A Computer Algorithm for the Complex Variable Boundary Element Method

Abstract

In this chapter, a computer algorithm for the Complex Variable Boundary Element Method will be developed for use in solving potential problems defined on a simply connected domain. The strategy of using the method is to (1) define the problem domain Ω and boundary Γ such that there are no singularities of the state variable φ(x, y) and conjugate stream function ψ(x, y) for z = x + iy and Z ε Ω ∪Γ; (2) develop an approximation function which is analytic in Ω and continuous on Γ and satisfies specified boundary conditions on Γ; and (3) determine an error distribution between the approximation function and the analytic solution of the boundary value problem to be used for error analysis and subsequent modeling refinement. Steps (1) and (2) will be discussed in this chapter, while the error analysis and subsequent modeling refinement methods will be developed in Chapter 5.