CUDA based fast numerical method to compute two dimensional spatial convolution of sufficiently smooth continuous functions using Gauss Hermite quadrature rule.
CUDA based parallel computation of the 2D spatial convolution. The Thrust C++ tempelate libraries are used here for abstraction and performace. The spatial convolution algorithm is implemented in the CUDA kernel file SpatialConvolutionGHQ.cu and the Jupyter nootbook Spatial_Convolution_GHQ.ipynb.
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The Python 3 Jupyter notebook Spatial_Convolution_GHQ.ipynb can be used on the Google colaboratory cloud service that provides a free access to the NVIDIA Tesla K80 GPU.
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The nodes and weights are stored as list of lists using bidimensional arrays. The Golub–Welsch algorithm is used to compute the Hermite nodes (roots of the Hermite polynomials) in the interval (-inf, inf). The mathematica nootbook Nodes-weights-Gauss-Hermite.nb is supplied in order to compute the Gauss-Hermite nodes and weights. NOTE: Here the weighting function exp(x^2) is absorbed into the weights w_i.
- Fast implementation of the Golub–Welsch algorithm to directly generate the Hermite nodes and weights for the Gauss-Hermite quadrature.
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Davis, P.J., and P. Rabinowitz. 1984. Methods of Numerical Integration. Academic Press.
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Jäckel, P. 2005. “A Note on Multivariate Gauss-Hermite Quadrature.” Mimeo.
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G. H. Golub and J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comp. 23 (1969), 221–230
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Hale, N., Townsend, A.: Fast and accurate computation of Gauss–Legendre and Gauss–Jacobi quadrature nodes and weights. SISC 35, A652—A672 (2013)
Licensed under the MIT License