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  • 1. Beilina, L.
    et al.
    Johnson, Claes
    A posteriori error estimation in computational inverse scattering2005In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 15, no 1, p. 23-35Article in journal (Refereed)
    Abstract [en]

    We prove an a posteriori error estimate for an inverse acoustic scattering problem, where the objective is to reconstruct an unknown wave speed coefficient inside a body from measured wave reflection data in time on parts of the surface of the body. The inverse problem is formulated as a problem of finding a zero of a Jacobian of a Lagrangian. The a posterori error estimate couples residuals of the computed solution to weights the reconstruction reflecting the sensitivity of the reconstruction obtained by solving an associated linaerized problem for the Hessian of the Lagrangian. We show concrete examples of reconstrution including a posteriori error estimation.

  • 2. Eriksson, K.
    et al.
    Johnson, Claes
    Logg, A.
    Explicit time-stepping for stiff ODES2003In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 25, no 4, p. 1142-1157Article in journal (Refereed)
    Abstract [en]

    We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis. For many stiff problems the cost of the stabilizing small time steps is small, so the improvement is large. We illustrate the technique on a number of well-known stiff test problems.

  • 3.
    Hoffman, Claes
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive finite element methods for incompressible flow2003In: Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics / [ed] Barth, Timothy J.; Deconinck, Herman, Springer , 2003Chapter in book (Refereed)
  • 4.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Vilela de Abreu, Rodrigo
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Computability and Adaptivity in CFD2018In: Encyclopedia of Computational Mechanics / [ed] Erwin Stein and René de Borst and Thomas J. R. Hughes, John Wiley & Sons, 2018, 2Chapter in book (Refereed)
  • 5.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    New Theory of Flight2016In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 18, no 2, p. 219-241Article in journal (Refereed)
    Abstract [en]

    We present a new mathematical theory explaining the fluid mechanics of sub-sonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl-Kutta-Zhukovsky formed 100 year ago. The new the-ory is based on our new resolution of d’Alembert’s paradox showing that slightlyviscous bluff body flow can be viewed as zero-drag/lift potential flow modified by3d rotational slip separation arising from a specific separation instability of po-tential flow, into turbulent flow with nonzero drag/lift. For a wing this separationmechanism maintains the large lift of potential flow generated at the leading edgeat the price of small drag, resulting in a lift to drag quotient of size15

  • 6.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A new approach to computational turbulence modeling2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 23-24, p. 2865-2880Article in journal (Refereed)
    Abstract [en]

    We present a new approach to computational fluid dynamics (CFD) using adaptive stabilized Galerkin finite element methods with duality based a posteriori error control for chosen output quantities of interest. We address the basic question of computability in CFD: For a given flow, what quantity is computable to what tolerance to what cost? We focus on incompressible Newtonian flow with medium to large Reynolds numbers involving both laminar and turbulent flow features. We estimate a posteriori the output of the computed solution with the output based on the exact solution to the Navier–Stokes equations, thus circumventing introducing and modeling Reynolds stresses in averaged Navier–Stokes equations. Our basic tool is a representation formula for the error in the quantity of interest in terms of a space–time integral of the residual of a computed solution multiplied by weights related to derivatives of the solution of an associated dual problem with data connected to the output. We use the error representation formula to derive an a posteriori error estimate combining residuals with computed dual weights, which is used for mesh adaptivity in space–time with the objective of satisfying a given error tolerance with minimal computational effort. We show in a concrete example that outputs such as a mean value in time of drag of a turbulent flow around a bluff body are computable on a PC with a tolerance of a few percent using a few hundred thousand mesh points in space. We refer to our methodology as adaptive DNS/LES, where automatically by adaptivity certain features of the flow are resolved in a direct numerical simulation (DNS), while certain other small scale turbulent features are left unresolved in a large eddy simulation (LES). The stabilization of the Galerkin method giving a weighted least square control of the residual acts as the subgrid model in the LES. The a posteriori error estimate takes into account both the error from discretization and the error from the subgrid model. We pay particular attention to the stability of the dual solution from (i) perturbations replacing the exact convection velocity by a computed velocity, and (ii) computational solution of the dual problem, which are the crucial aspects entering by avoiding using averaged Navier–Stokes equations including Reynolds stresses. A crucial observation is that the contribution from subgrid modeling in the a posteriori error estimation is small, making it possible to simulate aspects of turbulent flow without accurate modeling of Reynolds stresses.

