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  • 201.
    Kiessling, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Tempone, Raúl
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Computable error estimates of a finite difference scheme for option pricing in exponential Lévy modelsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Option prices in exponential L´evy models solve certain partial integrodifferential equations (PIDEs). This work focuses on a finite difference scheme that issuitable for solving such PIDEs. The scheme was introduced in [Cont and Voltchkova, SIAM J. Numer. Anal., 43(4):1596–1626, 2005]. The main results of this work are new estimates of the dominating error terms, namely the time and space discretization errors. In addition, the leading order terms of the error estimates are determined in computable form. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschtitz continuous as in previous works.

    If the underlying Lévy process has infinite jump activity, then the jumps smallerthan some ε> 0 are approximated by diffusion. The resulting diffusion approximationerror is also estimated, with leading order term in computable form, as well as its effecton the space and time discretization errors. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the parameter ε.

  • 202.
    Kiessling, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Tempone, Raúl
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Diffusion approximation of Lévy processes with a view towardsfinanceManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Let the (log-)prices of a collection of securities be given by a d–dimensional Lévy process Xt having infinite activity and a smooth density. The value of a European contract with payoff g(x) maturing at T is determined by E[g(XT )]. Let ¯XT be a finite activity approximation to XT , where diffusion is introduced to approximate jumps smaller than a given truncation level ε > 0. The main result of this work is a derivationof an error expansion for the resulting model error, E[g(XT )−g( ¯XT )], with computable leading order term. Our estimate depends both on the choice of truncation level ε and the contract payoff g, and it is valid even when g is not continuous. Numerical experiments confirm that the error estimate is indeed a good approximation of the model error.

    Using similar techniques we indicate how to construct an adaptive truncation type approximation. Numerical experiments indicate that a substantial amount of work is to be gained from such adaptive approximation. Finally, we extend the previous model error estimates to the case of Barrier options, which have a particular path dependent structure.

  • 203.
    Kreiss, Heinz-Otto
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Ystrom, J.
    A note on viscous conservation laws with complex characteristics2006Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 46, s. S55-S59Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    There are several physical set-ups involving multi-phase fluids that result in highly unstable behavior already at rather low flow rates. Mathematical models of these flow problems consist typically of conservation laws like conservation of mass and momentum for each phase together with coupling terms connecting the phases. For multi-phase flow the characteristics are often complex and without the dissipative terms the problem is ill-posed and not computable. We will discuss why the nonlinearity of the system can prevent blow-up.

  • 204.
    Kupiainen, Marco
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Compressible Turbulent Flows: LES and Embedded Boundary Methods2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
  • 205.
    Lindberg, Per Olov
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transportvetenskap, Transport- och lokaliseringsanalys. KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Eriksson, E.A.
    Mattsson, Lars-Göran
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transportvetenskap, Transport- och lokaliseringsanalys.
    Invariance of achieved utility in random utility models1995Ingår i: Environment and planning A, ISSN 0308-518X, E-ISSN 1472-3409, Vol. 27, s. 121-142Artikel i tidskrift (Refereegranskat)
  • 206.
    Lindberg, Per Olov
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transportvetenskap, Transport- och lokaliseringsanalys. KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Mitradjieva, Maria
    Linköpings Universitet.
    The Stiff is Moving - Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment2012Ingår i: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 47, nr 2, s. 280-293Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, Conjugate direction Frank-Wolfe (CFW), Bi-conjugate Frank-Wolfe (BFW) and ”PARTANized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to Bar-Gera’s origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements suggested by Boyce et al. We further show that CFW is globally convergent. We moreover point at independent studies by other researchers that show that our methods compare favourably with recent bush-based and gradient projection algorithms on computers with several cores.

