Browsing by Author "Li, Keran"

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    Compact High-order Finite Difference Schemes for Acoustic Wave Equations
    (2021-01-05) Li, Keran; Liao, Wenyuan; Lamoureux, Michael P.; Liao, Wenyuan; Braverman, Elena; Liang, Dong; Ware, Antony Frank
    This study developed three compact high-order finite difference schemes for acoustic wave equations. Benefiting from the compactness, the new schemes require less layers of boundary conditions than conventional finite difference schemes. All the three schemes work for acoustic wave equations with variable coefficients in homogeneous media, with the third one also being applicable to the case of heterogeneous density media. The first scheme is based on Padé approximation which is formally a product of the inverse of a finite difference operator and the conventional 2nd-order finite difference operator, thus some algebraic manipulation is necessary to discuss the product of operators. The second scheme is based on so-called combined finite difference method, which needs the boundary conditions for the second spatial derivatives and the needed boundary conditions can be derived by using the wave equation and usual Dirichlet boundary conditions themselves. The third scheme is also based on combined finite difference method, and it generalizes the second scheme so that it can also work in heterogeneous density media case, i.e., the Laplacian in the wave equations being divergence form. The stability of the first two schemes are established by an energy method, while the stability of the last scheme is obtained by an analogy of von Neumann analysis. All of these new schemes are proven to be conditionally stable with given Courant-Friedrichs-Lewy (CFL) numbers. Numerical experiments are conducted to verify the efficiency, accuracy and stability of the new schemes. It is expected that these new schemes will find extensive applications in both research and engineering areas.