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Unique solvability of the linear system appearing in the invariant scheme of the charge simulation method

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Abstract

We show that the linear system appearing in the invariant scheme of the charge simulation method is uniquely solvable when the scheme is applied to a two-dimensional Dirichlet problem for a disk, for an ellipse, and for an annulus with properly chosen charge points and collocation ones, which are extensions of the previous results due to Katsurada-Okamoto, Nishida, and Murota. We also prove the unique solvability in a ball of dimension ≥ 3, which we believe is entirely new.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Engineering, Ehime University, 790-8577, Matsuyama, Japan

    Hidenori Ogata, Dai Okano & Kaname Amano

  2. Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, 464-8603, Nagoya, Japan

    Masaaki Sugihara

Authors
  1. Hidenori Ogata
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  2. Dai Okano
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  3. Masaaki Sugihara
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  4. Kaname Amano
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Additional information

This work is partially supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology, and by “Research for the Future Program” of Japan Society for the Promotion of Science.

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Ogata, H., Okano, D., Sugihara, M. et al. Unique solvability of the linear system appearing in the invariant scheme of the charge simulation method. Japan J. Indust. Appl. Math. 20, 17 (2003). https://doi.org/10.1007/BF03167460

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  • DOI: https://doi.org/10.1007/BF03167460

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