Provably stable full-spectrum dispersion relation preserving schemes
C Williams, K Duru - arXiv preprint arXiv:2110.04957, 2021 - arxiv.org
arXiv preprint arXiv:2110.04957, 2021•arxiv.org
The dispersion error is often the dominant error for computed solutions of wave propagation
problems with high-frequency components. In this paper, we define and give explicit
examples of $\alpha $-dispersion-relation-preserving schemes. These are dual-pair finite-
difference schemes for systems of hyperbolic partial differential equations which preserve
the dispersion-relation of the continuous problem uniformly to an $\alpha\% $-error
tolerance. We give a general framework to design provably stable finite difference operators …
problems with high-frequency components. In this paper, we define and give explicit
examples of $\alpha $-dispersion-relation-preserving schemes. These are dual-pair finite-
difference schemes for systems of hyperbolic partial differential equations which preserve
the dispersion-relation of the continuous problem uniformly to an $\alpha\% $-error
tolerance. We give a general framework to design provably stable finite difference operators …
The dispersion error is often the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit examples of -dispersion-relation-preserving schemes. These are dual-pair finite-difference schemes for systems of hyperbolic partial differential equations which preserve the dispersion-relation of the continuous problem uniformly to an -error tolerance. We give a general framework to design provably stable finite difference operators that preserve the dispersion relation for hyperbolic systems such as the elastic wave equation. The operators we derive here can resolve the highest frequency (-mode) present on any equidistant grid at a tolerance of error. This significantly improves on the current standard that have a tolerance of error.
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