  • 7.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Adaptive DNS/LES: a new agenda in cfd2004In: Finite element methods: 1970s and beyond / [ed] L.P. Franca, T.E. Tezduyar and A. Masud, Barcelona: CIMNE , 2004Chapter in book (Refereed)
    Abstract [en]

    We show that using adaptive finite element methods it is possible to accurately simulate turbulent flow with the computational power of a PC. We argue that this possibility should set a new agenda in CFD. The key to this break-through is (i) application of the general approach to adaptitive error control in Galerkin methods based on duality, coupled with (ii) crucial properties of turbulent flow allowing accurate computation of mean value quantities such as drag and lift without full resolution of all scales.

  • 8.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Adaptive finite element methods for turbulent flow2004In: Numerical Mathematics And Advanced Applications, Proceedings / [ed] Feistauer, M.; Dolejší, V.; Knobloch, P.; Najzar, K., Springer , 2004, p. 430-439Conference paper (Refereed)
    Abstract [en]

    We present recent results using adaptive finite element methods, based on a posteriori error estimates, to compute various output functionals for incompressible flow problems in 3d, for both laminar and turbulent flows. The a posteriori error estimates are based on the solution of an associated dual problem with data connected to the output functional we want to compute.

  • 9.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive multiscale computational modeling of complex incompressible fluid flow2002In: Conference proceedings of WCCM Fifth World Congress on Computational Mechanics, 2002Conference paper (Refereed)
  • 10.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Blow up of incompressible Euler solutions2008In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 48, no 2, p. 285-307Article in journal (Refereed)
    Abstract [en]

    We present analytical and computational evidence of blowup of initially smooth solutions of the incompressible Euler equations into non-smooth turbulent solutions. We detect blowup by observing increasing L-2-residuals of computed solutions under decreasing mesh size.

  • 11.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Computability and adaptivity in CFD2007In: Encyclopedia of computational mechanics / [ed] E. Stein, R. de Borst,T.J.R. Hughes, Wiley , 2007Chapter in book (Refereed)
    Abstract [en]

    We briefly recall research on adaptive computational methods for laminar compressible and incompressible flow, and then move on to present recent work on computability and adaptivity for turbulent incompressible flow, based on adaptive stabilized Galerkin finite element methods with duality-based a posteriori error control for chosen output quantities of interest, here referred to asgeneral Galerkin G2 methods.

    We show in concrete examples that outputs such as mean values in time of drag and lift of turbulent flow around a bluff body are computable on a PC with a tolerance of a few percent using a few hundred thousand mesh points in space.

  • 12.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Computational turbulent incompressible flow: Applied mathematics: Body and soul 42007Book (Refereed)
    Abstract [en]

    This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body & Soul computational finite element methodology in the form of General Galerkin (G2), up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. The book shows that direct application of G2 without any turbulence or wall modeling, allows reliable computation on a PC of mean value quantities of turbulent flow such as drag and lift. The power of G2 is demonstrated by resolving several classical scientific paradoxes of fluid flow and by uncovering secrets of flying, sailing, racing and ball sports. The book presents new aspects on both mathematics and computation of turbulent flow, and challenges established approaches. The book is directed to a wide audience of computational mathematicians fluid dynamicists and scientists. The G2 solver is available as part the free software project FEniCS at www.fenics.org. The book has a dedicated dynamic web page, including movies from a wide variety of simulations, at www.bodysoulmath.org. The book is focussed on incompressible flow, but opens to compressible flow continued in Vol 5 on thermodynamics. The authors are experts on computational mathematics and technology.