  • 207.
    Lindbo, Dag
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation2011Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

      This work contains two separate but related parts: one on spectrally  accurate and fast Ewald methods for electrostatics and viscous flow,  and one on micro- and complex fluid interface problems.  In Part I we are concerned with fast and spectrally accurate methods  to compute sums of slowly decaying potentials over periodic  lattices. We consider two PDEs: Laplace (electrostatics, the Coulomb  potential) and Stokes (viscous flow, the ``Stokeslet''  potential). Moreover, we consider both full and planar periodicity,  the latter meaning that periodicity applies in two dimensions and  the third is ``free''. These are major simulation tasks in current  molecular dynamics simulations and in many areas of computational  fluid mechanics involving e.g. particle suspensions.   For each of the four combinations of PDE and periodic structure, we  give spectrally accurate and O(N log N) fast methods based on  Ewald's or Ewald-like decompositions of the underlying potential  sums. In the plane-periodic cases we derive the decompositions in a  manner that lets us develop fast methods. Associated error estimates  are developed as needed throughout. All four methods can be placed  in the P3M/PME (Particle Mesh Ewald) family. We argue that they  have certain novel and attractive features: first, they are spectral  accurate; secondly, they use the minimal amount of memory possible  within the PME family; third, each has a clear and reliable view of  numerical errors, such that parameters can be chosen  wisely. Analytical and numerical results are given to support these  propositions. We benchmark accuracy and performance versus an  established (S)PME method.  Part II deals with free boundary problems, specifically numerical  methods for multiphase flow. We give an interface tracking method  based on a domain-decomposition idea that lets us split the  interface into overlapping patches. Each patch is discretized on a  uniform grid, and accurate and efficient numerical methods are given  for the equations that govern interface transport. We demonstrate  that the method is accurate and how it's used in immersed boundary,  and interface, Navier-Stokes methods, as well as in a boundary  integral Stokes setting.  Finally, we consider a problem in complex fluidics where there is a  concentration of surfactants \emph{on} the interface and the  interface itself is in contact with a solid boundary (the contact  line problem). We argue that the domain-decomposition framework is  attractive for formulating and treating complex models  (e.g. involving PDEs on a dynamic interface) and proceed with  developing various aspects of such a method.

  • 208.
    Lindbo, Dag
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems2012Ingår i: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 136, nr 16, s. 164111-1-164111-16Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast particle mesh Ewald (PME)-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.

  • 209.
    Lindbo, Dag
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Fast and spectrally accurate summation of 2-periodic Stokes potentialsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition by Hasimoto, and is given in an explicit form not found in the literature. Truncation error estimates are provided to aid in selecting parameters. The fast, PME-type, method appears to be the first fast method for computing Stokeslet Ewald sums in planar periodicity, and has three attractive properties: it is spectrally accurate; it uses the minimal amount of memory that a gridded Ewald method can use; and provides clarity regarding numerical errors and how to choose parameters. Analytical and numerical results are give to support this. We explore the practicalities of the proposed method, and survey the computational issues involved in applying it to 2-periodic boundary integral Stokes problems.

  • 210.
    Lindbo, Dag
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Interface tracking using patches2011Manuskript (preprint) (Övrigt vetenskapligt)
  • 211.
    Lindbo, Dag
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Spectral accuracy in fast Ewald-based methods for particle simulations2011Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, nr 24, s. 8744-8761Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A spectrally accurate fast method for electrostatic calculations under periodic boundary conditions is presented. We follow the established framework of FFT-based Ewald summation, but obtain a method with an important decoupling of errors: it is shown, for the proposed method, that the error due to frequency domain truncation can be separated from the approximation error added by the fast method. This has the significance that the truncation of the underlying Ewald sum prescribes the size of the grid used in the FFT-based fast method, which clearly is the minimal grid. Both errors are of exponential-squared order, and the latter can be controlled independently of the grid size. We compare numerically to the established SPME method by Essmann et al. and see that the memory required can be reduced by orders of magnitude. We also benchmark efficiency (i.e. error as a function of computing time) against the SPME method, which indicates that our method is competitive. Analytical error estimates are proven and used to select parameters with a great degree of reliability and ease.

  • 212.
    Lindbo, Dag
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Spectrally accurate fast summation for periodic Stokes potentials2010Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, nr 23, s. 8994-9010Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to the reciprocal part of the sum, invoking the equivalence of multiplications in reciprocal space to convolutions in real space, thus using convolutions with a Gaussian function to place the point sources on a grid. Due to the spectral accuracy of the method, the grid size needed is low and also in practice, for a fixed domain size, independent of N. The leading cost, which is linear in N, arises from the to-grid and from-grid operations. Combining this FFT based method for the reciprocal sum with the direct evaluation of the real space sum, a spectrally accurate algorithm with a total complexity of 0(N log N) is obtained. This has been shown numerically as the system is scaled up at constant density. (C) 2010 Elsevier Inc. All rights reserved.

