University of Twente Student Theses


Spherical harmonics based aggregation in the multilevel fast multipole algorithm MSc Thesis

Hack, S.A. (2015) Spherical harmonics based aggregation in the multilevel fast multipole algorithm MSc Thesis.

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Abstract:Electromagnetic scattering problems such as radar-cross section computations are commonly formulated as boundary integral equations. Discretization using the boundary element method results in a dense system, which is solved using a Krylov subspace method. For realistic radar frequencies, the system matrix is too large even to be stored in the computer’s memory. In the multilevel fast multipole algorithm (MLFMA), the matrix-vector products in the Krylov subspace iterations are computed with complexity O(NlogN), rather than in O(N2) for dense matrix-vector multiplication, where N is the number of unknowns. We present a variant of the MLFMA where the far field radiation patterns are represented in spherical harmonics during aggregation. This allows a reduction in the sample rate by a factor of up to eight. An innovation is the use the real spherical harmonics, which results in CPU time savings. At the levels with large clusters, we intend to switch to Lagrange interpolation because it can be parallellized over the clusters. The preliminary test results indicate that the accuracy is similar to the customary Lagrange interpolation, and that the CPU times are reduced significantly at least at the levels with small clusters.
Item Type:Essay (Master)
National Aerospace Laboratory, Amsterdam, The Netherlands
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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