  • 13.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Irreversibility in reversible systems2006In: HERMIS The international journal of computer mathematics and its applications, ISSN 1108-7609, Vol. 6, p. 12-33Article in journal (Refereed)
  • 14.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Resolution of d'Alembert's Paradox2010In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 12, no 3, p. 321-334Article in journal (Refereed)
    Abstract [en]

    We propose a resolution of d'Alembert's Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and computational evidence that (i) potential flow cannot be observed because it is illposed or unstable to perturbations, (ii) computed viscosity solutions of the Euler equations with slip boundary conditions initiated as potential flow, develop into turbulent solutions which are wellposed with respect to drag/lift and which show substantial drag/lift, in accordance with observations.

  • 15.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Stability of the dual Navier-Stokes equations and efficient computation of mean output in turbulent flow using adaptive DNS/LES2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 13-16, p. 1709-1721Article in journal (Refereed)
    Abstract [en]

    We discuss aspects of adaptive DNS/LES, where adaptive finite element methods are used to accurately compute chosen output from a turbulent flow with the computational power of a PC. The key to this break-through is: (i) application of the general approach to adaptive error control in Galerkin methods based on duality.. coupled with (ii) crucial properties of turbulent flow allowing accurate computation of mean value quantities such as drag and lift without full resolution of all scales.

  • 16.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    The mathematical secret of flight2009In: Normat, ISSN 0801-3500, Vol. 57, no 4, p. 145-169Article in journal (Other academic)
  • 17.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    The mathematical theory of flight2009In: Normat, ISSN 0801-3500, Vol. 57, p. 145-169Article in journal (Refereed)
    Abstract [en]

    We show by computational solution of the incompressible Navier-Stokes equations with friction force boundary conditions, that the classical inviscid circulation theory by Kutta-Zhukovsky for lift of a wing and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century flight mechanics, do not correctly describe the real turbulent airflow around a wing. We show that lift and drag essentially originate from a turbulent wake of counter-rotating rolls of low-pressure streamwise vorticity generated by a certain instability mechanism of potential flow at rear separation. The new theory opens the possibility of computational prediction of flight characteristics of an airplane using millions of meshpoints without resolving thin boundary layers, instead of the imposssible quadrillions required according to state-of-the-art for boundary layer resolution.

  • 18.
    Hoffman, Johan
    et al.
    Mathematics, Chalmers.
    Johnson, Claes
    Bertoluzza, S.
    Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar Multiresolution analysis2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 1, p. 19-44Article in journal (Refereed)
    Abstract [en]

    In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.

  • 19.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    Logg, Anders
    Simula Research Laboratory.
    Dreams of Calculus: Perspectives on Mathematics Education2004Book (Other academic)
  • 20. Jansson, Johan
    et al.
    Johnson, Claes
    Logg, A.
    Computational modeling of dynamical systems2005In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 15, no 3, p. 471-481Article in journal (Refereed)
    Abstract [en]

    In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 10(-9) computed over the time interval [0, 100], and a lattice consisting of large and small point masses.

  • 21. Liu, Y. Q.
    et al.
    Bondeson, A.
    Bergstrom, R.
    Johnson, Claes
    Larson, M. G.
    Samuelsson, K.
    Eddy-current computations using adaptive grids and edge elements2002In: IEEE transactions on magnetics, ISSN 0018-9464, E-ISSN 1941-0069, Vol. 38, no 2, p. 449-452Article in journal (Refereed)
    Abstract [en]

    Results are presented from eddy-current computations using adaptive techniques, based on rigorous a posteriori error estimates. The adaptivity restores the quadratic convergence with grid size of the magnetic energy, despite singularities occurring at corners. A new procedure is introduced to satisfy the solvability condition for the curl-curl equation. The methods are applied to a model of a hydrogenerator, with anisotropic conductivity and permeability. The ungauged formulation with both vector and scalar potentials gives very significant improvements in rate of convergence for this problem. Reasons for the improved convergence are discussed.

1 - 21 of 21
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