An Amplitude Formulation to Reduce the Pollution Error in the Finite Element Solution of Time-Harmonic Scattering Problems

We present a procedure to gain significant accuracy in the finite element solution of electromagnetic scattering problems at high wavenumbers. The technique relies on the determination, at a low computational cost, of an approximate solution around the scattering obstacle, which is then used to formulate an alternative variational formulation in terms of a slowly-oscillatory amplitude. The proposed method does not require any new finite element basis functions, and can thus be easily implemented in existing finite element codes.