Fast frequency sweep computations using a multi-point Padé-based reconstruction method and an efficient iterative solver

Problems of the form Z( )u( )=f( ), where Z is a given matrix, f is a given vector, and is a circular frequency or circular frequency-related parameter arise in many applications including computational structural and fluid dynamics, and computational acoustics and electromagnetics. The straightforward solution of such problems for fine increments of is computationally prohibitive, particularly when Z is a large-scale matrix. This paper discusses an alternative solution approach based on the efficient computation of u and its successive derivatives with respect to at a few sample values of this parameter, and the reconstruction of the solution u( ) in the frequency band of interest using multi-point Pad´e approximants. This computational methodology is illustrated with applications from structural dynamics and underwater acoustic scattering. In each case, it is shown to reduce the CPU time required by the straightforward approach to frequency sweep computations by two orders of magnitude. Copyright q 2006 John Wiley & Sons, Ltd.