| 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. - 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. |
- Bürger, Raimund, et al.
(författare)
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Entropy solutions of a scalar conservation law modeling sedimentation in vessels with varying cross-sectional area
- 2017
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 77:2, s. 789-811
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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.
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| 3. |
- Choi, Doo Sung, et al.
(författare)
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Corner effects on the perturbation of an electric potential
- 2018
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 78:3, s. 1577-1601
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Tidskriftsartikel (refereegranskat)abstract
- We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coeffcients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coeffcients of a generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine a criteria for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, the Nystrom discretization, and recursively compressed inverse preconditioning.
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| 4. |
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| 5. |
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| 6. |
- 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. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 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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| 7. |
- Helsing, Johan, et al.
(författare)
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An extended charge-current formulation of the electromagnetic transmission problem
- 2020
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 80:2, s. 951-976
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Tidskriftsartikel (refereegranskat)abstract
- A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all wavenumbers in the closed upper half-plane belonging to argument sets for which Maxwell's equations have unique solutions. This includes the challenging combination of a real positive wavenumber in the outer region and an imaginary wavenumber inside the object. The formulation, or variants thereof, is particularly suitable for numerical field evaluations as confirmed by examples involving both smooth and nonsmooth objects.
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| 8. |
- Ivanenko, Yevhen, et al.
(författare)
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Passive Approximation and Optimization Using B-Splines
- 2019
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
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Tidskriftsartikel (refereegranskat)abstract
- A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
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| 9. |
- 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 Journal on 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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| 10. |
- Rikte, Sten
(författare)
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Existence, Uniqueness, and Causality Theorems for Wave Propagation in Stratified, Temporally Dispersive, Complex Media
- 1997
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 57:5, s. 89-1373
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Tidskriftsartikel (refereegranskat)abstract
- A mixed initial-boundary value problem for a nonlocal, hyperbolic equation is analyzed with respect to unique solubility and causality. The regularity of the step response and impulse response (the Green functions) is investigated, and a wave front theorem is proved. The problem arises, e.g., at time-varying, electromagnetic, plane wave excitation of stratified, temporally dispersive, bi-isotropic or anisotropic slabs. Concluding, the problem is uniquely solvable, strict causality holds, and a well-defined wave front speed exists. This speed is independent of dispersion and excitation, and depends on the nondispersive properties of the medium only.
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