Analytical solution for finite domain Laplacian equation with coexistent boundary conditions

This paper presents a new mathematical technique called the autocontrol image-recharge method for deriving highly accurate, computationally efficient, analytical solutions to the two-dimensional Finite Domain Laplacian Equation involving coexistent Neumann and Dirichlet boundary conditions (e.g., with both transmission and reflection) and for very irregular boundary shapes. This technique is an extension of recent work presented by Li et al. [1]and is based on developing an Expansion Coefficient Recurrence Relationship for two constant sequences for the coexistent boundary conditions.