CUT on a Quantum Computer Using QAOA. SN Computer Science. ISSN 2662-995X. 2(2). doi: 10.1007/s42979-020-00437-z. Fulltekst i vitenarkiv
• Fuchs, Franz Georg; Falch, Vemund & Johnsen, Christian Svingen (2020). Quantum Poker - a game for quantum computers suitable for benchmarking error mitigation techniques on NISQ devices. The European Physical Journal Plus. ISSN 2190-5444. 135. doi: 10.1140/epjp/s13360-020-00360-5. Vis sammendrag

  Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold ’em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum register that is “randomly” initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of 1’s that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit (Aleksandrowicz et al. in An open-source framework for quantum computing, 2019). A comparison of the results for the created circuits using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. For the success of noisy intermediate scale quantum (NISQ) computers, improvements on the error rates and error mitigation techniques are necessary, even for simple circuits. We show that quantum error mitigation (QEM) techniques can be used to improve expectation values of observables on real quantum devices.

• Tabib, Mandar; Rasheed, Adil & Fuchs, Franz Georg (2017). Analysis of Unsteady Hydrodynamics Related to Vortex Induced Vibrations on Bluff-Bodied Offshore Structure, ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering - Volume 2: Prof. Carl Martin Larsen and Dr. Owen Oakley Honoring Symposia on CFD and VIV. The American Society of Mechanical Engineers (ASME). ISSN 978-0-7918-5764-9. doi: 10.1115/OMAE2017-61207. Vis sammendrag

  Flows around a fixed cylinder with uniform and pulsating inflow conditions at different Reynolds numbers are simulated using Large Eddy Simulation (LES). For pulsating inflow, a sinusoidal profile, with an amplitude ΔU and a pulsation frequency fe, is superimposed onto the mean velocity U∞ at the inlet plane. The current study reveals that the pulsation can influence flow-physics in three possible ways as compared to uniform inflow conditions: (a) The vortex shedding pattern is seen to be more asymmetric for pulsating inflow than for uniform inflow. This needs to be validated with an experimental campaign devoted to the study of flow-asymmetricity due to pulsatile and uniform flow condition. (b) The dominant shedding frequency fd gets locked with respect to the frequency of the pulsating inflow fe, (for both the turbulent and transition regime) at a ratio of fe/fs0 equivalent to 0.65 – 0.75 (where fs0 is the vortex shedding frequency for uniform inflow) and ε = ΔU / (2πfeD) ≈ 0.2, where D is the diameter of the cylinder. This numerical observation is validated using the experimentally observed turbulent vortex regime work ( [1])in this range. For conditions with fe/fs0 > 0.75 the lock-in may happen at fe/2. (c) Compared to uniform inflow, the pulsating inflow leads to a larger drag coefficient. The drag coefficient is influenced by the ratios fe/fs0 and ΔU / U∞.

• Barth, Andrea & Fuchs, Franz Georg (2017). Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients. Applied Numerical Mathematics. ISSN 0168-9274. 121, s. 38–51. doi: 10.1016/j.apnum.2017.06.009. Fulltekst i vitenarkiv Vis sammendrag

  In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.

• Tabib, Mandar; Rasheed, Adil & Fuchs, Franz Georg (2016). Analyzing complex wake-terrain interactions and its implications on wind-farm performance. Journal of Physics: Conference Series (JPCS). ISSN 1742-6588. 753(3). doi: 10.1088/1742-6596/753/3/032063. Vis sammendrag

