  In this paper, we provide a candidate solution to obtain the coefficients of
the conformal mapping for a lower half plane containing a symmetrical
noncircular cavity using penalty function method and modified Particle Swarm
Method. The nonconvexity of the penalty function is proven via the concept of
convex function and proof of contradiction. The solution procedure is presented
very detailedly in pseudocodes to ensure that the solution can be fully
repeated and further improved. The solution accuracy and efficiency are also
discussed.
