Publication detail

Technique of 3D NILT based on Complex Fourier Series and Quotient-Difference Algorithm

BRANČÍK, L.

Original Title

Technique of 3D NILT based on Complex Fourier Series and Quotient-Difference Algorithm

English Title

Technique of 3D NILT based on Complex Fourier Series and Quotient-Difference Algorithm

Type

conference paper

Language

en

Original Abstract

The paper deals with a technique of the numerical inversion of three-dimensional Laplace transforms (3D NILT) based on a complex Fourier series approximation, in conjunction with a quotient-difference (q-d) algorithm. It is a generalization of a 2D NILT technique of the same principle to three variables. Especially, a detailed error analysis is done resulting in a formula giving a connection between a relative error and the paths of a numerical integration of a triple Bromwich integral. To evaluate triple infinite sums gained by the numerical integration, a partial inversion technique is applied while utilizing the FFT and IFFT algorithms for the fast evaluation, and the q-d algorithm to speed up the convergence of residual infinite series. The technique was algorithmized in a Matlab language and experimentally verified.

English abstract

The paper deals with a technique of the numerical inversion of three-dimensional Laplace transforms (3D NILT) based on a complex Fourier series approximation, in conjunction with a quotient-difference (q-d) algorithm. It is a generalization of a 2D NILT technique of the same principle to three variables. Especially, a detailed error analysis is done resulting in a formula giving a connection between a relative error and the paths of a numerical integration of a triple Bromwich integral. To evaluate triple infinite sums gained by the numerical integration, a partial inversion technique is applied while utilizing the FFT and IFFT algorithms for the fast evaluation, and the q-d algorithm to speed up the convergence of residual infinite series. The technique was algorithmized in a Matlab language and experimentally verified.

Keywords

numerical inversion; three-dimensional Laplace transform; complex Fourier series; quotient-difference algorithm

RIV year

2010

Released

12.12.2010

Publisher

IEEE CAS

Location

Athens, Greece

ISBN

978-1-4244-8156-9

Book

2010 IEEE International Conference on Electronics, Circuits, and Systems

Pages from

207

Pages to

210

Pages count

4

URL

BibTex


@inproceedings{BUT35145,
  author="Lubomír {Brančík}",
  title="Technique of 3D NILT based on Complex Fourier Series and Quotient-Difference Algorithm",
  annote="The paper deals with a technique of the numerical inversion of three-dimensional Laplace transforms (3D NILT) based on a complex Fourier series approximation, in conjunction with a quotient-difference (q-d) algorithm. It is a generalization of a 2D NILT technique of the same principle to three variables. Especially, a detailed error analysis is done resulting in a formula giving a connection between a relative error and the paths of a numerical integration of a triple Bromwich integral. To evaluate triple infinite sums gained by the numerical integration, a partial inversion technique is applied while utilizing the FFT and IFFT algorithms for the fast evaluation, and the q-d algorithm to speed up the convergence of residual infinite series. The technique was algorithmized in a Matlab language and experimentally verified.",
  address="IEEE CAS",
  booktitle="2010 IEEE International Conference on Electronics, Circuits, and Systems",
  chapter="35145",
  howpublished="electronic, physical medium",
  institution="IEEE CAS",
  year="2010",
  month="december",
  pages="207--210",
  publisher="IEEE CAS",
  type="conference paper"
}