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- Gustafsson, Mats, et al.
(author)
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An optimization approach to multi-dimensional time domain acoustic inverse problems
- 1997
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Reports (other academic/artistic)abstract
- An optimization approach to a multi-dimensional acoustic inverse problem in the time domain is considered. The density and/or the velocity are reconstructed by minimizing an objective functional. By introducing dual functions and using the Gauss divergence theorem, the gradient of the objective functional is found as an explicit expression. The parameters are then reconstructed by an iterative algorithm (the conjugate gradient method). The reconstruction algorithm is tested with noisy data, and these tests indicate that the algorithm is stable and robust. The computation time for the reconstruction is greatly improved when the analytic gradient is used.
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| 8. |
- Gustafsson, Mats
(author)
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The Bremmer series for a multi-dimensional acoustic scattering problem
- 1999
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Reports (other academic/artistic)abstract
- The Bremmer series is used to reduce a complex scattering problem to a sequence of simpler single scattering problems. In the Bremmer series, the wave equation is first decomposed into a coupled system of one-way wave equations. The system is then decoupled into a sequence of one-way wave equations with a fixed point iteration. In this paper, a left symbol representation of the decomposition operator and the vertical-propagation operator are used. Time-domain convergence of the Bremmer series is shown for a set of dispersive medium models. The non-dispersive case is treated with an approximation procedure.
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| 9. |
- Gustafsson, Mats
(author)
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Time domain theory of the macroscopic Maxwell equations
- 1997
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Reports (other academic/artistic)abstract
- A time domain description of linear macroscopic electromagnetic phenomena is considered. We show that it is always possible to model the constitutive relations with a symmetric, positive definite optical response together with a convolution integral. An initial-boundary value problem is formulated for the macroscopic Maxwell equations together with a reflection operator modeling the exterior region. It is shown that the initial-boundary value problem is well-posed. Dissipation and finite speed of propagation is also considered.
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