A comparative study of expansion functions using the boundary residual method on a linear dipole - Part I: Entire-domain functions

The Boundary Residual Method, which is a specialization of the Least Squares Method, is described. A significant benefit of the approach is that error in the residual satisfaction of the boundary condition is explicitly reported. Use of error values facilitates better monitoring of solution convergence as expansion functions are added to the underlying model. Furthermore, better discrimination between competing models is possible when errors are known. These concepts are explored and applied to dipoles of various lengths with key findings reported.