Approximating three-dimensional steady-state potential flow problems using two-dimensional complex polynomials

A new advance in the Complex Variable Boundary Element Method, or CVBEM, is its extension to three-dimension (3D). This advance breaks down the barrier of limiting CVBEM models to two-dimensional (2D) problems, and also opens the door to solving 3D potential problems with other 2D numerical analogs. In this paper, a 3D analog is developed using 2D basis functions of the complex analytic polynomial type. Thus, 2D complex polynomials are being applied to 3D potential problems. This new advance may be of interest to those involved in applied mathematics, complex variables, boundary elements, and numerical solution of partial differential equations of the Laplace of Poisson type.