Abstract
A novel adaptive strategy, dubbed m-adaptation, is developed for solving the acoustic wave equation (in the time domain) on square meshes. The finite element, the finite difference and a few other more recent methods are shown to be particular members of the mimetic family. Analysis of the parametric family of mimetic discretization methods is performed to find the optimal member that eliminates the numerical dispersion at the fourth-order (as in Ref. 1) and the numerical anisotropy at the sixth-order (higher than in Ref. 1). The stability condition for the optimal method is derived that turns out to be comparable to the classical Courant condition. The numerical experiments show that the new approach is consistently better than the classical methods for reducing a long-time integration error.
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