A fast and stable method for rotating spherical harmonic expansions

Z. Gimbutas; L. Greengard

doi:10.1016/j.jcp.2009.05.014

A fast and stable method for rotating spherical harmonic expansions

Z. Gimbutas, L. Greengard

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present a simple and efficient method for rotating a spherical harmonic expansion. This is a well-studied problem, arising in classical scattering theory, quantum mechanics and numerical analysis, usually addressed through the explicit construction of the Wigner rotation matrices. We show that rotation can be carried out easily and stably through "pseudospectral" projection, without ever constructing the matrix entries themselves. Existing fast algorithms, based on recurrence relations, are subject to a variety of instabilities, limiting the effectiveness of the approach for expansions of high degree.

Original language	English (US)
Pages (from-to)	5621-5627
Number of pages	7
Journal	Journal of Computational Physics
Volume	228
Issue number	16
DOIs	https://doi.org/10.1016/j.jcp.2009.05.014
State	Published - Sep 1 2009

Keywords

Fast multipole method
Rotation matrix
Spherical harmonics

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2009.05.014

Cite this

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AU - Greengard, L.

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N2 - In this paper, we present a simple and efficient method for rotating a spherical harmonic expansion. This is a well-studied problem, arising in classical scattering theory, quantum mechanics and numerical analysis, usually addressed through the explicit construction of the Wigner rotation matrices. We show that rotation can be carried out easily and stably through "pseudospectral" projection, without ever constructing the matrix entries themselves. Existing fast algorithms, based on recurrence relations, are subject to a variety of instabilities, limiting the effectiveness of the approach for expansions of high degree.

AB - In this paper, we present a simple and efficient method for rotating a spherical harmonic expansion. This is a well-studied problem, arising in classical scattering theory, quantum mechanics and numerical analysis, usually addressed through the explicit construction of the Wigner rotation matrices. We show that rotation can be carried out easily and stably through "pseudospectral" projection, without ever constructing the matrix entries themselves. Existing fast algorithms, based on recurrence relations, are subject to a variety of instabilities, limiting the effectiveness of the approach for expansions of high degree.

KW - Fast multipole method

KW - Rotation matrix

KW - Spherical harmonics

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EP - 5627

JO - Journal of Computational Physics

JF - Journal of Computational Physics

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ER -

A fast and stable method for rotating spherical harmonic expansions

Abstract

Keywords

ASJC Scopus subject areas

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