  Rotating wind turbine blades generate complex wakes involving vortices (helical tip-vortex, root-vortex etc.).These wakes are regions of high velocity deficits and high turbulence intensities and they tend to degrade the performance of down-stream turbines. Hence, a conservative inter-turbine distance of up-to 10 times turbine diameter (10D) is sometimes used in wind-farm layout (particularly in cases of flat terrain). This ensures that wake-effects will not reduce the overall wind-farm performance, but this leads to larger land footprint for establishing a wind-farm. In-case of complex-terrain, within a short distance (say 10D) itself, the nearby terrain can rise in altitude and be high enough to influence the wake dynamics. This wake-terrain interaction can happen either (a) indirectly, through an interaction of wake (both near tip vortex and far wake large-scale vortex) with terrain induced turbulence (especially, smaller eddies generated by small ridges within the terrain) or (b) directly, by obstructing the wake-region partially or fully in its flow-path. Hence, enhanced understanding of wake- development due to wake-terrain interaction will help in wind farm design. To this end the current study involves: (1) understanding the numerics for successful simulation of vortices, (2) understanding fundamental vortex-terrain interaction mechanism through studies devoted to interaction of a single vortex with different terrains, (3) relating influence of vortex-terrain interactions to performance of a wind-farm by studying a multi-turbine wind-farm layout under different terrains. The results on interaction of terrain and vortex has shown a much faster decay of vortex for complex terrain compared to a flatter-terrain. The potential reasons identified explaining the observation are (a) formation of secondary vortices in flow and its interaction with the primary vortex and (b) enhanced vorticity diffusion due to increased terrain-induced turbulence. The implications of this vortex-terrain interactions on wind-farm performance is observed by comparing two LES simulations of a multi-turbine wind-farm layout (in real actual complex terrain and a made-up flat terrain scenario) with the observed annual power data at the actual wind-farm. The comparison reveals drop in power production due to terrain and wake effects for flatter terrain case. The insights from this study can serve as a step towards enhancing wake-dissipation through either artificial obstruction or artificial terrain modifications.

• Fuchs, Franz Georg; Rasheed, Adil; Tabib, Mandar & Fonn, Eivind (2016). Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver. Journal of Physics: Conference Series (JPCS). ISSN 1742-6588. 753(8). doi: 10.1088/1742-6596/753/8/082031. Vis sammendrag

  Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid Eulerian- Lagrangian approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Værnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.

• Barth, Andrea & Fuchs, Franz Georg (2016). Uncertainty quantification for hyperbolic conservation laws with flux coefficients given by spatiotemporal random fields. SIAM Journal on Scientific Computing. ISSN 1064-8275. 38(4), s. A2209–A2231. doi: 10.1137/15M1027723. Vis sammendrag

  In this paper hyperbolic partial differential equations (PDEs) with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by correlated Gaussian random fields in space and Ornstein--Uhlenbeck processes in time. The resulting system of equations consists of a stochastic differential equation for each random parameter coupled to the hyperbolic conservation law. We define an appropriate solution concept in this setting and analyze errors and convergence of discretization methods. A novel discretization framework, based on Monte Carlo finite volume methods, is presented for the robust computation of moments of solutions to those random hyperbolic PDEs. We showcase the approach on two examples which appear in applications---the magnetic induction equation and linear acoustics---both with a spatiotemporal random background velocity field.

• Fuchs, Franz Georg & Hjelmervik, Jon M. (2016). Interactive Isogeometric Volume Visualization with Pixel-Accurate Geometry. IEEE Transactions on Visualization and Computer Graphics. ISSN 1077-2626. 22(2), s. 1102–1114. doi: 10.1109/TVCG.2015.2430337. Vis sammendrag

  A recent development, called isogeometric analysis, provides a unified approach for design, analysis and optimization of functional products in industry. Traditional volume rendering methods for inspecting the results from the numerical simulations cannot be applied directly to isogeometric models. We present a novel approach for interactive visualization of isogeometric analysis results, ensuring correct, i.e., pixel-accurate geometry of the volume including its bounding surfaces. The entire OpenGL pipeline is used in a multi-stage algorithm leveraging techniques from surface rendering, order-independent transparency, as well as theory and numerical methods for ordinary differential equations. We showcase the efficiency of our approach on different models relevant to industry, ranging from quality inspection of the parametrization of the geometry, to stress analysis in linear elasticity, to visualization of computational fluid dynamics results.

