Iterative solution of panel method discretizations for potential flow problems. The modal multipolar preconditioning

Abstract

The iterative solution of linear systems arising from panel method discretization of three-dimensional (3D) exterior potential problems coming mainly from aero-hydrodynamic engineering problems, is discussed. An original preconditioning based on an approximate eigenspace decomposition is proposed, which corrects bad conditioning arising from a pair of surfaces that are very close to each other, which is a very common situation in slender wings and other aerodynamic profiles. This preconditioning has been tested with the standard Bi-conjugate gradient (Bi-CG) and conjugate gradient squared (CGS) iterative methods.