A brief introduction to pseudospectral methods : application to diffusion problems

By Denys Dutykh. 2016

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Citations in the corpus

Modified Galerkin algorithm for solving multitype fractional differential equations (2019, unknown): “s=0 (−1)i+j+n−k−sn!Γ(γ + j + 1)Γ(δ + i + 1)Γ(k + 2n + 1 − s)Γ(γ + δ + k + i + 1) k!j!s!(i − k)!(n − s)!Γ(δ + k + 1)Γ(γ + δ + i + 1)Γ(k + 2n + 1 − ν2n − s) × Γ(k + 2n + δ + 1 − ν2n − s)(ν2n + s − k − 2n)j Γ(k + 2n + γ + δ + j + 2 − ν2n − s) , (42)”
Outlining the impact of induced magnetic field and thermal radiation on magneto-convection flow of dissipative fluid (2019, unknown): “Thus, according to the methodology of SQLM [40,42, 43], we have-0 where the vectors K j , and the matrices A i ; j ; B i ; j ( i ; j ¼ 1 ; 2 ; 3) are defined by-A where D is a Chebyshev differentiation matrix and its entries are clearly defined in Canuto et al. [44].”
NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy (2018, methodology): “The ability to obtain high-order accuracy with only edge point communication is an attractive feature of the spectral element method (Canuto et al., 2007; Maday & Patera, 1987).”
The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “For problems defined on regular computational domains but not with periodic boundary conditions, other spectral implementations are possible such as Chebyshev spectral methods for Dirichlet boundary conditions, see discussions in the following books and recent surveys [65, 85, 235, 242, 318, 378, 56”
On Sampling Spatially-Correlated Random Fields for Complex Geometries (2019, methodology): “Alternatively, one can select a Galerkin space Vh with an orthonormal basis, as for instance in spectral methods [3].”