  • 213.
    Loubenets, Alexei
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A non-conforming finite element method for interface Stokes problems and its application to two-phase Rayleigh-Taylor instability with solid obstacles2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we establish an immersed finite element method for the solution of interface Stokes problems. The main idea of the method is to use a fixed, uniform mesh everywhere over the computational domain except the vicinity of the interface, where specifically designed macro elements are employed, such that the jump conditions are well approximated. In general, the resulting immersed finite element space is non-conforming. The interface itself is represented with the help of Lagrangian markers. The capabillity of the method is illustrated in the case of a Rayleigh-Taylor two-phase flow instability problem with solid obstacles governed by the Stokes equations.

  • 214.
    Marcus, Lars
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Arkitektur, Stadsbyggnad.
    Ståhle, Alexander
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Arkitektur, Stadsbyggnad.
    Fitger, Martin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    The Place Syntax Tool (PST): Application for GIS MapInfo2005Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 215.
    Marin, Oana
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Quadrature rules for boundary integral methods applied to Stokes flow2011Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

     

    Fluid phenomena dominated by viscous effects can, in many cases, be modeled by the Stokes equations. The boundary integral form of the Stokes equations reduces the number of degrees of freedom in a numerical discretization by reformulating the threedimensional problem to two-dimensional integral equations to be discretized over the boundaries of the domain. Hence for the study of objects immersed in a fluid, such as drops or elastic or solid particles, integral equations are to be discretized over the surfaces of these objects only. As outer boundaries or confinements are added these must also be included in the formulation. This work is focused on the development and validation of such a wall treatment. An inherent difficulty in the numerical treatment of boundary integrals for Stokes flow is the integration of the singular fundamental solution of the Stokes equations – the so called Stokeslet. To alleviate this problem we developed a set of high-order quadrature rules for the numerical integration of the Stokeslet over a flat surface. Such a quadrature rule was first designed for singularities of the type 1/|x|. To assess the convergence properties of this quadrature rule a theoretical analysis has been performed. The slightly more complicated singularity of the Stokeslet required certain modifications of the integration rule developed for 1/|x|. To validate the quadrature rule developed for the Stokeslet against a physical model we use it in a classical problem in fluid dynamics, the sedimentation of a sphere onto a flat plate. This involves a direct discretization of the plane wall and at the same time of the immersed sphere. Without any special treatment the algebraic system given by the discrete problem is quite memory consuming since matrix blocks are full. By exploring the structure of the block matrices that build up the system we have found that the wall discretization leads to a matrix which is generated by only three of its columns. This information together with certain preconditioning considerations allowed us to use the Schur complement method thus leading to a less memory expensive solution to the algebraic system. As a final step it is shown that the numerical simulations match the analytical solution, within the limitations of the model. This wall treatment can be easily extended to the problem of two parallel walls, and it is also shown that the simulation is in good agreement with some known results for the two parallel walls problem.

     

  • 216.
    Marin, Oana
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30). KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30). KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30). KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    A highly accurate boundary treatment for confined Stokes flow2012Ingår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 66, s. 215-230Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom's method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls.

  • 217.
    Marin, Oana
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A wall treatment for confined Stokes flowArtikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

     

    The study of bodies immersed in Stokes flow is crucial in various microfluidic applications. Recasting the governing equations in a boundary integral formulation reduces the three-dimensional problem to two-dimensional integral equations to be discretized over the surface of the submerged objects. The present work focuses on the development and validation of a wall treatment where the wall is discretized in the same fashion as the immersed bodies. For this purpose, a set of high-order quadrature rules for the numerical integration of integrals containing the singular Green’s function-the so-called Stokeslet - has been developed. By coupling the wall discretization to the discretization of immersed objects, we exploit the structure of the block matrix corresponding to the wall discretization in order to substantially reduce the memory usage. For validation, the classical problem of a sedimenting sphere in the vicinity of solid walls is studied.

