Performance of iterative solvers for acoustic problems. Part I. Solvers and effect of diagonal preconditioning
Boundary element discretization of the KirchhoffHelmholtz integral equation gives rise to a linear system of equations. This system may be solved directly or iteratively. Application of direct solvers is quite common but turns out to be inefficient for large scale problem with 10,000 unknowns and more. These systems can be solved on behalf of iterative methods. This paper is dedicated to testing performance of four iterative solvers being the Restarted Bi-Conjugate Gradient Stabilized algorithm, the Conjugate Gradient method applied to the normal equations (CGNR), the Generalized Minimal Residual (GMRes) and the Transpose Free Quasi Minimal Residual. For that, we distinguish between internal and external problems. Performance of iterative solvers with respect to problem size, polynomial degree of interpolation, wave-number, wave-number over problem size, absorption at surface, and smoothness of the surface is investigated. Furthermore, the effect of diagonal preconditioning is illuminated. All examples consist of different meshes of up to more than 100,000 elements. In general, the methods perform well for the internal problems, a duct problem, a sedan cabin compartment and a fictitious small concert hall. GMRes proves to solve the problems most efficiently. External problems appear more challenging due to the hypersingular operator of the Burton and Miller formulation. Scattering of a plane wave at a sphere and at a cat's eye are investigated as well as a tire noise problem. The first two are remarkably efficiently solved in the medium and high frequency range by CGNR whereas the tire noise example is only solved by GMRes. In all examples, at least one or two solution methods turn out to require less operations than a direct solver. The effect of diagonal preconditioning is marginal especially for higher frequencies.
iterative solvers acoustics boundary elements frequency boundary element method