High-Order Methods for Incompressible Fluid Flow. By M. O. DEVILLE, P. F. FISCHER & E. H. MUND. Cambridge University Press, 2002. 528 pp. ISBN 0521453097. £60

By M. Deville, Paul F. Fischer, E. Mund, DK Gartling,. Journal of Fluid Mechanics, 2002

1,040 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7fc865c305bf89fa7809537d91f659c0e87c890c

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Citations in the corpus

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy (2009, background): “For a general presentation of this ambitious numerical strategy, see [8] where the authors focus on collocation and spectral elements for the simulation of incompressible flows.”
High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster (2010, methodology): “In that regard, it can be seen as a close-to-optimal hp method obtained by combining the advantages of h methods that use a dense mesh with the advantages of p methods that use high-degree basis functions (see for instance [17, 18, 19, 20, 21, 22, 23, 24], among many others).”
Formulation of a Galerkin spectral element-fourier method for three-dimensional incompressible flows in cylindrical geometries (2004, methodology): “A popular alternative to velocity (or pressure) correction schemes is to directly invert the Stokes operator which is a mixed-type problem and typically requires a PN–PN 2 discretisation for velocity and pressure, respectively [6,7].”
The Newmark scheme as velocity–stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics (2005, neutral): “(13) Denoting uhei |rst = uhei (ξ r , ξ s , ξ t ), a useful vector representation of the coefficients of the polynomial interpolation (see e.g. Deville et al. 2002), is uehi := ( uehi |1, · · · , uehi |l̂ , · · · , uehi |N )T := (uehi |000, uehi |100, · · · , uehi |rst , · · · , uehi |N N N )T ,…”
MFEM: a modular finite element methods library (2019, background): “This section introduce partial assembly and sum factorization [73, 33], which reduce both the assembly storage and number of floating point operations required to apply the operator, and discusses general algorithm opportunities and challenges in the MFEM code.”
Modular and flexible spectral-element waveform modelling in two and three dimensions (2018, background): “First, there are significant efficiency gains in this ‘on-the-fly’ computation of the stiffness matrix for all wave equation types, although these gains are restricted to hypercube-type elements with a tensorized basis (Deville et al. 2002).”
Description of the NCAR Community Atmosphere Model (CAM 3.0) (2004, methodology): “The SEM divergence, gradient and curl can all be evaluated at the (d+ 1)(3) GLL nodes within each element in O(d) operations per node using the tensor-product property of these points [Deville et al., 2002; Karniadakis and Sherwin, 2005].”
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, methodology): “Tensor products inside each element may be optimized to reach very high efficiency (Deville et al. 2002), and mesh point and element numbering may be optimized to reduce processor cache misses and improve cache reuse (Komatitsch et al. 2008).”
Spectral and High-Order Methods with Applications (2006, methodology): “We refer to the books[162, 89, 40, 56] for more details on the approximation of Navier-Stokes equations by finite elements, spectral and spectral element methods.”
Entropy viscosity method for nonlinear conservation laws (2011, neutral): “Details can be found in [7].”
On the front velocity of gravity currents (2007, methodology): “In this work we have employed two different numerical techniques: a spectral multidomain code (Deville et al. 2002) and a fully de-aliased pseudo-spectral code (Canuto et al.”
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model (2012, methodology): “Owingtothetensorproductdecom-position,theSEMdivergence,gradientandcurlcanallbe evaluatedatthe ð d þ 1 Þ 2 GLL nodes within each element in O ð d Þ operations per node using the tensor-product property of these points (Deville et al. 2002; Karniadakis and Sherwin 2005).”