Title :
Generating Gauss quadratures for Green´s function 1/r: a randomized algorithm
Author :
Pham, Hoan H. ; Nathan, Arokia
Author_Institution :
Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada
Abstract :
We report a randomized scheme for generating Gauss quadratures for an exponential integral representation of the Green´s function 1 /r. These Gauss quadratures form the basis of the exponential-expansion-based method, which has previously been developed for rapid and accurate evaluation of the potential field and its gradient in three dimensions. Given a desired degree of accuracy on the approximation of 1/r, the technique proposed here enables generation of exponential expansion with sizes as small as possible. It makes use of the standard Legendre-Gauss and Chebychev-Gauss quadratures, and does not require solving a large system of non-linear equations
Keywords :
Gaussian processes; Green´s function methods; approximation theory; integral equations; integration; randomised algorithms; Chebychev-Gauss quadrature; Gauss quadratures; Green´s function; approximation; exponential expansion; exponential integral representation; exponential-expansion-based method; gradient; potential field; randomized algorithm; standard Legendre-Gauss quadrature; Astrophysics; Computational efficiency; Electrostatics; Gaussian approximation; Gaussian processes; Green´s function methods; Information technology; Nonlinear dynamical systems; Physics; Plasmas;
Conference_Titel :
Electrical and Computer Engineering, 1998. IEEE Canadian Conference on
Conference_Location :
Waterloo, Ont.
Print_ISBN :
0-7803-4314-X
DOI :
10.1109/CCECE.1998.685582
