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  • 301.
    Belova, Anna
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Rigorous enclosures of rotation numbers by interval methods.2016Inngår i: Journal of Computational Dynamics, ISSN 2158-2491, Vol. 3, nr 1, 81-91 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the rotation number. A few numerical experiments are presented to show that the implementation of interval methods produces a good enclosure of the rotation number of a circle map.

  • 302.
    Belova, Anna
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Gorbovickis, Igors
    Critical points of the multiplier map for the quadratic family.Manuskript (preprint) (Annet vitenskapelig)
  • 303.
    Bengtsson, Martin
    Linköpings universitet, Matematiska institutionen.
    Analytical Expressions for the Hawking Mass in slowly rotating Kerr and Kerr-Newman Space-times2007Independent thesis Advanced level (degree of Magister), 20 poäng / 30 hpOppgave
    Abstract [en]

    Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.

  • 304.
    Berezovsky, Vladimir
    et al.
    Pomorskii State University, Arkhangelsk.
    Men'shikov, Leonid
    Russian Research Centre, Kurchatov Institute, Moscow.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Latham, Chris
    Effect of dipole-dipole interactions between atoms in an active medium2008Inngår i: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 25, nr 3, 458-462 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    On the basis of the results of numerical modeling, it is shown that dipole-dipole interactions among atoms in the active medium strongly influences the character of the associated superradiation. The main effect is to make the nuclear subsystem behave chaotically. Its strength increases with the atom density and leads to the suppression of distant collective correlations and superradiation. Near correlations between the atoms are established, causing a confinement effect: a shielding of radiation in the active medium.

  • 305.
    Berezovsky, V.V.
    et al.
    Lomonosov Pomor State University, Arkhangelsk.
    Men'shikov, L.I.
    Russian Research Centre, Kurchatov Institute, Moscow.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Latham, Chris
    Effect of the dipole-dipole interaction of particles in an active medium on the character of superradiation2008Inngår i: Plasma physics reports (Print), ISSN 1063-780X, E-ISSN 1562-6938, Vol. 34, nr 7, 555-561 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The motion of a system of interacting nonlinear charged oscillators is investigated numerically. Because of nonlinearity, the total collective electric field gives rise to a phasing effect-correlations in the phases of the oscillators. The consequence is superradiation-the enhanced spontaneous short-term emission of the energy stored in the oscillators. It is shown that the oscillations of the oscillators become stochastic because of the dipole-dipole interaction between them and their nearest neighbors. As a result, as the density of the oscillators increases, distant collective correlations are suppressed, superradiation ceases to be generated, and radiation is shielded in the medium. The phenomena considered in the present paper can play an important role in cyclotron emission from a plasma and thus should be taken into account in emission calculations. The process whereby the energy of the transverse electron motion in electron cooling devices decreases is analyzed as an example. This process occurs as a result of the development of cyclotron maser instability and has the nature of superradiation. The onset of correlations between individual electrons moving in their Larmor circles is the initial, linear stage of instability developing in the plasma. Superradiation is the final, nonlinear instability stage.

  • 306.
    Berg, Jens
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems2013Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software.

    We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models.

    The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.

  • 307.
    Berg, Jens
    Uppsala universitet, Avdelningen för beräkningsvetenskap.
    Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems2013Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software.

    We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models.

    The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.

  • 308.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    A stable and dual consistent boundary treatment using finite differences on summation-by-parts form2012Inngår i: Proc. ECCOMAS Congress 2012, Austria: Tech. Univ. Wien , 2012, 7557-7570 s.Konferansepaper (Fagfellevurdert)
  • 309.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    A stable and dual consistent boundary treatment using finite differences on summation-by-parts form2012Inngår i: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.

  • 310.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    A stable and dual consistent boundary treatment using finite differences on summation-by-parts form2012Rapport (Annet vitenskapelig)
  • 311.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2013Rapport (Annet vitenskapelig)
  • 312.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, 135-153 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 313.
    Berg, Jens
    et al.
    Uppsala University, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, 135-153 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive new farfield boundary conditions for the time-dependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.

    We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

  • 314.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Duality based boundary treatment for the Euler and Navier-Stokes equations2013Inngår i: Proc. 21st AIAA CFD Conference, AIAA , 2013Konferansepaper (Fagfellevurdert)
  • 315.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Duality based boundary treatment for the Euler and Navier-Stokes equations2013Inngår i: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, 1-19 s.Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions.

    According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals.

  • 316.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    On the impact of boundary conditions on dual consistent finite difference discretizations2013Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, 41-55 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier{Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are wellposed.

    The form of the boundary conditions is chosen such that reduction to rst order form with its complications can be avoided.

    The primal equation is discretized using finite difference operators on summation-by-parts form with weak boundary conditions. It is shown that the discretization can be made energy stable, and that energy stability is sufficient for dual consistency.

    Since reduction to rst order form can be avoided, the discretization is significantly simpler compared to a discretization using Dirichlet boundary conditions.

    We compare the new boundary conditions with standard Dirichlet boundary conditions in terms of rate of convergence, errors and discrete spectra. It is shown that the scheme with the new boundary conditions is not only far simpler, but also has smaller errors, error bounded properties, and highly optimizable eigenvalues, while maintaining all desirable properties of a dual consistent discretization.

