Trygve Kastberg Nilssen

• Jungeilges, Jochen; Nilssen, Trygve Kastberg; Pavletsov, Makar & Perevalova, Tatyana (2025). Noise-induced multistage transitions in a dynamic model of rational consumer choice. Decisions in Economics and Finance (DAF). ISSN 1593-8883. 48(2), s. 1811–1836. doi: 10.1007/s10203-025-00540-x. Fulltekst i vitenarkiv Vis sammendrag

  The present paper aims to further develop applicable methodology for studying the effect(s) of noise in dynamic economic settings. For that purpose we analyze a two-dimensional smooth non-invertible map modeling rational consumer choice in the presence of exogenous noise. To obtain a baseline, we first study the attractors of the deterministic system representing long-run consumption patterns, their basins of attraction and bifurcation scenarios. Here, we identify and characterize two areas of the parameter space in which extreme forms of multistability exist. In one of the parametric zones, all possible forms of attractors (fixed point, cycle, closed invariant curve, and chaotic attractor) coexist. To analyze noise-induced phenomena we use the stochastic sensitivity function technique and the confidence domain method. We describe successive multistage transitions between attractors and groups of attractors and define a dominant attractor characterizing the final state of long-run consumption behavior.

• Jungeilges, Jochen; Nilssen, Trygve Kastberg; Pavletsov, Makar & Perevalova, Tatyana (2024). Consumption Dynamics in Mixed-Income Neighborhoods with Connected Households. Computational Economics. ISSN 0927-7099. 65, s. 1051–1082. doi: 10.1007/s10614-024-10774-3. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the dynamics of household consumption in a setting in which households are connected across income classes. Low- and high-income households form preferences endogenously, conditional on their own and their neighbor’s past consumption. The modeling effort relies on a stochastic dynamic model of interdependent consumer choice in which the demand for commodities evolves according to a non-linear difference equation with stochastic initial states. The analysis targets a region of the parameter space that corresponds to salient features of a mixed-income neighborhood in which households are connected. Standard methods of asymptotic analysis of dynamic systems (e.g. bifurcation analysis) are combined with numerical simulation, statistical modelling of extreme events and statistical estimation techniques to investigate the dynamics. From the mathematical point of view, our analysis reveals the existence of intricate bifurcation pattern, coexistence of multiple attractors, complex basins and long transients. The essential economic finding states that key features of household consumption vary significantly in the influence the high-income households exert on the preference formation of the low-income households. In particular, we find that the prevalence of long transients, i.e. long waiting times before convergence to asymptotic states occur, is inversely related to the type of connectedness considered. We demonstrate that the dynamics of the consumption trajectory evolving over an extended time period before it settles on long-run simple consumption pattern, may not at all be captured by an asymptotic state. Thus, policies targeting the economies in mixed-income neighborhoods that are solely based on information about long-run consumption states, might trigger unwanted, unanticipated effects.

• Jungeilges, Jochen; Nilssen, Trygve Kastberg; Perevalova, Tatyana & Satov, Alexander (2021). Transitions between metastable long-run consumption behaviors in a stochastic peer-driven consumer network. Discrete and continuous dynamical systems. Series B. ISSN 1531-3492. 26(11), s. 5849–5871. doi: 10.3934/DCDSB.2021232. Fulltekst i vitenarkiv
• Eriksson, Marcus Karl Viren; Lempa, Jukka & Nilssen, Trygve Kastberg (2014). Swing options in commodity markets: A multidimensional Lévy diffusion model. Mathematical Methods of Operations Research. ISSN 1432-2994. 79(1), s. 31–67. doi: 10.1007/s00186-013-0452-7. Fulltekst i vitenarkiv Vis sammendrag

  We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples.

