2004/02/25 by Jason Maron, Maron, Jason
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #Image and Signal Denoising Methods #Model Reduction and Neural Networks #Seismic Imaging and Inversion Techniques #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0402606
20 pages, 7 figures
arxiv created 2004/02/25 · openalex publication_date 2004/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a fluid dynamics algorithm that performs with nearly spectral accuracy, but uses finite-differences instead of FFTs to compute gradients and thus executes 10 times faster. The finite differencing is not based on a high-order polynomial fit. The polynomial scheme has supurb accuracy for low-wavenumber gradients but fails at high wavenumbers. We instead use a scheme tuned to enhance high-wavenumber accuracy at the expense of low wavenumbers, although the loss of low-wavenumber accuracy is negligibly slight. A tuned gradient is capable of capturing all wavenumbers up to 80 percent of the Nyquist limit with an error of no worse than 1 percent. The fact that gradients are based on finite differences enables diverse geometries to be considered and eliminates the parallel communications bottleneck.