Construction of optimal quasi-conformal mappings for the 2D-numerical simulation of diffusion at microelectrodes. Part 1: Principle of the method and its application to the inlaid disk microelectrode

A new method leading to the definition of the optimal space for the numerical simulation of stationary and quasi-stationary diffusion-reaction problems at a microelectrode of any particular geometry amenable to a 2D formulation is introduced. In this first paper, the method basic concept is introduced and exemplified in full details using the classical example of pure diffusion at the microdisk electrode to demonstrate its performance. The method is primarily rooted on closed analytical formulation, yet its scope may be further expanded by utilizing spline functions for the case when the system geometry is such that the optimal coordinate compression function cannot be obtained in the form of a closed analytical expression. This generalized approach has also been applied to the inlaid microdisk electrode and the comparison between the resulting spline-function and the analytical compression function shows excellent convergence.