  • 218. Mesinger, Fedor
    et al.
    Popovic, Jelena
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Forward-backward scheme on the B/E grid modified to suppress lattice separation: the two versions, and any impact of the choice made?2010Ingår i: Meteorology and atmospheric physics (Print), ISSN 0177-7971, E-ISSN 1436-5065, Vol. 108, nr 1-2, s. 1-8Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Ever since its introduction to meteorology in the early 1970s, the forward-backward scheme has proven to be a very efficient method of treating gravity waves, with an added bonus of avoiding the time computational mode of the leapfrog scheme. It has been and it is used today in a number of models. When used on a square grid other than the Arakawa C grid, modification is or modifications are available to suppress the noise-generating separation of solutions on elementary C grids. Yet, in spite of a number of papers addressing the scheme and its modification, or modifications, issues remain that have either not been addressed or have been commented upon in a misleading or even in an incorrect way. Specifically, restricting ourselves to the B/E grid does it matter and if so how which of the two equations, momentum and the continuity equation, is integrated forward? Is there just one modification suppressing the separation of solutions, or have there been proposed two modification schemes? Questions made are addressed and a number of misleading statements made are recalled and commented upon. In particular, it is demonstrated that there is no added computational cost in integrating the momentum equation forward, and it is pointed out that this would seem advantageous given the height perturbations excited in the first step following a perturbation at a single height point. Yet, 48-h numerical experiments with a full-physics model show only a barely visible difference between the forecasts done using one and the other equation forward.

  • 219. Michiels, W.
    et al.
    Jarlebring, Elias
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Meerbergen, K.
    A projection approach for model reduction of large-scale time-delay systems2011Ingår i: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011, s. 1-8Konferensbidrag (Refereegranskat)
  • 220. Michiels, W.
    et al.
    Jarlebring, Elias
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Meerbergen, K.
    Krylov-Based Model Order Reduction of Time-delay Systems2011Ingår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 32, nr 4, s. 1399-1421Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a model order reduction method which allows the construction of a reduced, delay-free model of a given dimension for linear time-delay systems, whose characteristic matrix is nonlinear due to the presence of exponential functions. The method builds on the equivalent representation of the time-delay system as an infinite-dimensional linear problem. It combines ideas from a finite-dimensional approximation via a spectral discretization, on the one hand, and a Krylov–Padé model reduction approach, on the other hand. The method exhibits a good spectral approximation of the original model, in the sense that the smallest characteristic roots are well approximated and the nonconverged eigenvalues of the reduced model have a favorable location, and it preserves moments at zero and at infinity. The spectral approximation is due to an underlying Arnoldi process that relies on building an appropriate Krylov space for the linear infinite-dimensional problem. The preservation of moments is guaranteed, because the chosen finite-dimensional approximation preserves moments and, in addition, the space on which one projects is constructed in such a way that the preservation of moments carries over to the reduced model. The implementation of the method is dynamic, since the number of grid points in the spectral discretization does not need to be chosen beforehand and the accuracy of the reduced model can always be improved by doing more iterations. It relies on a reformulation of the problem involving a companion-like system matrix and a highly structured input matrix, whose structure are fully exploited.

  • 221. Moon, K.-S.
    et al.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tempone, Raúl
    Zouraris, G
    Hyperbolic differential equations and adaptive numerics2001Ingår i: / [ed] J. F. Blowey, J. P. Coleman and A. Craig, 2001Konferensbidrag (Refereegranskat)
  • 222.
    Moon, Kyoung-Sook
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Tempone, Raul
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Zouraris, Georgios
    Div of Applied Math - Statistics, Univ of Crete.
    Stochastic Dierential Equations: Model and Numerics2008Övrigt (Refereegranskat)
  • 223.
    Motamed, Mohammad
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Topics in Analysis and Computation of Linear Wave Propagation2008Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis concerns the analysis and numerical simulation of wave propagation problems described by systems of linear hyperbolic partial differential equations.

