Large-Scale Parallel Implementation of Hartree–Fock Exchange Energy on Real-Space Grids Using 3D-Parallel Fast Fourier Transform

2020 ◽  
Vol 60 (3) ◽  
pp. 1376-1389
Author(s):  
Hideaki Takahashi ◽  
Shun Sakuraba ◽  
Akihiro Morita
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Large Scale ◽  
Parallel Implementation ◽  
Real Space ◽  
Exchange Energy ◽  
Hartree Fock

scholarly journals A fast methodology for large-scale focusing inversion of gravity and magnetic data using the structured model matrix and the 2-D fast Fourier transform

2020 ◽  
Vol 223 (2) ◽  
pp. 1378-1397
Author(s):  
Rosemary A Renaut ◽  
Jarom D Hogue ◽  
Saeed Vatankhah ◽  
Shuang Liu
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Linear Systems ◽  
Large Scale ◽  
Surface Measurement ◽  
Magnetic Data ◽  
Uniform Grid ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Data Set

SUMMARY We discuss the focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid. For the uniform grid, the model sensitivity matrices have a block Toeplitz Toeplitz block structure for each block of columns related to a fixed depth layer of the subsurface. Then, all forward operations with the sensitivity matrix, or its transpose, are performed using the 2-D fast Fourier transform. Simulations are provided to show that the implementation of the focusing inversion algorithm using the fast Fourier transform is efficient, and that the algorithm can be realized on standard desktop computers with sufficient memory for storage of volumes up to size n ≈ 106. The linear systems of equations arising in the focusing inversion algorithm are solved using either Golub–Kahan bidiagonalization or randomized singular value decomposition algorithms. These two algorithms are contrasted for their efficiency when used to solve large-scale problems with respect to the sizes of the projected subspaces adopted for the solutions of the linear systems. The results confirm earlier studies that the randomized algorithms are to be preferred for the inversion of gravity data, and for data sets of size m it is sufficient to use projected spaces of size approximately m/8. For the inversion of magnetic data sets, we show that it is more efficient to use the Golub–Kahan bidiagonalization, and that it is again sufficient to use projected spaces of size approximately m/8. Simulations support the presented conclusions and are verified for the inversion of a magnetic data set obtained over the Wuskwatim Lake region in Manitoba, Canada.

Large-Scale Fast Fourier Transform

2011 ◽  
pp. 629-642
Author(s):  
Yifeng Chen ◽  
Xiang Cui ◽  
Hong Mei
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Large Scale

Large-scale fast Fourier transform on a heterogeneous multi-core system

2012 ◽  
Vol 26 (2) ◽  
pp. 148-158 ◽  
Author(s):  
Yan Li ◽  
Jeffrey R Diamond ◽  
Xu Wang ◽  
Haibo Lin ◽  
Yudong Yang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Large Scale ◽  
Core System
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