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- W2740918329 abstract "We consider a fractional Laplacian defined in bounded domains by the eigen-decomposition of the integer-order Laplacian, and demonstrate how to compute very accurately (using the spectral element method) the eigenspectrum and corresponding eigenfunctions in two-dimensional prototype complex-geometry domains. We then employ these eigenfunctions as trial and test bases to first solve the fractional diffusion equation, and subsequently to simulate two-phase flow based on the Navier--Stokes equations combined with a fractional Allen--Cahn mass-preserving model. A key point to the effectiveness of an exponential convergence of this approach is the use of a weighted Gram--Schmidt orthonormalization of the eigenfunctions that guarantees accurate projection and recovery of spectral accuracy for smooth solutions. We demonstrate that even when only part of the eigenspectrum is computed accurately we can still obtain exponential convergence if we employ the complete set of the eigenvectors of the discrete Laplacian...." @default.
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- W2740918329 date "2017-01-01" @default.
- W2740918329 modified "2023-10-18" @default.
- W2740918329 title "Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations" @default.
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- W2740918329 doi "https://doi.org/10.1137/16m1078197" @default.
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