Efficient spherical harmonic transforms on GPU and its use in planetary core dynamics simulations

2021 ◽  
Author(s):  
Nathanael Schaeffer
Keyword(s):  
Fourier Transform ◽  
Spherical Harmonic ◽  
High Performance ◽  
Peak Performance ◽  
Legendre Transform ◽  
Core Dynamics ◽  
Program Flow ◽  
Nvidia Gpu ◽  
The Fourier Transform ◽  
Dynamics Simulations

<p>Most of the new supercomputers now use acceleration technology such as GPUs. They promise much higher performance than traditional CPU-only servers, both in terms of floating point operation throughput and memory bandwidth. Furthermore, the electric consumption is significantly reduced, resulting in lower carbon emissions.<br>However, such high computation speeds can only be achieved if a set of more or less stringent rules are followed with respect to memory access and program flow. As a consequence some algorithms more easily approach peak performance.</p><p>Here, we present the results of an effort to achieve high performance on recent nvidia GPU accelerators for the spherical harmonic transform. The spherical harmonic transform can be split into a Legendre transform (which is compute bound) and a Fourier transform (which is memory bound).<br>By taking advantage of recent algorithmic improvements as well as by tuning the Fourier transform, the can now compute a full forward or backward spherical harmonic transform up to degree 8191 on a single 16GB Volta GPU in less than 0.35 seconds.<br>For lower resolution (up to degree 1023), a single Volta GPU performs a full transform more than 3 times faster than a 48-cores dual socket Skylake Xeon Platinum server.</p><p>We also present results of an ongoing effort to port the (simulation of planetary core fluid and magnetic field dynamics) to GPU-accelerated computers.</p>

The Utilization of Ftir (Fourier Transform Infra-Red) Method Combined with Chemometrics For Authentication of Indonesian Coffee Powder

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Firmansyah A. ◽  
Winingsih W. ◽  
Soebara Y S
Keyword(s):  
Fourier Transform ◽  
Natural Product ◽  
High Performance ◽  
Principal Component ◽  
Raw Material ◽  
Attenuated Total Reflectance ◽  
Coffee Bean ◽  
Product Analysis ◽  
Total Reflectance ◽  
And Cluster Analysis

Analysis of natural product remain challenging issues for analytical chemist, since natural products are complicated system of mixture. The most popular methods of choice used for quality control of raw material and finished product are high performance liquid chromatography (HPLC), gas chromatography (GC) and mass spectrometry (MS). The utilization of FTIR-ATR (Fourier Transform Infrared-Attenuated Total Reflectance) method in natural product analysis is still limited. This study attempts to expand the use of FTIR spectroscopy in authenticating Indonesian coffee powder.The coffee samples studied were taken from nine regions in Indonesia, namely Aceh Gayo, Flores, Kintamani, Mandheling, Papua, Sidikalang, Toraja, Kerinci and Lampung.The samples in the form of coffee bean from various regions were powdered . The next step conducted was to determine the spectrum using the FTIR-ATR (Attenuated Total Reflectance) using ZnSe crystal of 8000 resolution. Spectrum samples, then, were analyzed using chemometrics. The utilized chemometric model was the principal component analysis (PCA) and cluster analysis (CA). Based on the chemometric analysis, there are similarities between Aceh Gayo coffee with Toraja coffee, Mandailing coffee, Kintamani coffee and Flores coffee. Sidikalang coffee has a similarity to Flores coffee; Papua coffee has a similarity to Sidikalang coffee; Lampung coffee has a similarity to Sidikalang coffee, while Kerinci coffee has a similarity to Papua coffee.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

scholarly journals Convolutors on $${\mathcal S}_{\omega }({\mathbb R}^N)$$

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Angela A. Albanese ◽  
Claudio Mele
Keyword(s):  
Fourier Transform ◽  
Dual Space ◽  
Strong Operator ◽  
Dual Spaces ◽  
Structure Theorems ◽  
The Fourier Transform ◽  
Decreasing Functions

AbstractIn this paper we continue the study of the spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) and $${\mathcal O}_{C,\omega }({\mathbb R}^N)$$ O C , ω ( R N ) undertaken in Albanese and Mele (J Pseudo-Differ Oper Appl, 2021). We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) is the space of convolutors of the space $${\mathcal S}_\omega ({\mathbb R}^N)$$ S ω ( R N ) of the $$\omega $$ ω -ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $${\mathcal S}'_\omega ({\mathbb R}^N)$$ S ω ′ ( R N ) . We also establish that the Fourier transform is an isomorphism from $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) onto $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) . In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $${\mathcal L}_b({\mathcal S}_\omega ({\mathbb R}^N))$$ L b ( S ω ( R N ) ) and the last space is endowed with its natural lc-topology.

scholarly journals Heisenberg–Weyl Groups and Generalized Hermite Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1060
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano A. del del Olmo
Keyword(s):  
Hilbert Space ◽  
Fourier Transform ◽  
Heisenberg Group ◽  
Real Line ◽  
Hermite Functions ◽  
Unitary Representations ◽  
Weyl Groups ◽  
The Real ◽  
Symmetry Properties ◽  
The Fourier Transform

We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is, in some sense, shared by these “generalized Hermite functions”. The construction of these new bases is grounded on some symmetry properties of the real line under translations, dilations and reflexions as well as certain properties of the Fourier transform. We show how these generalized Hermite functions are transformed under the unitary representations of a series of groups, including the Weyl–Heisenberg group and some of their extensions.

scholarly journals Variety Identification of Orchids Using Fourier Transform Infrared Spectroscopy Combined with Stacked Sparse Auto-Encoder

Molecules ◽  
2019 ◽  
Vol 24 (13) ◽  
pp. 2506 ◽  
Author(s):  
Yunfeng Chen ◽  
Yue Chen ◽  
Xuping Feng ◽  
Xufeng Yang ◽  
Jinnuo Zhang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Principal Component ◽  
Fourier Transform Infrared ◽  
Spectroscopic Technique ◽  
Variety Identification ◽  
Support Vector ◽  
K Nearest Neighbors ◽  
Discriminant Models ◽  
The Fourier Transform ◽  
Better Than

The feasibility of using the fourier transform infrared (FTIR) spectroscopic technique with a stacked sparse auto-encoder (SSAE) to identify orchid varieties was studied. Spectral data of 13 orchids varieties covering the spectral range of 4000–550 cm−1 were acquired to establish discriminant models and to select optimal spectral variables. K nearest neighbors (KNN), support vector machine (SVM), and SSAE models were built using full spectra. The SSAE model performed better than the KNN and SVM models and obtained a classification accuracy 99.4% in the calibration set and 97.9% in the prediction set. Then, three algorithms, principal component analysis loading (PCA-loading), competitive adaptive reweighted sampling (CARS), and stacked sparse auto-encoder guided backward (SSAE-GB), were used to select 39, 300, and 38 optimal wavenumbers, respectively. The KNN and SVM models were built based on optimal wavenumbers. Most of the optimal wavenumbers-based models performed slightly better than the all wavenumbers-based models. The performance of the SSAE-GB was better than the other two from the perspective of the accuracy of the discriminant models and the number of optimal wavenumbers. The results of this study showed that the FTIR spectroscopic technique combined with the SSAE algorithm could be adopted in the identification of the orchid varieties.

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