| 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. |
- 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. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 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. |
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| 4. |
- 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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| 5. |
- Engström, Christian
(författare)
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Inverse bounds of two-component composites
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:3, s. 666-679
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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.
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| 6. |
- Engström, Christian, et al.
(författare)
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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:1, s. 231-247
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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.
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| 7. |
- 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. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 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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| 8. |
- Shestopalov, Youri, 1953-, et al.
(författare)
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Investigation of Electromagnetic Diffraction by a Dielectric Body in a Waveguide using the Method of Volume Singular Integral Equation
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM. - 0036-1399 .- 1095-712X. ; 70:3, s. 969-983
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Tidskriftsartikel (refereegranskat)abstract
- The problem of diffraction of an electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide of rectangular cross section isconsidered. This problem is reduced to solving a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem(BVP) for the system of Maxwell's equations and the equivalence of this BVP and VSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. A numerical Galerkin method for the solution of VSIE is proposed, and its convergence is proved
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| 9. |
- Vynnycky, M., et al.
(författare)
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ASYMPTOTIC REDUCTION FOR NUMERICAL MODELING OF POLYMER ELECTROLYTE FUEL CELLS
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:2, s. 455-487
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Tidskriftsartikel (refereegranskat)abstract
- Most existing three-dimensional (3D) models for the polymer electrolyte fuel cell (PEFC), as well as other types of fuel cells, are fully numerical and computationally expensive. While such models are undoubtedly useful, they cannot provide the qualitative understanding that comes from a complete prior nondimensional analysis of the problem. Here, earlier ideas for the derivation of a two-dimensional (2D) asymptotically reduced model to describe steady isothermal gas-phase flow in the cathode of a PEFC are extended to a 3D nonisothermal model for a whole PEFC with straight channel flow distributors. As well as providing characteristic current density and temperature difference scales for the whole cell, it is also possible to extract potential drops over individual cell components. The analysis indicates that, for realistic operating ranges, the PEFC is sufficiently isothermal with respect to the mass, momentum, and charge transport to enable the thermal problem to be decoupled from the rest, a simplification not noted previously. After the relevant nondimensional parameters have been identified, a reduced model is proposed and some preliminary numerical results comparing the polarization curves obtained from the reduced and 3D models are presented. Good agreement is found; most significantly, the reduced model is found to require between one and two orders of CPU time less than the full 3D model.
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| 10. |
- Öktem, Ozan, 1969-, et al.
(författare)
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Local tomography in electron microscopy
- 2008
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:5, s. 1282-1303
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Tidskriftsartikel (refereegranskat)abstract
- We present a new local tomographic algorithm applicable to electron microscope tomography. Our algorithm applies to the standard data acquisition method, single-axis tilting, as well as to more arbitrary acquisition methods including double axis and conical tilt. Using microlocal analysis we put the reconstructions in a mathematical context, explaining which singularities are stably visible from the limited data given by the data collection protocol in the electron microscope. Finally, we provide reconstructions of real specimens from electron tomography data.
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