The Ill-conditioning of infinite element stiffness matrices

In this paper, a method for improving the conditioning of infinite element stiffness matrices is proposed and examined for one-dimensional and two-dimensional infinite elements. This method is a preconditioning technique which is based on a Gram-Schmidt-like transformation induced by general sesquilinear forms. Although the preconditioning method can be applied to many types of infinite elements, it will be applied to improve the conditioning of the popular multipole infinite element. The paper is concluded with numerical examples demonstrating improved conditioning and convergence properties of the preconditioned multipole infinite elements.