1. 
 Andersson, Fredrik
(författare)

Fast inversion of the Radon transform using logpolar coordinates and partial backprojections
 2005

Ingår i: SIAM Journal on Applied Mathematics.  SIAM Publications.  00361399. ; 65:3, s. 818837

Tidskriftsartikel (refereegranskat)abstract
 In this paper a novel filtered backprojection 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 logpolar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the backprojection into several partial backprojections, inversion can be performed by means of finite convolutions and hence implemented by an FFTalgorithm. In this way, a fast and accurate reconstruction method is obtained.


2. 
 Andersson, LarsErik, 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.  00361399. ; 73:3, s. 10971116

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 twonode system. Counter examples are presented of “unstable” steadystate 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 quasistatic evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.


3. 
 Appelö, Daniel, et al.
(författare)

Perfectly matched layers for hyperbolic systems: : General formulation, wellposedness and stability
 2006

Ingår i: SIAM Journal on Applied Mathematics.  00361399. ; 67:1, s. 123

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 wellposed 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.


4. 
 Bamberger, A, et al.
(författare)

Higher order paraxial wave equation approximations in heterogeneous media
 1988

Ingår i: SIAM Journal on Applied Mathematics.  00361399. ; 48, s. 129154

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 wellposedness. The reflection and transmission are shown to be continuously dependent on material interfaces in heterogeneous media


5. 
 Bamberger, A, et al.
(författare)

Parabolic wave equation approximations in heterogenous media
 1988

Ingår i: SIAM Journal on Applied Mathematics.  00361399. ; 48, s. 99128

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.


6. 
 Bürger, Raimund, et al.
(författare)

Entropy solutions of a scalar conservation law modeling sedimentation in vessels with varying crosssectional area
 2017

Ingår i: SIAM Journal on Applied Mathematics.  SIAM Publications.  00361399. ; 77:2, s. 789811

Tidskriftsartikel (refereegranskat)abstract
 The sedimentation of an ideal suspension in a vessel with variable crosssectional area can be described by an initialboundary 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 downwarddecreasing crosssectional 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 spacetime 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 crosssectional area, and on curved surfaces.


7. 
 Engström, Christian
(författare)

Inverse bounds and bulk properties of complexvalued twocomponent composites
 2006

Ingår i: SIAM Journal on Applied Mathematics.  SIAM Publications.  00361399. ; 67:1, s. 194213

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 twocomponent 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 complexvalued measurements of bulk properties of the composite, is illustrated by numerical examples.


8. 
 Engström, Christian
(författare)

Inverse bounds of twocomponent composites
 2007

Ingår i: SIAM Journal on Applied Mathematics.  00361399. ; 68:3, s. 666679

Tidskriftsartikel (refereegranskat)abstract
 A method is presented for estimating microstructural parameters from permittivity measurements of twocomponent 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.


9. 
 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.  00361399. ; 70:1, s. 231247

Tidskriftsartikel (refereegranskat)abstract
 We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a realvalued 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.


10. 
 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.  00361399. ; 68:6, s. 16181640

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.

