Browsing by Author "Adams, Robert John"

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    A Class of Robust and Efficient Iterative Methods for Wave Scattering Problems
    Adams, Robert John (Virginia Tech, 1998-12-17)
    Significant effort has recently been directed towards the development of numerically efficient iterative techniques for the solution of boundary integral equation formulations of time harmonic scattering problems. The primary result of this effort has been the development of several advanced numerical techniques which enable the dense matrix-vector products associated with the iterative solution of boundary integral equations to be rapidly computed. However, an important aspect of this problem which has yet to be adequately addressed is the development of rapidly convergent iterative techniques to complement the relatively more mature numerical algorithms which expedite the matrix-vector product operation. To this end, a class of efficient iterative methods for boundary integral equation formulations of two-dimensional scattering problems is presented. This development is based on an attempt to approximately factor (i.e., renormalize) the boundary integral formulation of an arbitrary scattering problem into a product of one-way wave operators and a corresponding coupling operator which accounts for the interactions between oppositely propagating waves on the surface of the scatterer. The original boundary integral formulation of the scattering problem defines the coupling between individual equivalent sources on the surface of the scatterer. The renormalized version of this equation defines the coupling between the forward and backward propagating fields obtained by re-summing the individual equivalent sources present in the original boundary integral formulation of the scattering problem. An important feature of this class of rapidly convergent iterative techniques is that they are based on an attempt to incorporate the important physical aspects of the scattering problem into the iterative procedure. This leads to rapidly convergent iterative series for a number of two-dimensional scattering problems. The iterative series obtained using this renormalization procedure are much more rapidly convergent than the series obtained using Krylov subspace techniques. In fact, for several of the geometries considered the number of iterations required to achieve a specified residual error is independent of the size of the scatterer. This desirable property of the iterative methods presented here is not shared by other iterative schemes for wave scattering problems. Moreover, because the approach used to develop these iterative series depends only on the assumption that the total field can be approximately represented by a summation of independent and oppositely directed waves (and not on the presence of special geometries, etc.), the proposed iterative methods are very general and are thus applicable to a large number of complex scattering problems.
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    Incoherent short pulse scattering from penetrable geophysical media
    Adams, Robert John (Virginia Tech, 1995-04-11)
    A new model for incoherent short pulse scattering from penetrable geophysical media is developed. The model is obtained by assuming that the surface and volume scattered components of the total scattered waveform only minimally interact. A well-known form is used for the surface scattered component of the backscattered waveform while a new form is derived for the volume scattered component of the total scattered waveform. The new volume scattered waveform model is derived from the scalar equation of transfer. This development illustrates the inherent assumptions of the new model as well as previous models. This leads to a reconciliation of parameter estimates obtained using short pulse scattering models and those obtained using other techniques. In addition, the new model represents a generalization of previous volume scattered waveform models in that it incorporates the effects on the average scattered waveform due to surface roughness and layering in the electromagnetic properties of the scattering medium. Previous models are shown to be slightly incorrect special cases of the new model. Finally, the volume scattered waveform model developed herein is demonstrated to be numerically efficient in general, providing a time savings factor of up to 500 relative to a previous model. The scattered waveform model is subsequently used to analyze scattering data obtained over the Greenland ice sheet by the University of Massachusetts at Amherst's 13.5 GHz Advanced Aircraft Flight Experiment (AAFE) altimeter and NASA's 36 GHz Multimode Aircraft Radar Altimeter (MARA). These altimeters operated simultaneously from the same P-3 aircraft platform in September of 1991 and thus provide a dual frequency look at the scattering properties of the ice sheet. In addition, the large section of the ice sheet from which the scattering data is obtained provides an opportunity to evaluate the radar altimeter's ability to distinguish between the various regions of the ice sheet. The results of this analysis suggest that the altimeter provides a useful means for monitoring both short and long term variations in the near surface region of the ice sheet while simultaneously providing precise estimates of the ice sheet elevation.