Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering
Microwave and Optical Technology LettersPublished 1 September 1995
Jiming Song, Weng Cho Chew
Citations857
SJR quartileQ3
SJR score0.31
SNIP0.53
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The fast multipole method has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE).
Abstract
Abstract The fast multipole method (FMM) has been implemented to speed up the matrix‐vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N 2 ) to O(N 1.5 ). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592‐unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.
Keywords
EngineeringPhysics and Astronomy
American Journal of PhysicsHandbook of Mathematical Functions
40,436 Citations1966Donald A. McQuarrie
NatureA hierarchical O(N log N) force-calculation algorithm
3,685 Citations1986Josh Barnes, Piet Hut
A novel method of directly calculating the force on N bodies that grows only as N log N is described, using a tree-structured hierarchical subdivision of space into cubic cells, each is recursively divided into eight subcells whenever more than one particle is found to occupy the same cell.
IEEE Antennas and Propagation MagazineThe fast multipole method for the wave equation: a pedestrian prescription
1,474 Citations1993Ronald R. Coifman, Vladimir Rokhlin +1 more
The FMM provides an efficient mechanism for the numerical convolution of the Green's function for the Helmholtz equation with a source distribution and can be used to radically accelerate the iterative solution of boundary-integral equations.
Journal of Computational PhysicsRapid solution of integral equations of scattering theory in two dimensions
825 Citations1990Vladimir Rokhlin
An algorithm for rapid solution of boundary value problems for the Helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory is described.
Microwave and Optical Technology LettersA multilevel algorithm for solving a boundary integral equation of wave scattering
306 Citations1994Cai‐Cheng Lu, Weng Cho Chew
A multilevel algorithm is applied to the solution of an integral equation using the conjugate gradient method and shows that the complexity of a matrix-vector multiplication is proportional to N (log(N))2.
The Astrophysical Journal Supplement SeriesPerformance characteristics of tree codes
254 Citations1987Lars Hernquist
Computer Physics CommunicationsMultilevel computations of integral transforms and particle interactions with oscillatory kernels
232 Citations1991Achi Brandt
Algorithms for performing dense-matrix multiplication for n×n matrices representing the interaction of n particles or the discretization of integral transforms on n gridpoints are described.
Microwave and Optical Technology LettersFast multipole method solution using parametric geometry
117 Citations1994Jiming Song, W. C. Chew
The fast multipole method is used to solve the electromagnetic scattering from three-dimensional conducting bodies of arbitrary shape by discretizing the electric field integral equation by the method of moments.
Microwave and Optical Technology LettersA ray‐propagation fast multipole algorithm
95 Citations1994Robert Wagner, Weng Cho Chew
A nonnested, ray-propagation approach is used to compute a matrix-vector multiply in O(N4/3) operations, where N is the number of unknowns in the discretized integral equation.
Journal of Electromagnetic Waves and ApplicationsMoment method solutions using parametric geometry
66 Citations1995Jiming Song, Weng Cho Chew
A technique for computing the electromagnetic radiation and scattering from three-dimensional conducting bodies of general shape is presented and the electric field integral equation (EFIE) is discretized by the standard method of moments with specially designed basis functions for subdomains which now contain surface curvature.
IEEE Transactions on Antennas and PropagationScattering from the perfectly conducting cube
40 Citations1988Marc G. Cote, Margaret B. Woodworth +1 more
IEE Proceedings C Generation Transmission and DistributionModelling multiple injection bus in power system state estimation
39 Citations1993Chongxia Lu, Rong‐Ceng Leou +2 more
Journal of the Optical Society of America AMultiwavelength three-dimensional scattering with dual-surface integral equations
27 Citations1994Margaret B. Woodworth, Arthur D. Yaghjian