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Approximations on SO(3) by Wigner D-matrix and Applications

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Abstract

We consider approximations on SO(3) by Wigner D-matrix. We establish basic approximation properties of Wigner D-matrix, develop efficient numerical schemes using Wigner D-matrix for elliptic and parabolic equations on SO(3), and establish corresponding optimal error estimates. Numerical examples are presented to validate the theoretical estimates and illustrate a physical application.

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  1. www.cs.dartmouth.edu/~geelong/soft/.

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Acknowledgements

J. Shen is supported in part by NSF DMS-1620262 and AFOSR FA9550-16-1-0102. P. Zhang is supported in part by NSFC Grants 11421101 and 11421110001.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen & Jie Xu

  2. LMAM & School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Pingwen Zhang

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  1. Jie Shen
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  2. Jie Xu
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  3. Pingwen Zhang
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Correspondence to Jie Xu.

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Shen, J., Xu, J. & Zhang, P. Approximations on SO(3) by Wigner D-matrix and Applications. J Sci Comput 74, 1706–1724 (2018). https://doi.org/10.1007/s10915-017-0515-7

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  • DOI: https://doi.org/10.1007/s10915-017-0515-7

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