    A major challenge in wave propagation problems is numerical simulation of high frequency waves. When the wavelength is very small compared to the overall size of the computational domain, we encounter a multiscale problem. Examples include the forward and the inverse seismic wave propagation, radiation and scattering problems in computational electromagnetics and underwater acoustics. In direct numerical simulations, the accuracy of the approximate solution is determined by the number of grid points or elements per wavelength. The computational cost to maintain constant accuracy grows algebraically with the frequency, and for sufficiently high frequency, direct numerical simulations are no longer feasible. Other numerical methods are therefore needed. Asymptotic methods, for instance, are good approximations for very high frequency waves. They are based on constructing asymptotic expansions of the solution. The accuracy increases with increasing frequency for a fixed computational cost. Most asymptotic techniques rely on geometrical optics equations with frequency independent unknowns. There are however two deficiencies in the geometrical optics solution. First, it does not include diffraction effects. Secondly, it breaks down at caustics. Geometrical theory of diffraction provides a technique for adding diffraction effects to the geometrical optics approximation by introducing diffracted rays. In papers 1 and 2 we present a numerical algorithm for computing an important type of diffracted rays known as creeping rays. Another asymptotic model which is valid also at caustics is based on Gaussian beams. In papers 3 and 4, we present an error analysis of Gaussian beams approximation and develop a new numerical algorithm for computing Gaussian beams, respectively.

    Another challenge in computation of wave propagation problems arises when the system of equations consists of second order hyperbolic equations involving mixed space-time derivatives. Examples include the harmonic formulation of Einstein’s equations and wave equations governing elasticity and acoustics. The classic computational treatment of such second order hyperbolic systems has been based on reducing the systems to first order differential forms. This treatment has however the disadvantage of introducing auxiliary variables with their associated constraints and boundary conditions. In paper 5, we treat the problem in the second order differential form, which has advantages for both computational efficiency and accuracy over the first order formulation.

    Finally, paper 6 concerns the concept of well-posedness for a class of linear hyperbolic initial boundary value problems which are not boundary stable. The well-posedness is well established for boundary stable hyperbolic systems for which we can obtain sharp estimates of the solution including estimates at boundaries. There are, however, problems which are not boundary stable but are well-posed in a weaker sense, i.e., the problems for which an energy estimate can be obtained in the interior of the domain but not on the boundaries. We analyze a model problem of this type. Possible applications arise in elastic wave equations and Maxwell’s equations describing glancing and surface waves.

  • 224.
    Motamed, Mohammad
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Kreiss, Heinz-Otto
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hyperbolic Initial Boundary Value Problems which are not Boundary StableManuskript (Övrigt vetenskapligt)
  • 225.
    Motamed, Mohammad
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A Wave Front-based Gaussian Beam Method for Computing High Frequency WavesManuskript (Övrigt vetenskapligt)
  • 226.
    Motamed, Mohammad
    et al.
    Department of Mathematics, Simon Fraser University.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Taylor expansion and discretization errors in Gaussian beam superposition2010Ingår i: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 47, nr 7, s. 421-439Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error estimates related to the discretization of the superposition integral and the Taylor expansion of the phase and amplitude off the center of the beam. We show that in the case of odd order beams, the error is smaller than a simple analysis would indicate because of error cancellation effects between the beams. Since the cancellation happens only when odd order beams are used, there is no remarkable gain in using even order beams. Moreover, applying the error estimate to the problem with constant speed of propagation, we show that in this case the local beam width is not a good indicator of accuracy, and there is no direct relation between the error and the beam width. We present numerical examples to verify the error estimates.

  • 227.
    Motamed, Mohammad
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Taylor Expansion Errors in Gaussian Beam SummationManuskript (Övrigt vetenskapligt)
  • 228. Moussa, Ben
    et al.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Scalar conservation laws with boundary conditions and rough data measure solutions2002Ingår i: Methods and Applications of Analysis, ISSN 1073-2772, E-ISSN 1945-0001, Vol. 9, nr 4, s. 579-598Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Uniqueness and existence of $L^$#x221E;$ solutions to initial boundary value problems for scalar conservation laws, with continuous flux functions, is derived by $L^1$ contraction of Young measure solutions. The classical Kruzkov entropies, extended in Bardos, LeRoux and Nedelec’s sense to boundary value problems, are sufficient for the contraction. The uniqueness proof uses the essence of Kruzkov’s idea with his symmetric entropy and entropy flux functions, but the usual doubling of variables technique is replaced by the simpler fact that mollified measure solutions are in fact smooth solutions. The mollified measures turn out to have not only weak but also strong boundary entropy flux traces. Another advantage with the Young measure analysis is that the usual assumption of Lipschitz continuous flux functions can be relaxed to continuous fluxes, with little additional work

  • 229.
    Nazarov, Murtazo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow2011Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows.

    The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D.

    To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity.

