Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method

Figure 4

An illustration for the solution of the partial derivatives on the boundaries. The values of and on the top and bottom boundaries can be solved for directly using the BIEM with the improved formulation, and then the values of and can be obtained using the Cauchy-Riemann equations. Similarly, the values of and on the right and left boundaries can be solved for directly using the BIEM with the improved formulation, and then the values of and can be obtained using the Cauchy-Riemann equations.