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On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Session Papers 241 Electromagnetic Scattering by Spheroidal Particles
"... Clouds are of paramount importance for the global energy balance and, thereby, our climate. Changes in cloud cover and phase (liquid water versus ice), for example, through increased greenhouse forcing, may have significant and as of yet unknown impacts on our climate. The global climate models (GCM ..."
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Clouds are of paramount importance for the global energy balance and, thereby, our climate. Changes in cloud cover and phase (liquid water versus ice), for example, through increased greenhouse forcing, may have significant and as of yet unknown impacts on our climate. The global climate models (GCMs) designed to predict future climate, usually model the effects of clouds using the scattering and absorption properties of spherical particles at high latitudes as well as at high enough altitudes anywhere on our planet. This leads to errors of undetermined magnitude because the clouds there consist of ice crystals that are far from spherical in shape. Ice particles usually take on needlelike or flat, disklike shapes. The GCMs therefore cannot correctly predict the evolution of our climate. We have developed a new method for calculating the single scattering solution for spheroidal particles. The single scattering solution is needed for every particle shape that we want to include in a GCM. The spheroidal particles can easily be made to closely resemble actual ice particles, and we can hence, more accurately model the scattering and absorption of radiation by polar and high altitude clouds. An important part of the single scattering solution for spheroidal particles is the calculation of the expansion coefficients that we need in the angular and radial spheroidal functions. Problems that hampered previous implementations for finding these coefficients have been overcome, and we can now handle realistic sizes and shapes, as well as particle absorption in an effective manner. In this paper, we present our new method for computation of expansion coefficients.
PROCESS UTILIZING A FORMULATED EIGENFUNCTION EXPANSION OF SPHEROIDAL WAVEHARMONICS
, 2000
"... In the field of antenna design and analysis, often the need arises to numerically extrapolate the farzone performance of a radiating structure from its known (or assumed known) nearzone electromagnetic field. Mathematical processes developed to accomplish such a task are known in the literature as ..."
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In the field of antenna design and analysis, often the need arises to numerically extrapolate the farzone performance of a radiating structure from its known (or assumed known) nearzone electromagnetic field. Mathematical processes developed to accomplish such a task are known in the literature as nearzone to farzone transformations (NZFZTs) as well as nearfield farfield (NFFF) transformations. These processes make use of sampled nearzone field quantities along some virtual surface, viz., the transformation surface, that surrounds the radiating structure of interest. Depending upon the application, samples of the required nearzone field quantities are supplied via analytical, empirical, or computational means. Over the years, a number of NZFZT processes have been developed to meet the demands of many applications. In short, their differences include, but are not limited to, the following: (1) the size and shape of the transformation surface, (2) the required nearzone field quantities and how they are sampled, (3) the computational methodology used, and (4) the imbedding of various applicationdriven features. Each process has its pros and cons depending upon its specific application as well as the type of radiation structure
Oblate Spheroidal Radial Functions of the First and Second Kind and Their First Derivatives
, 1970
"... UJ MAY io tsn EISEITO'E c This document has been approved for public release and sale; iu distribution is unlimited. Roproducod by NATIONAL TECHNICAL ..."
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UJ MAY io tsn EISEITO'E c This document has been approved for public release and sale; iu distribution is unlimited. Roproducod by NATIONAL TECHNICAL