A fixed-point iteration method for high frequency vector wave equations

Abstract

For numerically solving the high frequency vector wave equations, we present a simple approach based on fixed point iterations, where the problem is transferred into a fixed-point problem related to an exponential operator. The associated functional evaluations are achieved by unconditionally stable operator-splitting based pseudospectral schemes such that large step sizes are allowed to reach the approximated fixed point efficiently for prescribed termination criteria. For the sub-operator that is related to non-constant relative permeability, the Krylov subspace method or Taylor expansion is adapted for approximating its exponential. Furthermore, the Anderson acceleration is incorporated to accelerate the convergence of the fixed-point iterations. Numerical experiments are presented to demonstrate the accuracy and efficiency of the method.