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In this paper, we provide a candidate solution to obtain the coefficients ofthe conformal mapping for a lower half plane containing a symmetricalnoncircular cavity using penalty function method and modified Particle SwarmMethod. The nonconvexity of the penalty function is proven via the concept ofconvex function and proof of contradiction. The solution procedure is presentedvery detailedly in pseudocodes to ensure that the solution can be fullyrepeated and further improved. The solution accuracy and efficiency are alsodiscussed.

On solution of conformal mapping for a lower half plane containing a symmetrical noncircular cavity