The Design and Implementation of FFTW3

Frigo, Matteo; Johnson, Steven G.

doi:10.1109/jproc.2004.840301

Cited by 4,085 publications

(2,510 citation statements)

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“…We tried different 3D FFT subprograms and our final choice was a FFT routine provided by the FFTW library. 59,60 All computations were performed on the shared-memory system IBM eServer pSeries 690 Regatta based on 64-bit IBM Power4 (1.1 GHz) processors running IBM AIX OS. Solving Poisson's equation to double precision on a single processor required 0.0049 s, 0.043 s, and 0.58 s for 32 3 , 64 3 and 128 3 grids, correspondingly.…”

Section: Appendix 2 Three-dimensional Poisson Solvermentioning

confidence: 99%

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Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

Nikolaev

Heeren

Popov

et al. 2007

Rapid Comm Mass Spectrometry

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Using a 'Particle-In-Cell' approach taken from plasma physics we have developed a new threedimensional (3D) parallel computer code that today yields the highest possible accuracy of ion trajectory calculations in electromagnetic fields. This approach incorporates coulombic ion-ion and ion-image charge interactions into the calculation. The accuracy is achieved through the implementation of an improved algorithm (the so-called Boris algorithm) that mathematically eliminates cyclotron motion in a magnetic field from digital equations for ion motion dynamics. It facilitates the calculation of the cyclotron motion without numerical errors. At every time-step in the simulation the electric potential inside the cell is calculated by direct solution of Poisson's equation. Calculations are performed on a computational grid with up to 128 T 128 T 128 nodes using a fast Fourier transform algorithm. The ion populations in these simulations ranged from 1000 up to 1 000 000 ions. A maximum of 3 000 000 time-steps were employed in the ion trajectory calculations. This corresponds to an experimental detection time-scale of seconds. In addition to the ion trajectories integral time-domain signals and mass spectra were calculated. The phenomena observed include phase locking of particular m/z ions (high-resolution regime) inside larger ion clouds. A focus was placed on behavior of a cloud of ions of a single m/z value to understand the nature of Fourier transform ion cyclotron resonance (FTICR) resolution and mass accuracy in selected ion mode detection. The behavior of two and three ion clouds of different but close m/z was investigated as well. Peak coalescence effects were observed in both cases. Very complicated ion cloud dynamics in the case of three ion clouds was demonstrated. It was found that magnetic field does not influence phase locking for a cloud of ions of a single m/z. The ion cloud evolution time-scale is inversely proportional to magnetic field. The number of ions needed for peak coalescence depends quadratically on the magnetic field. Copyright # 2007 John Wiley & Sons, Ltd.The leading role Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) plays in biological mass spectrometry is directly related to its unsurpassed resolution and mass accuracy combined with the possibility of utilizing all known ionization and fragmentation methods. Further improvement of mass accuracy will be greatly facilitated by a more detailed understanding of the motion of ions during ion introduction into the FTICR cell, excitation of their cyclotron motion, fragmentation and detection of induced signal. Starting from the early days of FTICR-MS the theory of ion motion in the ICR cell was an important research topic in this field. The dynamics of single particles inside the FTICR trap was analyzed by many groups in both the FTICR and physics communities. [1][2][3][4][5][6][7][8] The FTICR community has been interested mainly in obtaining a calibration formula, which connects measured frequency with ion mass. 9 The e...

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Section: Appendix 2 Three-dimensional Poisson Solvermentioning

confidence: 99%

“…We prefer an open-source library named FFTW being developed by Frigo and Johnson. 59,60 FFTW employs O(NlogN) algorithms for all sizes, including prime numbers. The current version, FFTW 3.1.2, includes parallel (multi-threaded) transforms for shared-memory systems (including OpenMP parallelism 61 ).…”

Section: Efficiency Of the Numerical Solutionmentioning

confidence: 99%

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

Nikolaev

Heeren

Popov

et al. 2007

Rapid Comm Mass Spectrometry

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“…The operators B and D (ov) are thus both block-diagonal, the first in position space and the latter in momentum space. In our approach we use a Fast Fourier Transform (FFT) [28] to switch between the position and momentum representations, such that all operator applications can be trivially performed due to their actual block-diagonal structure. This is particularly advantageous for the overlap operator, since the usual construction of this operator would be based on very demanding approximations, e.g.…”

Section: Jhep10(2007)001mentioning

confidence: 99%

The phase structure of a chirally invariant lattice Higgs-Yukawa model—numerical simulations

Gerhold

Jansen²

2007

J. High Energy Phys.

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Abstract:The phase diagram of a chirally invariant lattice Higgs-Yukawa model is explored by means of numerical simulations. The results revealing a rich phase structure are compared to analytical large N f calculations which we performed earlier. The analytical and numerical results are in excellent agreement at large values of N f . In the opposite case the large N f computation still gives a good qualitative description of the phase diagram. In particular we find numerical evidence for the predicted ferrimagnetic phase at intermediate values of the Yukawa coupling constant and for the symmetric phase at strong Yukawa couplings. Emphasis is put on the finite size effects which can hide the existence of the latter symmetric phase.

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“…2. To calculate the direct and inverse Fourier transforms we are using Python wrapper for FFTW3 library [23,24]. User can specify output frequency band, in this case all coefficients, corresponding to frequencies lower than user-selected lower bound are filled with zeroes, frequencies higher than upper-bound are truncated.…”

Section: Inverse Problem Solutionmentioning

confidence: 99%

Метода анализа данных магнитной энцефалографии в облачном сервисе MathBrain

Рыкунов¹

2017

Math.Biol.Bioinf.

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Abstract. MathBrain is a cloud-based application, distributed under Software as a Service model. This application provides access to several algorithms of the multichannel encephalography data analysis. Spectral methods include direct and inverse Fourier transforms and quantitative analysis. Statistical methods involve principal component analysis and independent component analysis. The field maps of elementary components can be used to solve the magnetic encephalography inverse problem and to display the result at the magnetic resonance image. The application is designed to be used in human brain studies without mathematical training.

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The Design and Implementation of FFTW3

Abstract: FFTW is an implementation of the discrete

Cited by 4,085 publications

References 58 publications

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle‐in‐cell approach

The phase structure of a chirally invariant lattice Higgs-Yukawa model—numerical simulations

Метода анализа данных магнитной энцефалографии в облачном сервисе MathBrain

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