    The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation.

  • 230.
    Nazarov, Murtazo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An adaptive finite element method for the compressible Euler equations2009Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This work develops a stabilized finite element method for the compressible Euler equations and proves an a posteriori error estimate for the approximated solution. The equations are approximated by the cG(1)cG(1) finite element method with continuous piecewise linear functions in space and time. cG(1)cG(1) gives a second order accuracy in space, and corresponds to a Crank-Nicholson type of discretization in time, resulting in second order accuracy in space, without a stabilization term.

    The method is stabilized by componentwise weighted least squares stabilization of the convection terms, and residual based shock capturing. This choice of stabilization gives a symmetric stabilization matrix in the discrete system. The method is successfully implemented for a number of benchmark problems in 1D, 2D and 3D. We observe that cG(1)cG(1) with the above choice of stabilization is robust and converges to an accurate solution with residual based adaptive mesh refinement.

    We then extend the General Galerkin framework from incompressible to compressible flow, with duality based a posteriori error estimation of some quantity of interest. The quantities of interest can be stresses, strains, drag and lift forces, surface forces or a mean value of some quantity. In this work we prove a duality based a posteriori error estimate for the compressible equations, as an extension of the earlier work for incompressible flow [25].

    The implementation and analysis are validated in computational tests both with respect to the stabilization and the duality based adaptation

     

     

     

  • 231.
    Nazarov, Murtazo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Convergence of a residual based artificial viscosity finite element method2011Rapport (Övrigt vetenskapligt)
  • 232.
    Nazarov, Murtazo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Guermond, Jean-Luc
    Popov, Bojan
    A posteriori error estimation for the compressible Euler equations using entropy viscosity2011Rapport (Övrigt vetenskapligt)
  • 233.
    Nazarov, Murtazo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An adaptive finite element method for inviscid compressible flow2010Ingår i: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 64, nr 10-12, s. 1102-1128Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 234.
    Nazarov, Murtazo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An adaptive finite element method for the compressible Euler equations2010Ingår i: INT J NUMER METHOD FLUID, 2010, Vol. 64, nr 10-12, s. 1102-1128Konferensbidrag (Refereegranskat)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 235.
    Nazarov, Murtazo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2011Rapport (Övrigt vetenskapligt)
  • 236.
    Nazarov, Murtazo
    et al.
    Texas A and M University, United States.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2012Ingår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, nr 4, s. A1905-A1924Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we present a computational study of the stability of time dependent dual problems for compressible flow at high Reynolds numbers in two dimensions. The dual problem measures the sensitivity of an output functional with respect to numerical errors and is a key part of goal oriented a posteriori error estimation. Our investigation shows that the dual problem associated with the computation of the drag force for the compressible Euler/Navier-Stokes equations, which are approximated numerically using different temporal discretization and stabilization techniques, is unstable and exhibits blow-up for several Mach regimes considered in this paper.

  • 237.
    Nazarov, Murtazo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Residual based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods2011Rapport (Övrigt vetenskapligt)
  • 238. Okamura, Allison M.
    et al.
    Mataric, Maja J.
    Christensen, Henrik I.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS. KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Medical and Health-Care Robotics Achievements and Opportunities2010Ingår i: IEEE robotics & automation magazine, ISSN 1070-9932, E-ISSN 1558-223X, Vol. 17, nr 3, s. 26-37Artikel i tidskrift (Refereegranskat)
  • 239. Olsson, K. Henrik A.
    et al.
    Ruhe, Axel
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Rational Krylov for eigenvalue computation and model order reduction2006Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 46, s. S99-S111Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A rational Krylov algorithm for eigenvalue computation and model order reduction is described. It is shown how to implement it as a modified shift-and-invert spectral transformation Arnoldi decomposition. It is shown how to do deflation, locking converged eigenvalues and purging irrelevant approximations. Computing reduced order models of linear dynamical systems by moment matching of the transfer function is considered. Results are reported from one illustrative toy example and one practical example, a linear descriptor system from a computational fluid dynamics application.

  • 240.
    Popovic, Jelena
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A Fast Method for Solving the Helmholtz Equation Based on Wave Splitting2009Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one--way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one--way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one--way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one--way wave equations are solved with GO with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge-Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is just O(ω1/p) for a p-th order Runge-Kutta method. This has been confirmed by numerical experiments.

