| 1. |
- 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. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 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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| 2. |
- Jonsson, B. Lars G., et al.
(författare)
-
Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal
- 2004
-
Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 64:6, s. 1954-1986
-
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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| 3. |
- Karlin, V, et al.
(författare)
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Numerical solution of nonlinear hypersingular integral equations of the Peierls type in dislocation theory
- 2000
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399 .- 1095-712X. ; 60:2, s. 664-678
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we analyze hypersingular integral equations of the Peierls type specified on the whole real axis. The method of "approximate approximations" [Maz'ya, Proceedings of the Eighth Conference on the Mathematics of Finite Elements and Applications, VIII, MAFELAP 1993, Brunel University, 1994, pp. 107-104] is employed in order to produce numerical solutions of high accuracy, and the results are applied to problems in the theory of dislocations. The critical Peierls stress is evaluated for different configurations of dislocations and for different types of the interatomic force law.
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| 4. |
- Liefvendahl, Mattias, et al.
(författare)
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Analytical and numerical investigation of the resolvent for plane Couette flow
- 2003
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399 .- 1095-712X. ; 63:3, s. 801-817
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Tidskriftsartikel (refereegranskat)abstract
- We present new bounds for the solution of the resolvent equation for plane Couette flow. Both analytic methods and computation, using the Chebyshev tau spectral method, are used. The emphasis is on determining the Reynolds number-dependence of the estimates. The main result is the introduction of a weighted norm, which leads to optimal asymptotic behavior of the resolvent for large Reynolds numbers.
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| 5. |
- Wellander, Niklas, et al.
(författare)
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Homogenization of the Maxwell Equations at Fixed Frequency
- 2003
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Ingår i: SIAM Journal on Applied Mathematics. - 0036-1399. ; 64:1, s. 170-195
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Tidskriftsartikel (refereegranskat)abstract
- The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calderón operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result on the correctors.
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