An integral equation method for conformal mapping of multiply connected regions onto an annulus with circular slits via the neumann kernel

• Main Authors: Hu, Laey Nee, M. Murid, Ali H., Mohamad, Mohd. Nor
• Format: Conference or Workshop Item
• Published: 2009
• Subjects: Q Science (General)
• Online Access: http://eprints.utm.my/id/eprint/14747/; http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:99360
• Institution: Universiti Teknologi Malaysia

We present an integral equation method for conformal mapping of multiply connected regions onto an annulus with circular slits. Using the boundary relationship satisfied by the mapping function, a related system of integral equation is constructed involving the unknown circular radii. For numerical experiment on triply connected regions, the integral equation is discretized which leads to a system of non-linear equations. The system is then solved using an optimization method. Numerical examples reveal that the present method offers an effective solution technique for the conformal mapping problem when the boundaries are sufficiently smooth.