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Fast Approximate Algorithms > Nail Gumerov
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Computation of 3D
Scattering from Clusters of Spheres using the Fast Multipole Method
Dr. Nail Gumerov
UMIACS at University of Maryland
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Abstract:
A T-matrix based method of solution of the multiple scattering problem presented
in our previous publication (JASA, 112, 2002, 2688-2701) in practice can be
applied for computation of relatively small size problems (up to hundredes of
scatterers), since the number of operations it requires grows with the number of
scatterers N as O(N^3). In this study we present a method, which combines
iterative techniques with the multilevel fast multipole method which employs
fast translation algorithms. We show that in this case the number of operations
grows with N as O(N) or O(NlogN) and the method is applicable to solution of
problems with large amount of scatterers. We present results of solution of test
problems obtained with the method where N can be substantially large (NĄ10000;
depends on the frequency of the acoustic field). We also discuss convergence of
the iterative techniques, and investigate dependencies of the errors in solution
for different wavenumbers, volume fractions of scatterers, boundary impedances,
and other parameters. While the method was tested for spherical scatterers
generalized consideration that enables extensions for scatterers of arbitrary
shape is presented. [Joint work with Ramani Duraiswami. This study has been
supported by the NSF awards 0086075 and 0219681].
[LECTURE SLIDES]
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