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Olof Runborg

  1. Multi-scale methods for wave propagation in heterogeneous media.

    Mon, 11/16/2009 - 16:01 — SomNambul
    Authors: Olof Runborg, Bjorn Engquist, Henrik Holst
    Subjects: Numerical Analysis
    Abstract

    Multi-scale wave propagation problems are computationally costly to solve by
    traditional techniques because the smallest scales must be represented over a
    domain determined by the largest scales of the problem. We have developed and
    analyzed new numerical methods for multi-scale wave propagation in the
    framework of heterogeneous multi-scale method. The numerical methods couples
    simulations on macro- and micro-scales for problems with rapidly oscillating
    coefficients.

  2. Resolution of the finite Markov moment problem.

    Mon, 11/02/2009 - 16:01 — SomNambul
    Authors: Olof Runborg, Laurent Gosse
    Subjects: Numerical Analysis
    Abstract

    We expose in full detail a constructive procedure to invert the so--called
    "finite Markov moment problem". The proofs rely on the general theory of
    Toeplitz matrices together with the classical Newton's relations.

  3. Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems.

    Thu, 10/29/2009 - 16:01 — SomNambul
    Authors: Olof Runborg, Laurent Gosse
    Subjects: Numerical Analysis
    Abstract

    We consider a class of finite Markov moment problems with arbitrary number of
    positive and negative branches. We show criteria for the existence and
    uniqueness of solutions, and we characterize in detail the non-unique solution
    families. Moreover, we present a constructive algorithm to solve the moment
    problems numerically and prove that the algorithm computes the right solution.

  4. Taylor Expansion and Discretization Errors in Gaussian Beam Superposition.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Mohammad Motamed, Olof Runborg
    Subjects: Numerical Analysis
    Abstract

    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.

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