An efficient compact difference-proper orthogonal decomposition algorithm for fractional viscoelastic plate vibration model

Abstract

In this article, we aim to prove the solvability for the fractional viscoelastic plate vibration model through the Galerkin argument in Sobolev spaces as a compensation for the absence of its mathematical theory, then propose an efficient compact difference-proper orthogonal decomposition (CD-POD) algorithm. Rigorous numerical analyses are conducted to show that the CD-POD algorithm inherits the merits of the compact difference and the proper orthogonal decomposition technique, that is, it is unconditionally stable, possesses the spatial and temporal convergence rates of fourth order and second order, respectively, and reduces greatly the storage and computing cost, and thus may adapts for long time simulation for the plate vibration model. As a bridge for the plate vibration model and the CD-POD algorithm, a compact difference scheme is also proposed and analyzed previously. Numerical experiments, one of which is for resonance case, indicate that the CPU time of the CD-POD algorithm is at least 20 times less than that of the compact difference scheme, for resonance case or for non-resonance case, and thus verifies again that the CD-POD algorithm is a reasonable computation candidate for long time simulation of the viscoelastic plate vibration model.