  • 317.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    On the impact of boundary conditions on dual consistent finite difference discretizations2013Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, 41-55 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 318.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    On the impact of boundary conditions on dual consistent finite difference discretizations2012Rapport (Annet vitenskapelig)
  • 319.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains2012Inngår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 62, 1620-1638 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 320.
    Berg, Jens
    et al.
    Division of Scientific Computing, Department of Information Technology, Uppsala University, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains2012Inngår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 62, nr 11, 1620-1638 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the heat and advectionequation in single and multipledomains. The equations are discretized using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices.

    It is shown how the spectrum of the singledomain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. The interface treatments are posed as a function of one parameter, and the impact on the spectrum and discretization error is investigated as a function of this parameter. Finally we briefly discuss the generalization to higher order accurate schemes.

  • 321.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, 7519-7532 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 322.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, nr 19, 7519-7532 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.

    The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.

  • 323.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012Rapport (Annet vitenskapelig)
  • 324.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, nr 20, 6846-6860 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Finitedifference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).

    In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way.

    The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergentfunctionaloutputs.

  • 325.
    Berg, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, 6846-6860 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 326.
    Berggren, Martin
    Department of Information Technology, Uppsala University.
    A vertex-centered dual discontinuous Galerkin method2006Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 192, nr 1, 175-181 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 327.
    Berggren, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A vertex-centered, dual discontinuous Galerkin method2006Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 192, 175-181 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 328.
    Berggren, Martin
    Department of Information Technology, Uppsala University.
    Approximations of very weak solutions to boundary-value problems2004Inngår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 42, nr 2, 860-877 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 329.
    Berggren, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Approximations of very weak solutions to boundary-value problems2004Inngår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 42, 860-877 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 330.
    Berggren, Martin
    Department of Computational and Applied Methematics, Rice University, Houston.
    Numerical solution of a flow-control problem: vorticity reduction by dynamic boundary action1998Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 19, nr 3, 829-860 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 331.
    Berggren, Martin
    Department of Computational and Applied Mathematics, Rice University, Houston, TX.
    Solving an advection-diffusion problem on the Connection Machine1994Inngår i: Concurrency: Practice and Experience, Vol. 6, nr 1, 55-68 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 332.
    Berggren, Martin
    FFA, the Aeronautical Research Institute of Sweden.
    The volume discharge approach to geometric conservation1999Inngår i: Computational Methods for Fluid-Structure Interaction / [ed] T. Kvamsdal, 1999Konferansepaper (Fagfellevurdert)
  • 333.
    Berggren, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    The volume discharge approach to geometric conservation1999Inngår i: Computational Methods for Fluid-Structure Interaction, Trondheim, Norway: Tapir Publishers , 1999, 133-141 s.Konferansepaper (Fagfellevurdert)
  • 334.
    Berggren, Martin
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Bängtsson, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Noreland, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Multifrequency shape optimization of an acoustic horn2003Inngår i: Computational Fluid and Solid Mechanics: 2003, Elsevier Science , 2003, 2204-2207 s.Konferansepaper (Fagfellevurdert)
  • 335.
    Berggren, Martin
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Ekström, Sven-Erik
    Department of Information Technology, Uppsala University.
    Nordström, Jan
    Department of Information Technology, Uppsala University.
    A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method2009Inngår i: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, nr 2-4, 456-468 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at lowest order. However, many of today's CFD codes use a vertex-centered FV method in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the method successfully handles shocks. We also discuss how to extend the FV edge-based data structure to support the new scheme. In this way, it will in principle be possible to extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.

  • 336. Berggren, Martin
    et al.
    Ekström, Sven-Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Nordström, Jan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method2009Inngår i: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, 456-468 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 337. Berggren, Martin
    et al.
    Ekström, Sven-Erik
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method2009Inngår i: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, 456-468 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 338.
    Berggren, Martin
    et al.
    Department of Computational and Applied Mathematics, Rice University, Houston TX.
    Glowinski, Roland
    Department of Mathematics, University of Houston, Houston, , TX .
    A spectral preconditioner for control problems associated with linear evolution equations1995Inngår i: East-West Journal on Numerical Mathematics, Vol. 3, nr 2, 81-109 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 339.
    Berggren, Martin
    et al.
    FFA, the Aeronautical Research Institute of Sweden, Bromma.
    Glowinski, Roland
    Department of Mathematics, University of Houston.
    Lions, Jacques-Louis
    College de France.
    A Computational Approach to Controllability Issues for Flow-Related Models. (I): Pointwise Control of the Viscous Burgers Equation1996Inngår i: International journal of computational fluid dynamics (Print), ISSN 1061-8562, E-ISSN 1029-0257, Vol. 7, nr 3, 237-252 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 340.
    Berggren, Martin
    et al.
    FFA, the Aeronautical Research Institute of Sweden, Bromma, Sweden.
    Glowinski, Roland
    Department of Mathematics, University of Houston, Houston.
    Lions, Jacques-Louis
    College de France, Rue d'Ulm, Paris, France .
    A computational approach to controllability issues for flow-related models. (II): Control of two-dimensional, linear advection-diffusion and Stokes models.1996Inngår i: International journal of computational fluid dynamics (Print), ISSN 1061-8562, E-ISSN 1029-0257, Vol. 6, nr 4, 253-274 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 341.
    Berggren, Martin
    et al.
    FFA, the Aeronautical Research Institute of Sweden.
    Heinkenschloss, Matthias
    Department of Computational and Applied Mathematics, Rice University, Houston, TX.
    Parallel Solution of Optimal-Control Problems by Time-Domain Decomposition1997Inngår i: Computational Science for the 21st Century / [ed] M.O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Périaux, and M. F. Wheeler, 1997Konferansepaper (Fagfellevurdert)
  • 342.
    Berglund, André
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical Simulations of Linear Stochastic Oscillators: driven by Wiener and Poisson processes2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The main component of this essay is the numerical analysis of stochastic differential equations driven by Wiener and Poisson processes. In order to do this, we focus on two model problems, the geometric Brownian motion and the linear stochastic oscillator, studied in the literature for stochastic differential equations only driven by a Wiener process. This essay covers theoretical as well as numerical investigations of jump - or more specifically, Poisson - processes and how they influence the above model problems.

