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Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation

Author

Listed:
  • Chein-Shan Liu
  • Zhuojia Fu
  • Chung-Lun Kuo

Abstract

We propose a simple extension of the two-dimensional method of fundamental solutions (MFS) to a two-dimensional like MFS for the numerical solution of the three-dimensional Laplace equation in an arbitrary interior domain. In the directional MFS (DMFS) the directors are planar orientations, which can take the geometric anisotropy of the problem domain into account, and more importantly the order of the logarithmic singularity with $\ln R$ of the new fundamental solution is reduced than that of the conventional three-dimensional fundamental solution with singularity $1/r$. Some numerical examples are used to validate the performance of the DMFS.

Suggested Citation

  • Chein-Shan Liu & Zhuojia Fu & Chung-Lun Kuo, 2017. "Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 112-123, December.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:112
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    References listed on IDEAS

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    1. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    4. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    5. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    7. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    8. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    9. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    10. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    11. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    12. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
    13. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    14. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
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    More about this item

    Keywords

    three-dimensional Laplace equation; directional method of fundamental solutions; irregular domain;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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