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

TL;DR

This paper introduces a detailed method combining penalty functions and particle swarm optimization to compute conformal mappings for a lower half plane with symmetrical noncircular cavities, emphasizing accuracy and repeatability.

Contribution

It presents a novel approach using penalty functions and modified particle swarm optimization for conformal mapping of complex geometries, with detailed pseudocode for reproducibility.

Findings

Proven nonconvexity of the penalty function.

Detailed pseudocode for the solution process.

Discussion on solution accuracy and efficiency.

Abstract

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.