• Benth, Fred Espen; Lempa, Jukka & Nilssen, Trygve Kastberg (2012). On the optimal exercise of swing options in electricity markets. Journal of Energy Markets. ISSN 1756-3607. 4(4), s. 3–28. doi: 10.21314/jem.2011.065. Fulltekst i vitenarkiv Vis sammendrag

  This is the pre-peer reviewed version of the following article: Benth, Fred Espen; Lempa, Jukka; Nilssen, Trygve Kastberg, On the optimal exercise of swing options in electricity markets, Journal of Energy Markets. 2012, 4 (4), 3-28, which has been published in final form at http://www.risk.net/journal-of-energy-markets/technical-paper/2160760/on-optimal-exercise-swing-options-electricity-markets.

• Nilssen, Trygve Kastberg; Staff, Gunnar Andreas & Mardal, Kent-Andre (2011). Order Optimal Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations. Numerical Methods for Partial Differential Equations. ISSN 0749-159X. 27(5), s. 1290–1312. doi: 10.1002/num.20582. Fulltekst i vitenarkiv Vis sammendrag

  The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly positive-definite matrices is introduced and analyzed.

• Nilssen, Trygve Kastberg; Staff, Gunnar Andreas & Mardal, Kent-Andre (2010). Order optimal preconditioners for fully implicit Runge-Kutta schemes applied to the bidomain equations. Numerical Methods for Partial Differential Equations. ISSN 0749-159X. doi: 10.1002/num.20582. Fulltekst i vitenarkiv Vis sammendrag

  The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge–Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that the preconditioned systems have bounded condition numbers given that the Runge–Kutta scheme is A-stable and irreducible with an invertible coefficient matrix. A new proof of order optimality of the preconditioners for the one-leg discretization in time of the bidomain equations is also presented. The theoretical results are verified by numerical experiments. Additionally, the concept of weakly positive-definite matrices is introduced and analyzed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010

• Nilssen, Trygve Kastberg; Karlsen, Kenneth Hvistendahl; Mannseth, T. & Tai, XC (2009). Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Computational Geosciences. ISSN 1420-0597. 13(3), s. 317–329. Fulltekst i vitenarkiv Vis sammendrag

  Numerical identification of diffusion parameters in a nonlinear convection-diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed.

• Nilssen, Trygve Kastberg (2009). Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Computational Geosciences. ISSN 1420-0597. 13(3), s. 317–329. Fulltekst i vitenarkiv
• Mardal, Kent-Andre; Nilssen, Trygve & Staff, Gunnar (2007). Order Optimal Preconditioners for Implicit Runge-Kutta Schemes Applied to Parabolic PDE's. SIAM Journal on Scientific Computing. ISSN 1064-8275. 29, s. 361–375. Fulltekst i vitenarkiv Vis sammendrag

  In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank-Nicolson schemes can be reused for higher-order fully implicit Runge-Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order-optimal for A-stable and irreducible Runge-Kutta schemes with invertible coefficient matrices. The theoretical investigations are confirmed by numerical experiments.

• Mardal, Kent-Andre & Nilssen, Trygve (2006). Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs. Journal of Numerical Mathematics. ISSN 1570-2820. 14, s. 103–122. Fulltekst i vitenarkiv
• Staff, Gunnar; Mardal, Kent-Andre & Nilssen, Trygve (2006). Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs. Model. Identif. Control. 27, s. 109–123. Fulltekst i vitenarkiv Vis sammendrag

  Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs \cite{mns}. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or Crank-Nicolson. It was proven that the preconditioner is optimal with respect to the timestep and the discretization parameter in space. In this paper we will improve the convergence by considering other preconditioners like the upper and the lower block Gauss-Seidel preconditioners, both in a left and right preconditioning setting. Finally, we improve the condition number by using a generalized Gauss-Seidel preconditioner.

