Fundamentals of Grid Generation

By Patrick M. Knupp, S. Steinberg. 2020

383 citations recorded by the source corpus.

Preliminaries. Application to Hosted Equations. Grid Generation on the Line. Vector Calculus and Differential Geometry. Classical Planar Grid Generation. Variational Planar Grid Generation. Tensor Analysis and Transformation Relationships. Advanced Planar Variational Grid Generation. Grid Generation in Three Dimensions. Variational Grid Generation on Curves and Surfaces. Contravariant Functionals: Alignment and Diagonalization. Tensor Coefficients. Fortran Code Directory. A Rogue's Gallery of Grids.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/eeb45e5349474d8d9b03059dd9a2b1e393edeb81

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

Citations in the corpus

Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated qu (2000, background): “m (‘2 m + ‘ 2 m+1) =gm − 2 There are a number of related objective functions: FModLiao =FCNG + M gives the discrete form of the ‘modi"ed Liao’ functional proposed in Reference [12].”
On the Fibonacci k-numbers (2007, background): “Grid generation and, in particular, the construction of ‘quality’ grids is a major issue in both geometric modeling and engineering analysis [42–46].”
Untangling of 2D meshes in ALE simulations (2004, positive): “The next example shows the untangling of a structured mesh, called the “horseshoe” mesh shown in Figure 16b obtained by simple Laplacian smoothing of the mesh shown in Figure 16a [20].”
Mathematical Principles of Anisotropic Mesh Adaptation (2006, background): “, see [9, 10, 23, 41, 54] and the books [24, 40, 45, 53], and the references therein.”
Dynamics and breakup of a contracting liquid filament (2004, methodology): “Their method consists of constructing a weighted combination of functionals which impose orthogonality of coordinate lines, smoothness of coordinate lines and a controlled distribution of elements (see e.g. Knupp & Steinberg 1993).”
Numerical Methods for Elliptic and Parabolic Partial Differential Equations (2003, background): “Methods to produce structured grids can be found, for instance, in the books [23] or [33].”
Variational mesh adaptation II: error estimates and monitor functions (2003, background): “, see [5,6,11,14,17,19,20,25,29] and the books [12,18,22,26] and references therein.”
Isogeometric Shape Optimization of Vibrating Membranes (2011, background): “The identity gives rise to Winslow functional [33] p In order to make g “as identically diagonal as possible” we would like to minimize W ; however, to ensure the positivity of the determinant we consider the following constrained optimization problem: (cid:0)b (cid:1) In (22), z 0 > 0 is computed…”
Mesh Generation (2020, methodology): “References [12] and [13] are detailed expositions of structured mesh generation.”