The Experts below are selected from a list of 12468 Experts worldwide ranked by ideXlab platform
Junichiro Makino - One of the best experts on this subject based on the ideXlab platform.
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Yet Another Fast Multipole Method without Multipoles-Pseudoparticle Multipole Method
Journal of Computational Physics, 1999Co-Authors: Junichiro MakinoAbstract:In this paper we describe a new approach to implement theO(N) fast Multipole Method andO(NlogN) tree Method, which uses pseudoparticles to express the potential field. The new Method is similar to Anderson's Method, which uses the values of potential at discrete points to represent the potential field. However, for the same expansion order the new Method is more accurate.
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PPSC - A Simple Formulation of the Fast Multipole Method: Pseudo-Particle Multipole Method.
1999Co-Authors: Atsushi Kawai, Junichiro MakinoAbstract:We present the pseudo-particle Multipole Method (PM), a new Method to handle Multipole expansion in fast Multipole Method and treecode. This Method uses a small number of pseudo-particles to express Multipole expansion. With this Method, the implementation of FMM and treecode with high-order Multipole terms is greatly simplified. We applied PM to treecode and combined it with special-purpose computer GRAPE. Extensive tests on the accuracy and calculation cost demonstrate that the new Method is quite attractive.
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A Simple Formulation of the Fast Multipole Method: Pseudo-Particle Multipole Method
arXiv: Astrophysics, 1998Co-Authors: Atsushi Kawai, Junichiro MakinoAbstract:We present the pseudo-particle Multipole Method (P2M2), a new Method to handle Multipole expansion in fast Multipole Method and treecode. This Method uses a small number of pseudo-particles to express Multipole expansion. With this Method, the implementation of FMM and treecode with high-order Multipole terms is greatly simplified. We applied P2M2 to treecode and combined it with special-purpose computer GRAPE. Extensive tests on the accuracy and calculation cost demonstrate that the new Method is quite attractive.
Ross C. Mcphedran - One of the best experts on this subject based on the ideXlab platform.
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Differential Multipole Method for microstructured optical fibers
Journal of the Optical Society of America B, 2004Co-Authors: S Campbell, Ross C. Mcphedran, C. Martijn De Sterke, Lindsay C. BottenAbstract:We describe the differential Multipole Method, an extended Multipole Method used to calculate the modes of microstructured optical fibers with noncircular inclusions. We use a Multipole expansion centered on each inclusion and a differential Method to calculate the scattering properties of the individual inclusions. Representative results for a fiber with one ring of elliptical inclusions are presented, and a direct comparison is made with an existing Method. The new Method is also applied to a microstructured optical fiber with seven rings of elliptical inclusions, which is found, in effect, to support a single polarization of the fundamental mode.
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Multipole Method for microstructured optical fibers. I. Formulation
Journal of the Optical Society of America B, 2002Co-Authors: Thomas P. White, Ross C. Mcphedran, C. Martijn De Sterke, Boris T. Kuhlmey, Daniel Maystre, Gilles Renversez, Lindsay C. BottenAbstract:We describe a Multipole Method for calculating the modes of microstructured optical fibers. The Method uses a Multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the Method and give representative results.
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The Rayleigh Multipole Method for linear elasticity
Journal of the Mechanics and Physics of Solids, 1994Co-Authors: Ross C. Mcphedran, Alexander MovchanAbstract:Abstract A plane-strain elasticity problem is studied by means of an adaptation of the Rayleigh Multipole Method for a domain with a set of circular elastic inclusions. The complex potentials of Kolosov-Muskhelishvili are obtained in the form of Laurent series outside the inclusions. The results of the calculation of the Multipole coefficients have been compared with those obtained by means of an integral approximation for two cases: a pair of identical inclusions and a square array of inclusions.
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Advances in the Rayleigh Multipole Method for Problems in Photonics and Phononics
IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media, 1Co-Authors: Ross C. Mcphedran, Lindsay C. Botten, N. A. Nicorovici, Alexander MovchanAbstract:We review the basis of the Rayleigh Multipole Method for scattering and propagation problems in photonics and phononics. The Method assumes the corresponding problem for a single inclusion has been solved, and generalizes the solution to a periodic array of such inclusions. We discuss the link between the Method and representations of Green’s functions involving lattice sums.
Lindsay C. Botten - One of the best experts on this subject based on the ideXlab platform.
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Differential Multipole Method for microstructured optical fibers
Journal of the Optical Society of America B, 2004Co-Authors: S Campbell, Ross C. Mcphedran, C. Martijn De Sterke, Lindsay C. BottenAbstract:We describe the differential Multipole Method, an extended Multipole Method used to calculate the modes of microstructured optical fibers with noncircular inclusions. We use a Multipole expansion centered on each inclusion and a differential Method to calculate the scattering properties of the individual inclusions. Representative results for a fiber with one ring of elliptical inclusions are presented, and a direct comparison is made with an existing Method. The new Method is also applied to a microstructured optical fiber with seven rings of elliptical inclusions, which is found, in effect, to support a single polarization of the fundamental mode.
