| 1. |
- Berggren, Martin, et al.
(författare)
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Acoustic boundary layers as boundary conditions
- 2018
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 371, s. 633-650
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Tidskriftsartikel (refereegranskat)abstract
- The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an O (delta) perturbation, where delta is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier-Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model.
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| 2. |
- Bernland, Anders, et al.
(författare)
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Acoustic shape optimization using cut finite elements
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - Hoboken : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 113:3, s. 432-449
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Tidskriftsartikel (refereegranskat)abstract
- Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.
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| 3. |
- Bernland, Anders
(författare)
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Bandwidth Limitations for Scattering of Higher Order Electromagnetic Spherical Waves with Implications for the Antenna Scattering Matrix
- 2012
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Ingår i: IEEE Transactions on Antennas and Propagation. - 0018-926X. ; 60:9, s. 4345-4353
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Tidskriftsartikel (refereegranskat)abstract
- Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive Yagi-Uda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the low-frequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.
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| 4. |
- Bernland, Anders
(författare)
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Bandwidth limitations for scattering of higher order electromagnetic spherical waves with implications for the antenna scattering matrix
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive Yagi-Uda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the low-frequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.
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| 5. |
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| 6. |
- Bernland, Anders, et al.
(författare)
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Estimation of Spherical Wave Coefficients from 3D Positioner Channel Measurements
- 2012
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Ingår i: IEEE Antennas and Wireless Propagation Letters. - 1548-5757. ; 11, s. 608-611
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Tidskriftsartikel (refereegranskat)abstract
- Electromagnetic vector spherical waves have been used recently to model antenna-channel interaction and the available degrees of freedom in MIMO systems. However, there are no previous accounts of a method to estimate spherical wave coefficients from channel measurements. One approach for this, using a 3D positioner, is presented and analyzed in this letter. Measurement results are presented and discussed. It is concluded that estimates based on randomly positioned measurements within a volume are less sensitive to noise than those based only on measurements on the surface.
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| 7. |
- Bernland, Anders, et al.
(författare)
-
Estimation of Spherical Wave Coefficients from 3D Positioner Channel Measurements
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Electromagnetic vector spherical waves have been used recently to model antenna channel interaction and the available degrees of freedom in MIMO systems. However, there are no previous accounts of a method to estimate spherical wave coefficients from channel measurements. One approach, using a 3D positioner, is presented in this letter, both in theory and practice. Measurement results are presented and discussed. One conclusion is that using randomly positioned measurements within a volume is less sensitive to noise than using only measurements on the surface.
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| 8. |
- Bernland, Anders
(författare)
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Integral Identities for Passive Systems and Spherical Waves in Scattering and Antenna Problems
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Sum rules and physical limitations within electromagnetic theory and antenna theory have received significant attention in the last few years. However, the derivations are often relying on application specific and sometimes unsupported assumptions, and therefore a mathematically rigorous and generally applicable approach seems timely. Such an approach is presented in this thesis, along with examples and all the necessary proofs. The approach is also applied in the thesis to derive sum rules and physical limitations on electromagnetic spherical wave scattering. This has not been done before, despite the widespread use of spherical wave decompositions. For example, spherical waves and the antenna scattering matrix provide a complete and compact description of all the important properties of an antenna, are crucial parts in spherical near-field antenna measurements, and have been used recently to model antenna-channel interaction and multiple-input multiple-output (MIMO) communication systems. This thesis is also the first to present a method to estimate spherical wave coefficients from propagation channel measurements. The results of this thesis can roughly be divided into three categories: Firstly, a general approach to derive sum rules and physical limitations on input-output systems based on the assumptions of causality and passivity is presented (Paper I). Secondly, sum rules and physical limitations on the scattering and matching of electromagnetic spherical waves are derived, and the implications for antennas are explored (Papers II-IV). Thirdly, a method to estimate spherical wave coefficients from channel measurements, and the results of a measurement campaign, are presented and analysed (Paper V). The thesis consists of a General Introduction and five appended papers.
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| 9. |
- Bernland, Anders
(författare)
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On physical limitations for broadband electromagnetic scattering --- high order spherical waves
- 2011
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Ingår i: [Host publication title missing]. ; , s. 619-622
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Konferensbidrag (refereegranskat)abstract
- Limitations on the scattering matrix are derived for a wide class of objects, restricting their broadband interaction with electromagnetic vector spherical waves in terms of their size, shape and static material properties. In particular, it is seen that the order of the dominating term for electrically small objects increases with the order of the spherical wave. The results are applicable to many areas concerned with electromagnetic waves interacting with matter. For instance, they open up a new approach to derive bounds on antenna performance. They can also be generalized to acoustic and elastodynamic scattering. Two intermediate results presented are a set of sum rules for and the low-frequency asymptotic expansions of the scattering and transition matrices of a general scatterer.
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| 10. |
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