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Haar wavelets method for solving Poisson equations with jump conditions in irregular domain

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Abstract

In this paper, Haar wavelets method is used to solve Poisson equations in the presence of interfaces where the solution itself may be discontinuous. The interfaces have jump conditions which need to be enforced. It is critical for the approximation of the boundaries of the irregular domain. An irregular domain can be treated by embedding the domain into a rectangular domain and Poisson equation is solved by using Haar wavelets method on the rectangle. Firstly, we demonstrate this method in the case of 1-D region, then we consider the solution of the Poisson equations in the case of 2-D region. The efficiency of the method is demonstrated by some numerical examples.

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Authors and Affiliations

  1. School of Science, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Shi Zhi, Xu Yan-hua & Zhao Jun-ping

Authors
  1. Shi Zhi
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  2. Xu Yan-hua
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  3. Zhao Jun-ping
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Corresponding author

Correspondence to Shi Zhi.

Additional information

Communicated by: Raymond H. Chan

This paper was supported by the scientific research program of the Shannxi higher education institutions (No.12JK0868)

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Zhi, S., Yan-hua, X. & Jun-ping, Z. Haar wavelets method for solving Poisson equations with jump conditions in irregular domain. Adv Comput Math 42, 995–1012 (2016). https://doi.org/10.1007/s10444-015-9450-z

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  • DOI: https://doi.org/10.1007/s10444-015-9450-z

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