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A multilevel algorithm for solving a boundary integral equation of wave scattering
Author(s) -
Lu CaiCheng,
Chew Weng Cho
Publication year - 1994
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.4650071013
Subject(s) - multipole expansion , conjugate gradient method , multiplication (music) , integral equation , matrix (chemical analysis) , fast multipole method , mathematics , boundary (topology) , algorithm , mathematical analysis , physics , combinatorics , quantum mechanics , materials science , composite material
In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix‐vector multiplication, requiring O(N 2 ) floating‐point operations. The fast multipole method (FMM) reduced the operation to O(N 15 ). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix‐vector multiplication is proportional to N (log(N)) 2 . © 1994 John Wiley & Sons, Inc.