| 1. |
- Andersson, Fredrik
(författare)
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Fast inversion of the Radon transform using log-polar coordinates and partial back-projections
- 2005
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Ingår i: SIAM JOURNAL ON APPLIED MATHEMATICS. - SIAM PUBLICATIONS. - 0036-1399. ; 65:3, s. 818-837
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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.
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| 2. |
- Appelö, Daniel, et al.
(författare)
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Perfectly matched layers for hyperbolic systems: : General formulation, well-posedness and stability
- 2006
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 67:1, s. 1-23
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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.
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| 3. |
- Bamberger, A, et al.
(författare)
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Higher order paraxial wave equation approximations in heterogeneous media
- 1988
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 48, s. 129-154
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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
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| 4. |
- Bamberger, A, et al.
(författare)
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Parabolic wave equation approximations in heterogenous media
- 1988
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 48, s. 99-128
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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.
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| 5. |
- Engström, Christian
(författare)
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Inverse bounds and bulk properties of complex-valued two-component composites
- 2006
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Ingår i: Siam Journal On Applied Mathematics. - Siam Publications. - 0036-1399. ; 67:1, s. 194-213
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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.
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| 6. |
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| 7. |
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| 8. |
- Gosse, Laurent, et al.
(författare)
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Existence, uniqueness, and a constructive solution algorithm for a class of finite Markov moment problems
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 68:6, s. 1618-1640
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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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| 9. |
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| 10. |
- Jonsson, B. Lars G., et al.
(författare)
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Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal
- 2004
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Ingår i: SIAM J. Appl. Math.. - Society for Industrial and Applied Mathematics. - 0036-1399. ; 64:6, s. 1954-1986
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small.
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