High dimensional harmonic balance dealiasing techniques for a Duffing oscillator

A dealiasing study of the high dimensional harmonic balance method is conducted using a Duffing oscillator as a prototypical nonlinear dynamical system. Previous study has shown that aliasing can occur when the high dimensional harmonic balance method is used to solve systems that contain nonlinearities. We demonstrate that frequency filtering techniques, such as the Fourier smoothing method, can sufficiently reduce or eliminate the effects of aliasing. The drawback is that Fourier filtering requires redundant coordinate transformations between the time and frequency domains, resulting in unnecessary computational expense. As an alternative, temporal filters are constructed based upon compact finite difference schemes with spectral-like resolution. It is shown that the temporal filtering schemes successfully replicate the performance of the Fourier smoothing method with improved computational economy.