The GMRES(m) Method for Numerical Conformal Mapping of Bounded Multi-Connected Domains

WU Kang; LÜ Yibin; SHI Yunlong; WANG Yingzi

doi:10.21656/1000-0887.420305

Volume 43 Issue 9

Sep. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(9): 1026-1033

WU Kang, LÜ Yibin, SHI Yunlong, WANG Yingzi. The GMRES(m) Method for Numerical Conformal Mapping of Bounded Multi-Connected Domains[J]. Applied Mathematics and Mechanics, 2022, 43(9): 1026-1033. doi: 10.21656/1000-0887.420305

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The GMRES(m) Method for Numerical Conformal Mapping of Bounded Multi-Connected Domains

doi: 10.21656/1000-0887.420305

1.
Faculty of Science, Kunming University of Science and Technology, Kunming 650500, P.R.China
2.
Computer Center, Kunming University of Science and Technology, Kunming 650500, P.R.China

Received Date: 2021-10-11
Rev Recd Date: 2022-03-06

Available Online: 2022-09-07

Publish Date: 2022-09-30

Abstract

Abstract

It is difficult to solve conformal mapping functions for complex multi-connected domains. In order to overcome this difficulty, the problem of solving conformal mapping functions was transformed into using the charge simulation method to solve a pair of conjugate harmonic functions in the problem domain. The conjugate harmonic functions should satisfy given boundary conditions, which construct a system of linear equations. Then the simulation charges can be computed by means of the GMRES(m) (the generalized minimal residual method) algorithm to solve the linear systems. The approximate conformal mapping functions were constructed accurately to map the bounded multi-connected domain onto 3 unbounded canonical slit domains. Numerical results show that the presented method is effective.
- bounded multi-connected domain,
- charge simulation method,
- GMRES(m) algorithm,
- numerical conformal mapping

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References(17)

References

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