  • 241.
    Popovic, Jelena
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Fast Adaptive Numerical Methods for High Frequency Waves and Interface Tracking2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The main focus of this thesis is on fast numerical methods, where adaptivity is an important mechanism to lowering the methods' complexity. The application of the methods are in the areas of wireless communication, antenna design, radar signature computation, noise prediction, medical ultrasonography, crystal growth, flame propagation, wave propagation, seismology, geometrical optics and image processing.  

    We first consider high frequency wave propagation problems with a variable speed function in one dimension, modeled by the Helmholtz equation. One significant difficulty of standard numerical methods for such problems is that the wave length is very short compared to the computational domain and many discretization points are needed to resolve the solution. The computational cost, thus grows algebraically with the frequency w. For scattering problems with impenetrable scatterer in homogeneous media, new methods have recently been derived with a provably lower cost in terms of w. In this thesis, we suggest and analyze a fast numerical method for the one dimensional Helmholtz equation with variable speed function (variable media) that is based on wave-splitting. The Helmholtz equation is split into two one-way wave equations which are then solved iteratively for a given tolerance. We show rigorously that the algorithm is convergent, and that the computational cost depends only weakly on the frequency for fixed accuracy. 

    We next consider interface tracking problems where the interface moves by a velocity field that does not depend on the interface itself. We derive fast adaptive  numerical methods for such problems. Adaptivity makes methods robust in the sense that they can handle a large class of problems, including problems with expanding interface and problems where the interface has corners. They are based on a multiresolution representation of the interface, i.e. the interface is represented hierarchically by wavelet vectors corresponding to increasingly detailed meshes. The complexity of standard numerical methods for interface tracking, where the interface is described by marker points, is O(N/dt), where N is the number of marker points on the interface and dt is the time step. The methods that we develop in this thesis have O(dt^(-1)log N) computational cost for the same order of accuracy in dt. In the adaptive version, the cost is O(tol^(-1/p)log N), where tol is some given tolerance and p is the order of the numerical method for ordinary differential equations that is used for time advection of the interface.  

    Finally, we consider time-dependent Hamilton-Jacobi equations with convex Hamiltonians. We suggest a numerical method that is computationally efficient and accurate. It is based on a reformulation of the equation as a front tracking problem, which is solved with the fast interface tracking methods together with a post-processing step.  The complexity of standard numerical methods for such problems is O(dt^(-(d+1))) in d dimensions, where dt is the time step. The complexity of our method is reduced to O(dt^(-d)|log dt|) or even to O(dt^(-d)).

  • 242.
    Popovic, Jelena
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A Fast Method for Solving the Helmholtz Equation Based on Wave-Splitting2009Ingår i: WAVES 2009 / [ed] Barucq, H.; Bonnet-Bendhia, A.-S.; Cohen, G.; Diaz, J.; Ezziani, A.; Joly, P., 2009, s. 220-221Konferensbidrag (Refereegranskat)
  • 243.
    Popovic, Jelena
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive Fast Interface Tracking Methods: Part I: Time AdaptivityManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we present a fast adaptive numerical method for interface tracking that uses an explicit multiresolution description of the interface. The interface is represented by wavelet vectors that correspond to the details of the interface on different scale levels.The complexity of standard numerical methods for interface tracking, where the interface is described by marker points, is O(N/dt), where N is the number of points on the interface and dt is the time step. The methods that we propose in this paper have O(tol^(-1/p)log N) computational cost, where tol is some given tolerance and p is the order of the numerical method for ordinary differential equations that is used for time advection of the interface. The adaptivity makes methods robust in the sense  that they can handle problems with both smooth and non-smooth interfaces (i.e. interfaces with corners) while keeping low computational cost.

  • 244.
    Popovic, Jelena
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive Fast Interface Tracking Methods: Part II: Spatial AdaptivityManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we present a fast space-time adaptive numerical method for interface propagation in a time varying velocity field based on a multiresolution description of the interface. The interface is represented by wavelet vectors that correspond to the details of the interface on different scale levels.The method is an extension of the method proposed in "J. Popovic and O. Runborg, Adaptive fast interface tracking methods: Part I, preprint (2012)", which is only time adaptive and it is thus not suitable for problems with expanding interfaces. The method that we propose in this paper, remedies that disadvantage of the time adaptive method in an efficient way. 

