Fourier Based Fast Multipole Method for the Helmholtz Equation

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Abstract:

The multilevel fast multipole method MLFMM is an algorithm that has had great success in reducing the computational time required to find the solution to the Galerkin boundary integral form of the Helmholtz equation. We present a new formulation of the MLFMM using Fourier basis functions rather than spherical harmonics in order to accelerate and simplify the time-critical stages of the algorithm. With modifications to the transfer function in the precomputation stage of the MLFMM, the interpolation and anterpolation algorithms become straightforward applications of FFT interpolations only. Using spectral methods, constructive algorithms are derived to determine a near-optimal quadrature for a given level in the algorithm and an a-priori estimate of the integration error.

Author(s):
Cecka, C. ; Darve, E.
Author Organization(s):
STANFORD UNIV CA
Descriptive Note:
Conference paper
Supplementary Note:
See also ADM002187. Presented at the Army Science Conference (26th) held in Orlando, Florida on 1-4 December 2008. Published in the Proceedings of the Army Science Conference (26th), December 2008. The original document contains color images.
Pagination:
0009

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR
Identifying Numbers
Monitor Series:
AHPCRC
 Subject Terms
Joint Capability Areas:
JCA_1.4.2_Health Service Delivery; JCA_1.4_Force Support; JCA_6_Net Centric; JCA_5_Command and Control; JCA_1_Force Support; JCA_5.3_Planning; JCA_6.1_Information Transport; JCA_8_Building Partnerships
Modernization Areas:
Quantum Science and Computing
Communities of Interest:
No COI(s) Identified
Descriptor(s):
*INTERPOLATION, *ALGORITHMS, *FAST FOURIER TRANSFORMS, SPHERICAL HARMONICS, GALERKIN METHOD, MULTIPOLARITY, HELMHOLTZ EQUATIONS, ACCELERATION, COMPUTATIONS, SYMPOSIA, ERRORS
Field(s)/Group(s):
Numerical Mathematics
Keyword(s):
MLFMM(MULTILEVEL FAST MULTIPOLE METHOD)
Report Date:
2008 Dec 01
Creation Date:
2009 Sep 30