### ASA 126th Meeting Denver 1993 October 4-8

## 2aUW3. A sparse boundary-element method for scattering from a rigid body
of revolution.

**Erik M. Rosen
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*SFA, Inc., 1401 McCormick Dr., Landover, MD 20785
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**Luise S. Couchman
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*Naval Res. Lab., Washington, DC 20375
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**Francis X. Canning
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*Rockwell Sci. Ctr., Thousand Oaks, CA 91360
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A sparse boundary-element method is used to calculate the scattered
acoustic field of a rigid body of revolution. The NxN full matrix resulting
from the discretization of the Helmholtz integral is transformed to a sparse
NxN matrix using the impedance matrix localization (IML) method. When applied
to integral equations for wave phenomena, the IML method produces a sparse
matrix by partitioning the scatterer into several regions, over which the
response is represented by basis functions with directional radiation patterns.
The number of important physical interactions is reduced to a small number over
each region, leaving a large number of matrix elements with relative magnitudes
less than 10[sup -4] which can be approximated by zero. Used in conjunction
with existing BEM codes, the IML method reduces the memory and storage
requirements from N[sup 2] to approximately 100N, while the solution time is
O(N) compared to O(N[sup 3]) for the full untransformed case. The resulting
sparse matrix can be approximately inverted leading to a convergent solution in
less than five iterations. Results are given for scattering from a
hemispherically endcapped cylinder of L/a=110 for ka=1 to ka=17.