Fundamentals of Engineering Numerical Analysis

By Parviz Moin. 2001

407 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/52a6a086e67e5c9c592877653df9a62cdd1d0c95

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In Computational Mechanics

Citations in the corpus

Characterizing possible failure modes in physics-informed neural networks (2021, background): “In the context of PDEs, F can be taxonomized into a parabolic, hyperbolic, or elliptic differential operator [23].”
A numerical method for large-eddy simulation in complex geometries (2004, neutral): “Keywords: Large-eddy simulation; Unstructured grids; Complex geometries; Energy-conserving schemes; Gas-turbine combustor”
Explicit Filtering and Reconstruction Turbulence Modeling for Large-Eddy Simulation of Neutral Boundary Layer Flow (2005, background): “Reconstruction is limited, however, by numerical errors (NE), which increase near the grid cutoff because of the modified wavenumber effect on finitedifference evaluation of derivatives (Moin 2001).”
Numerical Simulation of Flowing Blood Cells (2014, methodology): “Resolution can be quantified via the spectral properties of the discretization, comparing the effective wave number implied by a numerical approximation of, for example, a derivative with the exact wave number (Moin 2010).”
A steel–concrete composite beam model with partial interaction including the shear deformability of the steel component (2007, neutral): “This approximation implies that [14]: ∫ t”
Mobile Sensor Network Control Using Mutual Information Methods and Particle Filters (2010, methodology): “This integration can then be performed using an appropriate numerical quadrature technique [34].”
When and why PINNs fail to train: A neural tangent kernel perspective (2020, positive): “forward Euler [44]) discretization of above ODE system, the maximum learning rate should be less than or equal to 2/λmax(K̃(t)).”
The role of continuity in residual-based variational multiscale modeling of turbulence (2007, background): “A community of researchers focused on understanding fundamental physical behavior of turbulence through numerical simulation typically makes use of very simple geometries and high-order spectral or compact finite difference methods (see, e.g., [32, 34 ]).”
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, background): “This analysis has the flavor of what are usually referred to as ‘‘spectral methods,’’ which are accurate and efficient procedures, typically utilized for performing detailed studies of geometrically simple but physically complex phenomena, such as turbulence (see [46,47] for detailed descriptions an”
A high-resolution code for turbulent boundary layers (2009, background): “(5) are expanded in cosines along x, and the problem reduces to a series of one-dimensional Helmholtz problems along y, with a modified wavenumber for each cosine representing the finite differences in x [29].”
A further study of numerical errors in large-eddy simulations (2003, methodology): “Thus, the frequencies beyond the grid wavenumber cutoff are incorrectly ‘‘aliased’’ to wavenumbers that are resolved [7].”