• Fuchs, Franz Georg; McMurry, Andrew David; Risebro, Nils Henrik & Mishra, Siddhartha (2014). Explicit and implicit finite volume schemes for radiation MHD and the effects of radiation on wave propagation in stratified atmospheres. I Ancona, Fabio; Bressan, Alberto; Marcati, Pierangelo & Marson, Andrea (Red.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Fourteenth International Conference on Hyperbolic Problems held in Padova, June 25-29, 2012. American Institute of Mathematical Sciences (AIMS) Press. ISSN 978-1-60133-017-8. s. 41–59. Vis sammendrag

  We present a radiation MHD model based on moments (M1) of the radiative transport equation. This M1 model is approximated numerically by robust finite volume schemes. We compare explicit and semi-implicit schemes and show how radiation affects wave propagation in stratified atmospheres.

• Fuchs, Franz Georg; McMurry, Andrew David; Mishra, Siddhartha & Waagan, Knut (2011). Simulating waves in the upper solar atmosphere with Surya: a well-balanced high-order finite-volume code. The Astrophysical Journal (ApJ). ISSN 0004-637X. 732(2). doi: 10.1088/0004-637X/732/2/75.
• Fuchs, Franz Georg; McMurry, Andrew David; Mishra, Siddhartha; Risebro, Nils Henrik & Waagan, Knut (2011). Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations. Communications in Computational Physics. ISSN 1815-2406. 9(2), s. 324–362. doi: 10.4208/cicp.171109.070510a.
• Fuchs, Franz Georg; McMurry, Andrew David; Mishra, Siddhartha; Risebro, Nils Henrik & Waagan, Knut (2010). Finite Volume Methods for Wave Propagation in Stratified Magneto-Atmospheres. Communications in Computational Physics. ISSN 1815-2406. 7(3), s. 403–638. doi: 10.4208/cicp.2009.08.154.
• Fuchs, Franz Georg; McMurry, Andrew David; Mishra, Siddhartha; Risebro, Nils Henrik & Waagan, Knut (2010). High order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres. Journal of Computational Physics. ISSN 0021-9991. 229(11), s. 4033–4058. doi: 10.1016/j.jcp.2010.01.038.
• Fuchs, Franz Georg; McMurry, Andrew David & Mishra, Siddhartha (2009). High-order finite volume schemes for wave propagation in stratified atmospheres. I Tadmor, Eitan; Liu, Jian-Guo & Tzavaras, Athanasios E. (Red.), Hyperbolic Problems: Theory, Numerics and Applications. American Mathematical Society (AMS). ISSN 978-0-8218-4728-2. s. 575–584.
• Fuchs, Franz Georg; Mishra, Siddhartha & Risebro, Nils Henrik (2009). Splitting based finite volume schemes for ideal MHD equations. Journal of Computational Physics. ISSN 0021-9991. 228(3), s. 641–660. doi: 10.1016/j.jcp.2008.09.027.
• Karlsen, Kenneth Hvistendahl; Fuchs, Franz Georg; Mishra, Siddhartha & Risebro, Nils Henrik (2009). Stable upwind schemes for the magnetic induction equation. Modélisation mathématique et analyse numérique. ISSN 0764-583X. 43(5), s. 825–852. doi: 10.1051/m2an/2009006.

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• Fuchs, Franz Georg (2024). Introduction to Tensor Networks. Vis sammendrag

  Tensor networks (TN) have important applications in mathematics, chemistry, physics, and machine learning. They can for instance be used to describe quantum many-body systems, simulate quantum circuits, or compress neural networks. In this talk I will give a gentle introduction to the mathematical framework of TNs. After introducing the basic concepts and notation, I well go through some well-known algorithms/methods for sampling, calculating inner products, and time evolution.

