@article{Li2025, 
author = {Dongyi Li and Yibin Lu},
title = {A method of numerical conformal mapping of bounded regions with a rectilinear slit},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8422-8445},
keywords = {conformal mapping, charge simulation method, pre-map function, LU-CGS method, spiral point vortex},
url = {https://www.sciopen.com/article/10.3934/math.2025388},
doi = {10.3934/math.2025388},
abstract = {This paper presented a numerical method based on the charge simulation method for calculating conformal mappings from the bounded multiply connected regions with a rectilinear slit onto the first category canonical slit domains. First, we proposed utilizing a pre-map function to expand a rectilinear slit in the bounded multiply connected regions. Second, to address pathologically constrained equation systems, we proposed a conjugate gradient squared (CGS) method combined with LU decomposition. Third, the conformal mappings were applied to simulate spiral point vortex bypass flow in regions with a rectilinear slit. Finally, numerical experiments validated the correctness of the mapping, the method's superiority, and its effectiveness in spiral point vortex bypass flow simulations.}
}