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Sökning: L773:0036 1399

  • Resultat 1-10 av 27
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  • Andersson, Fredrik (författare)
  • Fast inversion of the Radon transform using log-polar coordinates and partial back-projections
  • 2005
  • Ingår i: SIAM Journal on Applied Mathematics. - SIAM Publications. - 0036-1399. ; 65:3, s. 818-837
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform and its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, inversion can be performed by means of finite convolutions and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.
  • Andersson, Lars-Erik, et al. (författare)
  • Attractors in Frictional Systems Subjected to Periodic Loads
  • 2013
  • Ingår i: SIAM Journal on Applied Mathematics. - Society for Industrial and Applied Mathematics. - 0036-1399. ; 73:3, s. 1097-1116
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.
  • Appelö, Daniel, et al. (författare)
  • Perfectly matched layers for hyperbolic systems: : General formulation, well-posedness and stability
  • 2006
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 67:1, s. 1-23
  • Tidskriftsartikel (refereegranskat)abstract
    • Since its introduction the perfectly matched layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limited to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters, which is applicable to all hyperbolic systems and which we prove is well-posed and perfectly matched. We also introduce an automatic method for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell's equations, the linearized Euler equations, and arbitrary 2 x 2 systems in (2 + 1) dimensions.
  • Bamberger, A, et al. (författare)
  • Higher order paraxial wave equation approximations in heterogeneous media
  • 1988
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 48, s. 129-154
  • Tidskriftsartikel (refereegranskat)abstract
    • A new family of paraxial wave equation approximations is derived. These approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computational problems, e.g., in seismology, underwater acoustics and as artificial boundary conditions. The equations are written as systems which simplify computations. The support and singular support are studied; energy estimates are given which prove the well-posedness. The reflection and transmission are shown to be continuously dependent on material interfaces in heterogeneous media
  • Bamberger, A, et al. (författare)
  • Parabolic wave equation approximations in heterogenous media
  • 1988
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 48, s. 99-128
  • Tidskriftsartikel (refereegranskat)abstract
    • The properties of different variants of parabolic approximations of scalar wave equations are analyzed. These equations are of general form which includes those used in seismology, underwater acoustics and other applications. A new version of the parabolic approximation is derived for heterogeneous media. It has optimal properties with respect to wave reflection at material interfaces. The amplitud of the reflected and transmitted waves depend continuously on the interface. Existence, uniqueness and energy estimates are proved.
  • Bürger, Raimund, et al. (författare)
  • Entropy solutions of a scalar conservation law modeling sedimentation in vessels with varying cross-sectional area
  • 2017
  • Ingår i: SIAM Journal on Applied Mathematics. - SIAM Publications. - 0036-1399. ; 77:2, s. 789-811
  • Tidskriftsartikel (refereegranskat)abstract
    • The sedimentation of an ideal suspension in a vessel with variable cross-sectional area can be described by an initial-boundary value problem for a scalar nonlinear hyperbolic conservation law with a nonconvex flux function and a weight function that depends on spatial position. The sought unknown is the local solids' volume fraction. For the most important cases of vessels with downward-decreasing cross-sectional area and flux functions with at most one infection point, entropy solutions of this problem are constructed by the method of characteristics. Solutions exhibit discontinuities that mostly travel at variable speed, i.e., they are curved in the space-time plane. These trajectories are given by ordinary differential equations that arise from the jump condition. It is shown that three qualitatively different solutions may occur in dependence of the initial concentration. The potential application of the findings is a new method of flux identification via settling tests in a suitably shaped vessel. Related models also arise in flows of vehicular traffic, pedestrians, in pipes with varying cross-sectional area, and on curved surfaces.
  • Engström, Christian (författare)
  • Inverse bounds and bulk properties of complex-valued two-component composites
  • 2006
  • Ingår i: SIAM Journal on Applied Mathematics. - SIAM Publications. - 0036-1399. ; 67:1, s. 194-213
  • Tidskriftsartikel (refereegranskat)abstract
    • The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quantified in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the effective permittivity, we present a general scheme to estimate the microstructural parameters such as the volume fraction and the anisotropy of two-component composites. The estimates are given as bounds, that is, the largest parameter region which is compatible with the available information. Thus, more information produces better estimates on the microstructural parameters. The method, which uses complex-valued measurements of bulk properties of the composite, is illustrated by numerical examples.
  • Engström, Christian (författare)
  • Inverse bounds of two-component composites
  • 2007
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 68:3, s. 666-679
  • Tidskriftsartikel (refereegranskat)abstract
    • A  method is presented for estimating microstructural parameters from permittivity measurements of two-component composites. This structural information is described by a particular positive measure in the Stieltjes integral representation of the effective permittivity. The dependence on the geometrical structure can be reduced to the problem of calculating the moments of the measure. We present a method that uses measurement data at a set of distinct frequencies or temperatures to calculate bounds on several moments. These inverse bounds are improved when the volume fraction is known or the material is isotropic. Composites with known geometrical structure illustrate the method.
  • Engström, Christian, et al. (författare)
  • On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
  • 2009
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 70:1, s. 231-247
  • Tidskriftsartikel (refereegranskat)abstract
    • We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.
  • Gosse, Laurent, et al. (författare)
  • Existence, uniqueness, and a constructive solution algorithm for a class of finite Markov moment problems
  • 2007
  • Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 68:6, s. 1618-1640
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider a class of finite Markov moment problems with an arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the nonunique solution families. Moreover, we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution.
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