• Fuchs, Franz Georg (2024). Kvantedatamaskiner og kryptografi. Vis sammendrag

  Hvilke betingelser må være oppfylt for at en kvantedatamaskin skal kunne bryte RSA-krypteringen? Implementeringen av feilkorrigering for kvantedatamaskiner medfører betydelige ressurskrav. Hva kreves for å konstruere en "tilstrekkelig stor" kvantedatamaskin, og når kan man forvente at dette vil være mulig? https://nsm.no/kurs-og-konferanser/sikkerhetskonferansen/sikkerhetskonferansen-2024/program/kvantedatamaskiner-og-kryptografi

• Stasik, Alexander Johannes & Fuchs, Franz Georg (2023). QUantum reservoir computing.
• Fuchs, Franz Georg & Sævold, Heidi (2023). Kvantedatamaskin tilgjengelig for europeiske selskaper. [Internett]. digi.no.
• Bassa, Ruben Pariente & Fuchs, Franz Georg (2023). Hands-On experiments with quantum gates and quantum circuits: QAOA for MaxCut .
• Bassa, Ruben Pariente & Fuchs, Franz Georg (2023). Exploring the Quantum Landscape in Norway and Advancements in Quantum Approximate Optimization Algorithm.
• Fuchs, Franz Georg (2023). Introduction to use cases for optimisation: QAOA.
• Fuchs, Franz Georg & Ola, Tangen Kulseng (2023). Her tester de løsninger for fremtidens kvantedatamaskiner. [Internett]. https://www.digi.no/.
• Fuchs, Franz Georg (2023). Optimal mixers restricted to subspaces and the stabilizer formalism.
• Fuchs, Franz Georg (2023). Hamiltonians with time evolution restricted to subspaces.
• Fuchs, Franz Georg (2023). Avtale på plass: Norske forskere får bruke europeisk kvantedatamaskin. [Internett]. https://www.digi.no/.
• Fuchs, Franz Georg (2023). Quantum Computing: Separating Hype from Realistic Expectations.
• Fuchs, Franz Georg (2023). Kvantedatamaskiner - Hva er det og hva kan de brukes til?
• Fuchs, Franz Georg (2022). Kvantedatamaskiner – er vi nær et paradigmeskifte?
• Fuchs, Franz Georg (2022). Why we need research on quantum computing in Norway.
• Fuchs, Franz Georg (2022). Quantum Computing and the Gemini Center.
• Fuchs, Franz Georg (2022). An introduction to quantum error mitigation. Vis sammendrag

  Quantum error mitigation (QEM) aims to reduce the errors that occur on quantum chips when a quantum algorithm is executed. In this talk I will give an introduction to two popular methods for QEM. The first one is based on extrapolation techniques, and the second on quasiprobabilistic decompositions. I will also highlight differences and similarities of QEM and quantum error correction.

• Fuchs, Franz Georg (2022). Quantum computing as enabling technology for Norway. Vis sammendrag

  https://www.tekna.no/kursarkiv/kvanterevulosjonen-rykker-narmere-44012/ https://www.tekna.no/fag-og-nettverk/IKT/ikt-bloggen/Kvanterevolusjonen/

• Fuchs, Franz Georg & Persson, Aksel Faanes (2022). Podcast Smart forklart. 50. Quantum computing: Fremtidens superraske datamaskiner. [Internett]. https://www.sintef.no/smart-forklart/. Vis sammendrag

  https://play.acast.com/s/60b75c5b8c26f80013d5ebce/630faf7543400800124d24b4

• Fuchs, Franz Georg & Olsen, Jan Willie (2022). Skal kartlegge kvanteteknologi i Norge. [Internett]. https://khrono.no/skal-kartlegge-kvanteteknologi-i-norge/707.
• Gjøsteen, Kristian; Fuchs, Franz Georg & Engesvik, Sara (2022). Kvantedatamaskiners destruktive potensiale: – Vi må forsikre oss mot at verden ramler sammen . [Internett]. https://www.digi.no/artikler/kvantedatamaskiners-destruktive.
• Fuchs, Franz Georg (2022). Hands-on: Qiskit applied to use cases for optimisation.
• Fuchs, Franz Georg (2022). Optimisation and variational methods: QAOA/QUBO, VQE, and more.
• Fuchs, Franz Georg (2022). Variational quantum algorithms: Challenges and Opportunities.
• Fuchs, Franz Georg (2022). Constrained mixers for the quantum approximate optimization algorithm (QAOA).
• Fuchs, Franz Georg (2022). Quantum Optimization for Research and Business.
• Fuchs, Franz Georg (2021). The disruptive power of quantum computers: Hype or reality? Vis sammendrag

  Opening keynote: Our modern society relies heavily on the ever-increasing processing power of digital computers for all kinds of applications. But there are important problems that businesses and society face that will remain intractable even for the best supercomputers we can hope to build. Quantum computers, a new computing paradigm, have the potential to help solve some of the most pressing problems humanity is facing. In this talk I will separate the hype from the reality.