  • 343.
    Berglund, André
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Svensson, Carl
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    On the risk relation between Economic Value of Equity and Net Interest Income2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The Basel Committee has proposed a new Pillar 2 regulatory framework for evaluating the interest rate risk of a bank's banking book appropriately called Interest Rate Risk in the Banking Book. The framework requires a bank to use and report two different interest rate risk measures: Economic Value of Equity (EVE) risk and Net Interest Income (NII) risk. These risk measures have previously been studied separately but few models have been proposed to investigate the relationship between them. Based on previous research we assume that parts of the banking book can be approximated using a portfolio strategy of rolling bonds and propose a model for relating the connection between the portfolio maturity structure, EVE risk and NII risk. By simulating from both single- and multi-factor Vasicek models and measuring risk as Expected Shortfall we illustrate the resulting risk profiles. We also show how altering certain theoretical assumptions seem to have little effect on these risk profiles.

  • 344.
    Berglund, Erik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    LQR and MPC control of a simulated data center2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    One of the largest contributions to a data center’s power usage is its cooling system. To decrease the energy usage of the cooling system, an automatic control scheme that adapts the capacity of the cooling units is needed. In this master thesis, a Simulink model of a data center is developed, along with several LQR and one MPC controller. The controllers control the outlet temperature and volumetric airflow of two CRAH units in the simulated data center. Simulations are performed in which the controllers are judged based on their estimated energy usage and how often the server temperatures in the data center exceed 35°C. Based on the experimental results, recommendations are made regarding what kinds of controllers to investigate in ABB’s further research.

  • 345.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik.
    Brodnik, Andrej
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Mrozek, Kent
    Staffansson, Mats
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Minimum curvature variation B-splines: validation of a path-planning model2004Rapport (Annet vitenskapelig)
  • 346.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik.
    Brodnik, Andrej
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Staffansson, Mats
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles2010Inngår i: IEEE Transactions on Automation Science and Engineering, ISSN 1545-5955, E-ISSN 1558-3783, Vol. 7, nr 1, 167-172 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the problem of automatic generation of smooth and obstacle-avoiding planar paths for efficient guidance of autonomous mining vehicles. Fast traversal of a path is of special interest. We consider four-wheel four-gear articulated vehicles and assume that we have an a priori knowledge of the mine wall environment in the form of polygonal chains. Computing quartic uniform B-spline curves, minimizing curvature variation, staying at least at a proposed safety margin distance from the mine walls, we plan high speed paths.

  • 347.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, EISLAB.
    Erikson, Ulf
    Luleå tekniska universitet.
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Mrozek, Kent
    Navigator AB.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Automatic generation of smooth paths bounded by polygonal chains2001Inngår i: CIMCA 2001: 2001 international conference on computational intelligence for modelling, control & automation : 9-11 July 2001, Las Vegas, Nevada, USA : proceedings / [ed] M. Mohammadian, CIMCA , 2001, 528-535 s.Konferansepaper (Fagfellevurdert)
  • 348. Berglund, Tomas
    et al.
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    An obstacle-avoiding minimum variation B-spline problem2003Inngår i: Proceedings: 2003 International Conference on Geometric Modeling and Graphics, GMAG 2003 ; 16 - 18 July 2003, London, England, Los Alamitos, Calif: IEEE Communications Society, 2003, 156-161 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

  • 349.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, EISLAB.
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The problem of computing an obstacle-avoiding minimum variation B-spline2003Rapport (Annet vitenskapelig)
    Abstract [en]

    We study the problem of computing a planar curve restricted to lie between two given polygonal chains such that the integral of the square of arc- length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

  • 350.
    Berglund, Tomas
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik.
    Strömberg, Thomas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Jonsson, Håkan
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, Datavetenskap.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Epi-convergence of minimum curvature variation B-splines2003Rapport (Annet vitenskapelig)
    Abstract [en]

    We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

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