Fast algorithms and imaging in strongly-scattering media
- In recent years, wave propagation in heterogeneous media has given rise to much academic interest. Indeed, both theory and experiments have demonstrated the vast array of physical phenomena, and the technical potential offered by such media. Examples include sub-wavelength imaging, filtering and beam shaping as well as cloaking. Computational results on the other hand are scarcer. The reason for this lies in the high computational cost associated with the solution of such problems. In the present dissertation, I developed an efficient algorithm allowing for the computational study and understanding of acoustic wave phenomena in highly heterogeneous media beyond the scope of current tools. This is done through the introduction of a new hybrid fast algorithm based on the Fast Multipole Method (FMM) and related ideas. I also use this new tool in order to investigate a phenomenon known as super-resolution, where energy is focused beyond the diffraction limit through time-reversal by adding small scatterers in the vicinity of a point source. I validated the concept through numerical experiments, and put forward some theoretical explanations based on the theory of homogenization for hyperbolic systems. In the final chapters of the dissertation, the reader will find a description of fast algorithms from a more general perspective through the introduction of a general black-box fast algorithm. The method is based on expansions of integral kernels through short exponential sums. Two schemes leading to such expansions are presented: one based on the Cauchy integral formula for analytic kernels, and the other based on a novel kind of quadrature called approximate Gaussian quadratures.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Institute for Computational and Mathematical Engineering.
|Statement of responsibility
|Submitted to the Institute for Computational and Mathematical Engineering.
|Thesis (Ph.D.)--Stanford University, 2013.
- © 2013 by Pierre-David Letourneau
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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