• Fuchs, Franz Georg (2021). Using quantum computers to solve combinatorial optimization problems.
• Fuchs, Franz Georg (2021). The disruptive power of​ quantum computers: Hype or reality?
• Fuchs, Franz Georg (2021). Kvanteteknologi skal gjøre Norge klar for ny datarevolusjon. [Internett]. Elmagasinet.no.
• Fuchs, Franz Georg (2021). NTNU: First Norwegian centre for quantum technology is being rolled out. [Internett]. Sciencebusiness.net. Vis sammendrag

  Også publisert her: Norwegianscitechnews.com, Telecomrevy.no, Elektronikknett.no

• Fuchs, Franz Georg (2021). Kvanteteknologi skal gjøre Norge klar for ny datarevolusjon. [Internett]. NTB kommunikasjon.
• Fuchs, Franz Georg & Røise, Martin Braathen (2021). Spår trøbbel for norsk næringsliv hvis vi ikke kjapt får kompetanse på denne teknologien. [Internett]. https://www.digi.no/.
• Fuchs, Franz Georg & Øyvann, Stig (2021). Vil bringe Norge inn i kvante-alderen. [Internett]. https://www.cw.no/artikkel/forskning/vil-bringe-norge-inn-kv.
• Fuchs, Franz Georg (2021). NISQ devices: Error mitigation techniques and combinatorial optimization problems.
• Fuchs, Franz Georg & Leine, Jan Erlend (2021). Kvantemaskinen - den nye teknospranget. [Radio]. https://radio.nrk.no/serie/ekko/sesong/202102/MDFP02002821. Vis sammendrag

  Det er et kvantesprang på gang i verden, med datatmaskiner som må regne mye raskere enn i dag. Men er Norge på banen?

• Fuchs, Franz Georg (2020). Quantum Computing: An introduction.
• Fuchs, Franz Georg (2020). Error mitigation and the weighted MAX k-CUT on NISQ devices.
• Fuchs, Franz Georg (2020). When will I get a quantum computer and what can I do with it?
• Fuchs, Franz Georg (2019). QUANTUM COMPUTING IN THE NISQ ERA - QUANTUM POKER AND ERROR MITIGATION​.
• Ulla Gjeset, Schjølberg & Fuchs, Franz Georg (2019). Google hevder deres kvantedatamaskin kan løse oppgave som er umulig for vanlige datamaskiner. [Internett]. forskning.no.
• Fuchs, Franz Georg (2019). What is a quantum computer?
• Caroline, Enge; Fuchs, Franz Georg; Vemund, Falch & Christian, Johnsen (2019). Norske studenter lager spill til «den neste store teknologien»: Kvantedatamaskinen. [Avis]. Aftenposten.
• Fuchs, Franz Georg; Nilsen, Halvor Møll; Sartor, Giorgio; Remonato, Filippo & Schittny, Robert (2019). The landscape of quantum algorithms.
• Fuchs, Franz Georg (2019). Quantum Advantage in the NISQ computing era.
• Fuchs, Franz Georg (2019). Quantum computing - possibilities and limitations.
• Fuchs, Franz Georg (2019). The second quantum revolution.
• Fuchs, Franz Georg (2019). Quantum Computing and Quantum Supremacy.
• Fuchs, Franz Georg (2019). Quantum Computing and Optimization.
• Fuchs, Franz Georg (2017). Interactive and Pixel-Accurate Rendering of Locally Refined (LR-)Splines and Isogeometric Volumes.
• Hjelmervik, Jon M. & Fuchs, Franz Georg (2016). Direct Interactive Visualization of LR- and T-Spline Volumes for Use in Large-Scale Scientific Computing and Isogeometric Analysis.
• Fuchs, Franz Georg; Rasheed, Adil; Tabib, Mandar & Fonn, Eivind (2016). Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver.
• Hjelmervik, Jon M. & Fuchs, Franz Georg (2015). Interactive Pixel-Accurate Rendering of LR-Splines and T-Splines. Eurographics State of the Art Reports. ISSN 1017-4656. s. 65–68. doi: 10.2312/egsh.20151016. Vis sammendrag

