Smooth and convex grid generation over general plane regions

Tinoco-Ruiz, José Gerardo; Barrera-Sánchez, P.

doi:10.1016/s0378-4754(98)00074-3

Cited by 21 publications

(8 citation statements)

References 5 publications

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“…If rectangular elements are used, as has been done in this paper, the methods here presented can be applied in domains with shapes of considerable generality, since the problem domain does not need to be a rectangle, and many of the nice matrix properties are preserved. However, the geometrical diversity of the possible problem domains is enhanced if the method is applied using rectangular meshes of the type reported Barrera-Sanchez et al (see [15,16]), or triangles.…”

Section: Discussionmentioning

confidence: 99%

TH-collocation for the biharmonic equation

Díaz¹,

Herrera

2005

Advances in Engineering Software

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Section: Discussionmentioning

confidence: 99%

TH-collocation for the biharmonic equation

Díaz¹,

Herrera

2005

Advances in Engineering Software

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“…. , Inverse Smoothness, (iength)-l. This objective function is an ad-hoc generalization that appears in [1] and others: Note that jlS(A) = f.s(A-l).…”

Section: Fa~~oint(a) =1 Adja 12= 02 I A-' 12mentioning

confidence: 99%

Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II?A framework for volume mesh optimization and the condition number of the Jacobian matrix

Knupp

2000

Int. J. Numer. Meth. Engng.

215

142

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SUMMARYThree-dimensional unstructured tetrahedral and hexahedral "nite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most e!ective in attaining valid, high-quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2;2 matrices do not hold for 3;3 matrices, signi"cant di!erences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equality in two dimensions of the smoothness and condition number of the Jacobian matrix objective functions does not extend to three dimensions and further, that the equality of the Oddy and condition number of the metric tensor objective functions in two dimensions also fails to extend to three dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral &whisker-weaved' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure. Published in 2000 by John Wiley & Sons, Ltd.KEY WORDS: unstructured grid generation; "nite element mesh; mesh optimization; smoothing; condition number A By valid it is meant that the elements are properly oriented with locally positive Jacobian determinant.

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“…The domains of interest here are simply connected polygonal domains -mostly irregular-which can not be decomposed into rectangles. For such domains, it is possible to generate suitable convex structured grids using the direct optimization method, as discussed in detail in [3,10,12,13,16]. To introduce the required notation for the grids, let m and n be the number of "vertical" and "horizontal" numbers of nodes on the "sides" of a typical domain boundary; the latter is the positively oriented polygonal Jordan curve γ of vertices…”

Section: Introductionmentioning

confidence: 99%

An heuristic finite difference scheme on irregular plane regions

Domínguez-Mota¹,

Fernandez-Valdez²,

Ruiz-Diaz³

et al. 2014

ams

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In this paper, we present an heuristic finite difference scheme for the second-order linear operator, which is derived from an unconstrained least squares problem defined by the consistency condition on the residuals of order one, two and three in the Taylor expansion of the local truncation error. It is based on a non-iterative calculation of the difference coefficients and can be used to solve efficiently Poisson-like equations on non-rectangular domains which are approximated by structured convex grids.

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Smooth and convex grid generation over general plane regions

Cited by 21 publications

References 5 publications

TH-collocation for the biharmonic equation

TH-collocation for the biharmonic equation

Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II?A framework for volume mesh optimization and the condition number of the Jacobian matrix

An heuristic finite difference scheme on irregular plane regions

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