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Multipole Method for microstructured optical fibers. I. Formulation
Journal of the Optical Society of America B, 2002Co-Authors: Thomas P. White, Ross C. Mcphedran, C. Martijn De Sterke, Boris T. Kuhlmey, Daniel Maystre, Gilles Renversez, Lindsay C. BottenAbstract:We describe a Multipole Method for calculating the modes of microstructured optical fibers. The Method uses a Multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the Method and give representative results.
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Advances in the Rayleigh Multipole Method for Problems in Photonics and Phononics
IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media, 1Co-Authors: Ross C. Mcphedran, Lindsay C. Botten, N. A. Nicorovici, Alexander MovchanAbstract:We review the basis of the Rayleigh Multipole Method for scattering and propagation problems in photonics and phononics. The Method assumes the corresponding problem for a single inclusion has been solved, and generalizes the solution to a periodic array of such inclusions. We discuss the link between the Method and representations of Green’s functions involving lattice sums.
Kubilay Sertel - One of the best experts on this subject based on the ideXlab platform.
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Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems
IEEE Transactions on Antennas and Propagation, 2007Co-Authors: C. Waltz, Kubilay Sertel, M. A. Carr, B.c. Usner, John L. VolakisAbstract:We describe a massively parallel version of the single-level fast Multipole Method (FMM) that employs the fast Fourier transform (FFT) for the translation stage. The proposed FMM-FFT Method alleviates the communication bottleneck and has a lower complexity, O(N4/3 log2/3 N), as compared to the conventional single level FMM which scales as O(N3/2), where N is the number of unknowns. Through numerical examples we demonstrate that the proposed parallel fast Multipole Method yields a faster solution time than its multilevel counterpart for very large problems in a distributed memory parallel setting.
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Multilevel fast Multipole Method for modeling permeable structures using conformal finite elements.
2003Co-Authors: Kubilay SertelAbstract:MULTILEVEL FAST Multipole Method FOR MODELING PERMEABLE STRUCTURES USING CONFORMAL FINITE ELEMENTS by Kubilay Sertel Chair: John L. Volakis The analysis of penetrable structures has traditionally been carried out using partial differential equation Methods due to the large computation time and memory requirements of integral equation Methods. To reduce this computational bottleneck, this thesis focuses on fast integral equation Methods for modeling penetrable geometries with both dielectric and magnetic material properties. Previous works have employed the multilevel fast Multipole Method for impenetrable targets in the context of flat-triangular geometry approximations. In this thesis, we integrate the multilevel fast Multipole Method with surface and volume integral equation techniques to accurately analyze arbitrarily curved inhomogeneous targets. It is demonstrated that conformal geometry modeling using curvilinear elements achieve higher accuracy at lower sampling rates. Also, the combined use of curvilinear elements and the multilevel fast Multipole Method allows for significantly faster and more efficient numerical Methods. The proposed Method reduces the traditional O(N) computational cost down to O(N log N) and thus practical size geometries can be analyzed. Several example calculations are given in the thesis along with comparisons with partial differential equation Methods. ∇× E(r, t) = − ∂ ∂t B(r, t), ∇×H(r, t) = − ∂ ∂t D(r, t) + J(r, t), ∇ ·B(r, t) = 0, ∇ ·D(r, t) = ρ(r, t). Dedicated to my parents and my brother.
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Multilevel fast Multipole Method implementation using parametric surface modeling
IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction, 2000Co-Authors: Kubilay Sertel, J.l. VolakisAbstract:We present a multilevel fast Multipole Method (FMM) implementation for MoM formulations of electromagnetic scattering problems involving curved targets modeled with curved parametric surface elements. Validations and estimates for the computational complexity of the implementations are provided.
Alexander Movchan - One of the best experts on this subject based on the ideXlab platform.
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The Rayleigh Multipole Method for linear elasticity
Journal of the Mechanics and Physics of Solids, 1994Co-Authors: Ross C. Mcphedran, Alexander MovchanAbstract:Abstract A plane-strain elasticity problem is studied by means of an adaptation of the Rayleigh Multipole Method for a domain with a set of circular elastic inclusions. The complex potentials of Kolosov-Muskhelishvili are obtained in the form of Laurent series outside the inclusions. The results of the calculation of the Multipole coefficients have been compared with those obtained by means of an integral approximation for two cases: a pair of identical inclusions and a square array of inclusions.
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Advances in the Rayleigh Multipole Method for Problems in Photonics and Phononics
IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media, 1Co-Authors: Ross C. Mcphedran, Lindsay C. Botten, N. A. Nicorovici, Alexander MovchanAbstract:We review the basis of the Rayleigh Multipole Method for scattering and propagation problems in photonics and phononics. The Method assumes the corresponding problem for a single inclusion has been solved, and generalizes the solution to a periodic array of such inclusions. We discuss the link between the Method and representations of Green’s functions involving lattice sums.
