A high-order fast method for computing convolution integral with smooth kernel

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In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the ... continued below

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Qiang, Ji September 28, 2009.

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In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.

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  • Journal Name: Computer Physics Communication

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  • Report No.: LBNL-2667E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 974162
  • Archival Resource Key: ark:/67531/metadc932360

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  • September 28, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Jan. 4, 2017, 3:07 p.m.

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Qiang, Ji. A high-order fast method for computing convolution integral with smooth kernel, article, September 28, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc932360/: accessed September 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.