  Flexible surface types on irregular grids, such as T-splines and LR-splines, are gaining popularity in science and industry due to the possibility for local grid refinement. We present a novel rendering algorithm for those surface types that guarantees pixel-accurate geometry and water-tight tessellation (no drop-outs). Before rendering, we extract the Bézier coefficients. The resulting irregular grids of Bézier patches are then rendered using a multistage algorithm, that decouples the tesselator and the patch geometry. The implementation using OpenGL utilizes compute shaders and hardware tessellation functionality. We showcase interactive rendering achieved by our approach on three representative use cases.

• Fuchs, Franz Georg & Hjelmervik, Jon M. (2014). Interactive Direct Visualization of Isogeometric CFD Results.
• Hjelmervik, Jon M.; Fuchs, Franz Georg; Dyken, Erik Christopher & Bjønnes, Erik W (2014). Real-Time Isogeometric Volume Visualization.
• Hjelmervik, Jon M.; Bjønnes, Erik W; Dyken, Erik Christopher & Fuchs, Franz Georg (2013). Fast Volumetric Visualization of Isogeometric Models. Vis sammendrag

  Learn how to achieve real-time, pixel-accurate volume visualization of volumetric splines objects using OpenGL 4.3. See unprecedented fast ray-casting through volumetric spline models where both the geometric shape and attached simulation results are represented as volumetric splines. The presented rendering method consists of two passes; the first pass use tessellator and atomic counters to find all ray-surface intersection points, while a second compute pass performs the ray traversal. Simulations using volumetric spline models are called isogeometric analysis, because they allow the same representation to be shared throughout the modeling and simulation stages. We provide fast, reliable visualization, achieving the ultimate goal in isogeometric analysis.

• Fuchs, Franz Georg; Hjelmervik, Jon M.; Dyken, Erik Christopher & Bjønnes, Erik W (2013). Real-Time Pixel-Accurate Isogeometric Volume Visualization.
• McMurry, Andrew David; Mishra, Siddhartha & Fuchs, Franz Georg (2012). Semi-implicit solutions to Radiation-magnetohydrodynamics.
• Fuchs, Franz Georg (2009). HIGH ORDER WELL BALANCED FINITE VOLUME SCHEMES FOR SIMULATING WAVE PROPAGATION IN STRATIFIED MAGNETIC ATMOSPHERES.
• Fuchs, Franz Georg; McMurry, Andrew David & Mishra, Siddhartha (2008). High-order finite volume schemes for wave propagation in stratified atmospheres.
• Fuchs, Franz Georg (2008). Splitting Based Finite Volume Schemes For The Ideal MHD equations.
• Fuchs, Franz Georg (2006). Operator splitting for the magnetohydrodynamic equations.
• Fuchs, Franz Georg (2006). Euler's Elastica and Curvature-Based Inpainting.
• Fuchs, Franz Georg (2006). Euler's Elastica and Curvature-Based Inpainting.
• Tabib, Mandar; Fuchs, Franz Georg & Rasheed, Adil (2016). Report on wake vortex micro-scale turbulent airflow interaction methodologies. SESAR 12.2.2 Report.
• Rasheed, Adil; Tabib, Mandar & Fuchs, Franz Georg (2016). Wake Vortex Micro-Scale Turbulence Prototype Development and Sensitivity Studies. SESAR 12.2.2.
• Fuchs, Franz Georg (2009). Simulating waves in the solar atmosphere with MHD. Unipub forlag. ISSN 1501-7710.

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