Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations
Authors:
- Michael A. EptonMEMichael A. Epton
- Benjamin DembartBDBenjamin Dembart
- 1 July 1995
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 16 (4) , 865-897
Abstract
The mathematical theory of multipole translation operators for the three-dimensional Laplace and Helmholtz equations is summarized and extended. New results for the Laplace equation include an elementary proof of the inner-to-inner translation theorem, from which follows the definition of a far-field signature function analogous to that of the Helmholtz equation. The theory for the Helmholtz equation is developed in terms of a new convolutional form of the translation operator, which is connected to Rokhlin’s diagonal form by means of Wigner 3-j symbols.Keywords
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