On-Line Simulation of 2D Resonators with Reduced Dispersion Error using Compact Implicit Finite Difference Methods

This paper presents a method for on-line simulation of 2D resonators with reduced direction-dependent frequency error. The use of a compact implicit finite difference (FD) technique is proposed to reduce the dispersion error remarkably. In particular, a computationally efficient method that allows solving 2D implicit problems with a set of three-diagonal equations, namely the alternating direction implicit is discussed. Efficient equation factorisation together with optimally matched free parameters allows more accurate simulation for wider frequency ranges. With the use of this technique, the dispersion error is limited to 1.1% within the bandwidth up to half of the Nyquist frequency. The compact implicit scheme is compared to compact explicit FD schemes in terms of numerical dispersion error, membrane impulse response, and computational cost.