  • 245.
    Popovic, Jelena
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension2011Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, nr 3, s. 721-755Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge-Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is asymptotically just for a pth order Runge-Kutta method, where omega is the frequency. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method and can be close to the asymptotic rate.

  • 246.
    Popovic, Jelena
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Time Upscaling for Hamilton-Jacobi EquationsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

     In this paper, we suggest an accurate and computationally efficient numerical method for time-dependent Hamilton-Jacobi equations with convex Hamiltonians. The method is based on a reformulation of the Hamilton-Jacobi equation as a front tracking problem, which is solved with the fast interface tracking methods together with a post-processing step. The complexity of standard numerical methods for such problems is O(dt^(-(d+1))) in d dimensions, where dt is the time step. The complexity of the method that we propose in this paper is reduced to O(dt^(-d)|log dt|) or even to O(dt^(-d)).

  • 247. Rizzi, A
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Selected topics in the theory and practice of computational fluid dynamics1987Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 72, s. 1-69Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Computational fluid dynamics (CFD) is a large branch of scientific computing that lately has undergone explosive growth. It draws upon elements from related disciplines: fluid mechanics, numerical analysis, theory of partial differential equations, computer science, and computational geometry. By selecting certain topics we try to trace the way the dramatic growth came about and to illustrate the interplay of the related disciplines. The scope is broad and the emphasis is on discussing the underlying fundamentals in order to present an overall perspective on CFD. The focus is on the evolution of nonsmooth features in inviscid flows, primarily macroscale discontinuities like shock waves and vortex sheets admitted as solutions to the Euler equations, but also with some view to their possible unstable progression into small-scale features, ending ultimately in turbulence. Some of the current finite-difference methods, and the theory they are based upon, which are used to treat these problems are reviewed, and different grid generation techniques are introduced. Together with some principles for using advanced supercomputers, we also discuss how the methods are implemented on these machines. A number of computed results, some of them new and of large scale with up to one million grid points, are presented which reflect the limits of the theory and the current status of the field.

  • 248.
    Rizzi, Arthur
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Aerodynamik.
    Oppelstrup, Jesper
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Zhang, Mengmeng
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Aerodynamik.
    Tomac, Maximillian
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, Aerodynamik.
    Coupling parametric aircraft lofting to CFD & CSM grid generation for conceptual design2011Ingår i: 49th AIAA Aerospace Sciences Meeting, 2011, 2011Konferensbidrag (Refereegranskat)
  • 249. Rott, Oliver
    et al.
    Jarlebring, Elias
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An iterative method for the multipliers of periodic delaydifferential equations and the analysis of a PDE milling model2010Ingår i: Proceedings of the 9th IFAC Workshop on Time Delay Systems / [ed] Vyhlidal, Tomas; Zitek, Pavel, 2010, s. 1-6Konferensbidrag (Refereegranskat)
    Abstract [en]

    Locally convergent iterative schemes have turned out to be very useful in the analysis of the characteristic roots of delay-differential equations (DDEs) with constant coefficients. In this work we present a locally convergent iterative scheme for the characteristic multipliers of periodic-coefficient DDEs. The method is an adaption of an iterative method called residual inverse iteration. The possibility to use this method stems from an observation that the characteristic matrix can be expressed with the fundamental solution of a differential equation. We apply the method to a coupled milling model containing a partial and an ordinary differential equation. The conclusion of the numerical results is that the stability diagram of the coupled model differs significantly from the combined stability diagrams for each subsystem.

  • 250.
    Rubensson, Emanuel H.
    et al.
    KTH, Skolan för bioteknologi (BIO), Teoretisk kemi.
    Zahedi, Sara
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Computation of interior eigenvalues in electronic structure calculations facilitated by density matrix purification2008Ingår i: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, nr 17, s. 176101-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Density matrix purification, is in this work, used to facilitate the computation of eigenpairs around the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) in electronic structure calculations. The ability of purification to give large separation between eigenvalues close to the HOMO-LUMO gap is used to accelerate convergence of the Lanczos method. Illustrations indicate that a new eigenpair is found more often than every second Lanczos iteration when the proposed methods are used.

23456 201 - 250 av 293
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