Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball

Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball Full article

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2019, Volume: 13, Number: 3, Pages: 480-499 Pages count : 20 DOI: 10.1134/S1990478919030098

Tags

Mie representation; solenoidal; toroidal and poloidal vector fields; vector spherical harmonic; Zernike polynomial

Authors

Kazantsev S.G. ¹ , Kardakov V.B. ²

Affiliations

1	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University of Architecture and Civil Engineering, ul. Leningradskaya 113, Novosibirsk, 630113, Russian Federation

Under study is the polynomial orthogonal basis system of vector fields in the ball which corresponds to the Helmholtz decomposition and is divided into the three parts: potential, harmonic, and solenoidal. It is shown that the decomposition of a solenoidal vector field with respect to this basis is a poloidal-toroidal decomposition (the Mie representation). In this case, the toroidal potentials are Zernike polynomials, whereas the poloidal potentials are generalized Zernike polynomials. The polynomial system of toroidal and poloidal vector fields in a ball can be used for solving practical problems, in particular, to represent the geomagnetic field in the Earth’s core. © 2019, Pleiades Publishing, Ltd.

Kazantsev S.G. , Kardakov V.B.
Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball
Journal of Applied and Industrial Mathematics. 2019. V.13. N3. P.480-499. DOI: 10.1134/S1990478919030098 Scopus OpenAlex

Казанцев С.Г. , Кардаков В.Б.
Полоидально-тороидальное разложение соленоидальных векторных полей в шаре
Сибирский журнал индустриальной математики. 2019. Т.22. №3. С.74-95. DOI: 10.33048/sibjim.2019.22.307 OpenAlex

Scopus:	2-s2.0-85071637102
OpenAlex:	W2970698497

DB	Citing
Scopus	9
OpenAlex	9