Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
A new compact spectral scheme for turbulence simulations
Journal of Computational Physics
Optimized prefactored compact schemes
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Finite difference schemes for long-time integration
Journal of Computational Physics
An optimized spectral difference scheme for CAA problems
Journal of Computational Physics
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Conventional explicit finite-difference methods have difficulties in handling high-frequency components due to strong numerical dispersions. One can reduce the numerical dispersions by optimizing the constant coefficients of the finite-difference operator. Different from traditional optimized schemes that use the 2-norm and the least squares, we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing algorithm. Both theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three aspects. First, it provides us with much more flexibility when designing the objective functions; thus we can use various possible forms and contents to make the objective functions more reasonable. Second, it allows for tighter error limitation, which is shown to be necessary to avoid rapid error accumulations for simulations on large-scale models with long travel times. Finally, it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits, which means greater savings in computational efforts and memory demand.