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Titolo:
Evaluation of toroidal harmonics
Autore:
Segura, J; Gil, A;
Indirizzi:
Univ Miguel Hernandez, Inst Bioingn, Edificio Galia, Alicante 03202, SpainUniv Miguel Hernandez Alicante Spain 03202 Galia, Alicante 03202, Spain
Titolo Testata:
COMPUTER PHYSICS COMMUNICATIONS
fascicolo: 1, volume: 124, anno: 2000,
pagine: 104 - 122
SICI:
0010-4655(200001)124:1<104:EOTH>2.0.ZU;2-H
Fonte:
ISI
Lingua:
ENG
Keywords:
toroidal harmonics; Legendre functions; Laplace's equation; toroidal coordinates;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
12
Recensione:
Indirizzi per estratti:
Indirizzo: Segura, J Univ Miguel Hernandez, Inst Bioingn, Edificio Galia, Alicante 03202, Spain Univ Miguel Hernandez Alicante Spain 03202 icante 03202, Spain
Citazione:
J. Segura e A. Gil, "Evaluation of toroidal harmonics", COMP PHYS C, 124(1), 2000, pp. 104-122

Abstract

Three algorithms to evaluate toroidal harmonics, i.e., Legendre functions of integral order and half-odd degree of the first and second kinds for real arguments larger than one, are presented. The first algorithm (DTORH1) allows the evaluation of the set {P-n-1/2(m)(x), Q(n-1/2)(m)(x)} for fixed (integer and positive) values of m and n = 0,1,..., N. The algorithms DTORH2 and DTORH3 extend the method used in DTORH1 to obtain the set {P-n-1/2(m)(x), Q(n-1/2)(m)(x)} for m = 0,..., M and n = 0, 1,..., N. The output of DTORH2 is equivalent to the result of the application of DTORH1 M times (m = 0, 1,..., M). However, due to the organization of the algorithm, DTORH2 is faster than DTORH1 when several orders and degrees are calculated. DTORH2 is better suited than DTORH3 when high orders and degrees are needed. On the other hand DTORH3, though more restrictive on the maximumevaluable degrees N, is even faster than DTORH2. Our tests of accuracy, show that the three codes achieve a precision of one pall in 10(12). We discuss the performance of our codes, their speed and their range of validity. The application of the algorithms to solve Laplace's and Poisson's equations in toroidal coordinates is discussed and an explicit numerical example is shown. (C) 2000 Elsevier Science B.V. All rights reserved.

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Documento generato il 05/04/20 alle ore 03:38:16