A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles

Ong, Ee Ping; Lim, Kian Meng; Lee, K. H.; Lee, H. P.

doi:10.1016/j.jcp.2003.07.004

Cited by 34 publications

(34 citation statements)

References 24 publications

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“…Given such a regular grid, they are much faster then FMM based schemes, but require more memory resources [26]. The fast Fourier transform on multipoles (FFTM) technique [27] developed by Ong et al is a combination of the FMM and FFT method. It still needs a regular grid, but shows more flexibility -adaptive discretizationcompared to a pure FFT scheme.…”

Section: Micromagnetic Hysteresis Modelmentioning

confidence: 99%

Energy considerations in a micromagnetic hysteresis model and the Preisach model

Wiele

Vandenbossche

Dupré

et al. 2010

Journal of Applied Physics

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Finding the relations between the microstructural material parameters and the macroscopic hysteresis behavior is indispensable in the design of ferromagnetic materials with minimal (hysteresis) losses. Micromagnetic hysteresis simulations enable a rigorous and structured investigation of these relations since in the numerical model each material parameter can be altered independently. This paper describes a procedure to extract the Preisach distribution function, quantifying the macroscopic hysteresis properties, from micromagnetic simulations incorporating the materials' microstructure. Furthermore, the instantaneously added, stored and dissipated energy while running through the hysteresis loop as described in the macroscopic Preisach model and in the micromagnetic hysteresis model are compared, evidencing a very good agreement. Moreover, using the micromagnetic model, the energy rearrangements between the different micromagnetic interaction terms is studied at each time point of the hysteresis loop. It is concluded that the micromagnetic hysteresis model is a valuable tool in the study of hysteresis properties and loss mechanisms in ferromagnetic materials.

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Section: Micromagnetic Hysteresis Modelmentioning

confidence: 99%

Energy considerations in a micromagnetic hysteresis model and the Preisach model

Wiele

Vandenbossche

Dupré

et al. 2010

Journal of Applied Physics

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“…The FFTM has been developed for solving the Laplace equation with Dirichlet boundary conditions [12][13][14]. It is used to accelerate the matrix-vector multiplication in the inner loops of GMRES, reducing the operations from O(N 2 ) to O(N log N ).…”

Section: Indirect Formulationmentioning

confidence: 99%

“…Recently, an alternative fast algorithm that combines the FFT and multipoles, the fast Fourier transform on multipole (FFTM) [12][13][14], was proposed. It performs the potential evaluation rapidly by combining the use of multipole expansions and FFT.…”

Section: Introductionmentioning

confidence: 99%

Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method

Lim

2007

Comput Mech

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In this paper, the fast Fourier transform on multipole (FFTM) algorithm is used to accelerate the matrixvector product in the boundary element method (BEM) for solving Laplace equation. This is implemented in both the direct and indirect formulations of the BEM. A new formulation for handling the double layer kernel using the direct formulation is presented, and this is shown to be related to the method given by Yoshida (Application of fast multipole method to boundary integral equation method, Kyoto University, Japan, 2001). The FFTM algorithm shows different computational performances in direct and indirect formulations. The direct formulation tends to take more computational time due to the evaluation of an extra integral. The error of FFTM in the direct formulation is smaller than that in the indirect formulation because the direct formulation has the advantage of avoiding the calculations of the free term and the strongly singular integral explicitly. The multipole and local translations introduce approximation errors, but these are not significant compared with the discretization error in the direct or indirect BEM formulation. Several numerical examples are presented to compare the computational efficiency of the FFTM algorithm used with the direct and indirect BEM formulations.

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“…There is also a multitude of alternative methods for representing electrostatic interactions. Examples are methods based on a cut-off [17][18][19], tree and multipole based methods [20][21][22][23][24][25], multigrid methods [26][27][28], reaction field methods [29][30][31], the particle mesh method [32,33] and the isotropic sum method [34].…”

Section: Introductionmentioning

confidence: 99%

Non-Uniform FFT and Its Applications in Particle Simulations

Wang¹,

Hedman²,

Porcu³

et al. 2014

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A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles

Cited by 34 publications

References 24 publications

Energy considerations in a micromagnetic hysteresis model and the Preisach model

Energy considerations in a micromagnetic hysteresis model and the Preisach model

Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method

Non-Uniform FFT and Its Applications in Particle Simulations

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