Analysis of numerical integration error for Bessel integral identity in fast multipole method for 2D Helmholtz equation

2010 ◽  
Vol 15 (6) ◽  
pp. 690-693 ◽  
Author(s):  
Hai-jun Wu ◽  
Wei-kang Jiang ◽  
Yi-jun Liu
Keyword(s):  
Helmholtz Equation ◽  
Numerical Integration ◽  
Integral Identity ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Integration Error ◽  
Multipole Method ◽  
Numerical Integration Error

A wideband fast multipole method for the Helmholtz equation in three dimensions

2006 ◽  
Vol 216 (1) ◽  
pp. 300-325 ◽  
Author(s):  
Hongwei Cheng ◽  
William Y. Crutchfield ◽  
Zydrunas Gimbutas ◽  
Leslie F. Greengard ◽  
J. Frank Ethridge ◽  
...  
Keyword(s):  
Helmholtz Equation ◽  
Fast Multipole Method ◽  
Three Dimensions ◽  
Fast Multipole ◽  
Multipole Method

A PARALLEL FAST MULTIPOLE METHOD FOR THE HELMHOLTZ EQUATION

1995 ◽  
Vol 05 (02) ◽  
pp. 263-274 ◽  
Author(s):  
MARK A. STALZER
Keyword(s):  
Helmholtz Equation ◽  
Parallel Algorithm ◽  
Fast Multipole Method ◽  
Iterative Solvers ◽  
Dense Matrix ◽  
Vector Product ◽  
Fast Multipole ◽  
Multipole Method ◽  
The Matrix ◽  
Matrix Vector

Presented is a parallel algorithm based on the fast multipole method (FMM) for the Helmholtz equation. This variant of the FMM is useful for computing radar cross sections and antenna radiation patterns. The FMM decomposes the impedance matrix into sparse components, reducing the operation count of the matrix-vector multiplication in iterative solvers to O(N3/2) (where N is the number of unknowns). The parallel algorithm divides the problem into groups and assigns the computation involved with each group to a processor node. Careful consideration is given to the communications costs. A time complexity analysis of the algorithm is presented and compared with empirical results from a Paragon XP/S running the lightweight Sandia/University of New Mexico operating system (SUNMOS). For a 90,000 unknown problem running on 60 nodes, the sparse representation fits in memory and the algorithm computes the matrix-vector product in 1.26 seconds. It sustains an aggregate rate of 1.4 Gflop/s. The corresponding dense matrix would occupy over 100 Gbytes and, assuming that I/O is free, would require on the order of 50 seconds to form the matrix-vector product.

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