Minimization of Numerical Dispersion Errors in Finite Element Models of Non-homogeneous Waveguides

Abstract

The paper presents the approach for the reduction of numerical errors, which are inherent for simulations based on wave propagation models in discrete meshes. The discrete computational models always tend to generate errors of harmonic wave propagation velocities in higher frequency ranges, which can be treated as numerically-induced errors of dispersion curves. The result of the errors is the deterioration of the shapes of simulated waves as the time of simulation increases. The presented approach is based on the improvement of the matrices of elements of the finite element model by means of correction of the modal frequencies and modal shapes of an individual element. The approach developed by the authors earlier and proved to work in the case of a uniform waveguide now has been demonstrated to be valid for simulations of waves in networks of waveguides. The non-reflecting boundary conditions can be implemented by combining synthesized and lumped mass elements in the same model. The propagating wave pulses can be satisfactorily simulated in comparatively rough meshes, where only 6-7 finite elements per wavelength are used.