• Staff, Gunnar Andreas; Mardal, Kent-Andre & Nilssen, Trygve Kastberg (2005). Preconditioning of fully implicit Runge-Kutta schemes for parabolic PDEs. I Amundsen, J; Andersson, H; Celledoni, E; Gravdahl, T; Michelsen, F; Nagel, H & Natvig, T (Red.), SIMS 2005. 46th Conference on Simulation and Modeling. Tapir Akademisk Forlag. ISSN 9788251920933. s. 315–324. Fulltekst i vitenarkiv
• Ingebrigtsen, Linda; Nilssen, Trygve Kastberg; Langtangen, Hans Petter & Tveito, Aslak (2003). On the accuracy of operator splitting for a fluid-structure interaction problem. International journal of nonlinear sciences and numerical simulation. ISSN 1565-1339. 4, s. 209–218. Fulltekst i vitenarkiv
• Lyche, Tom Johan; Nilssen, Trygve Kastberg & Winther, Ragnar (2002). Preconditioned Iterative Methods for Scattered Data Interpolation. Advances in Computational Mathematics. ISSN 1019-7168. 17, s. 237–256. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg; Tai, Xue-Cheng & Winther, Ragnar (2001). A robust nonconforming H2-element. Mathematics of Computation. ISSN 0025-5718. 70, s. 489–505. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Mølland, Eirin; Nilssen, Trygve Kastberg & Andersson, Kjetil (2025). Feedback and Performance in Higher Education. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg & Andersson, Kjetil (2024). Study Effort and Academic Achievements. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg (2023). Risk management for concession power in the Norwegian electricity market. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg (2023). Estimating the requirements for equity for Konsesjonskraft IKS and pricing swing options. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg (2022). Risikoberegninger i kraftmarkedet. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg (2022). Risikoberegninger med snittreverserende prosesser i kraftmarkedet. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg; Jungeilges, Jochen & Ryazanova, Tatyana (2019). Modelling behavioral change in a peer-driven consumer network. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg (2012). Pricing Swing Options in Electricity Markets. Fulltekst i vitenarkiv
• Staff, Gunnar; Mardal, Kent-Andre; Nilssen, Trygve; Wesseling, P. & Oñate, E. (2006). Block Preconditioners for Fully Implicit Runge-Kutta Schemes Applied to the Bidomain Equations. Fulltekst i vitenarkiv Vis sammendrag

  Recently, the authors presented different block preconditioners for implicit Runge-Kutta discretization of the heat equation. The preconditioners were block Jacobi and block Gauss-Seidel preconditoners where the blocks reused existing preconditioners for the implicit Euler discretization of the same equation. In this paper we will introduce similar block preconditioners for the implicit Runge-Kutta discretization of the Bidomain equation. We will, by numerical experiments, show the properties of the preconditoners, and that higher-order Runge-Kutta discretization of the Bidomain equation may be superior to lower-order in some cases.

• Mardal, Kent-Andre; Staff, Gunnar Andreas & Nilssen, Trygve Kastberg (2005). Preconditioning of fully implicit Runge-Kutta schemes for parabolic PDEs. Fulltekst i vitenarkiv
• Nilssen, Trygve & Mardal, Kent-Andre (2004). Reuse of Standard Preconditioners for Higher-Order Time Discretizations of Parabolic PDEs. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg & Mardal, Kent-Andre (2004). Reuse of Standard Preconditioners for Higher--Order Time Discretizations of Parabolic PDEs. Fulltekst i vitenarkiv
• Mardal, Kent-Andre; Nilssen, Trygve Kastberg & Staff, Gunnar Andreas (2005). Order optimal preconditioners for implicit Runge-Kutta schemes applied to parabolic PDE's. Simula Research Laboratory. Fulltekst i vitenarkiv
• Nilssen, Trygve Kastberg; Ingebrigtsen, Linda; Hanslien, Monica; Lines, Glenn Terje & Tveito, Aslak (2004). Resolution requirements for a 1D monodomain model for simulating. Simula Research Laboratory. Fulltekst i vitenarkiv

Se alle arbeider i NVA