This paper presents the formulation, validation, and application of a spectral/hp algorithm for numerical solution of the Navier–Stokes and heat/scalar transport equations in arbitrarily moving complex geometries. The new spectral element algorithm is based on the arbitrary Lagrangian Eulerian formulation and utilizes modal expansion of Jacobi polynomials in mixed triangular and quadrilateral e...

This paper describes an algorithm for generating unstructured triangular meshes from a continuous two-dimensional object represented by an image. The algorithm uses squares as a background grid from which to build the quadrilateral elements that conform to the input contours. Then the triangulation is obtained by automatically choosing the diagonals that optimize the angles of the triangles. Th...

We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a multidimensional lattice characterized by the planarity of its elementary quadrilaterals. Therefore the linear property of planarity seems to be a basic geometric property underlying integrability....

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last s...

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal order interpolation for the velocity and pressure fields. Finally, we show by counterexample ...

Adaptive finite element procedures are presented for the analysis of broad classes of two-dimensional problems in visco plasticity which involve internal state variables. Several a posteriori error estimates are developed and used as a basis for refinements of meshes of triangular and quadrilateral elements. Algorithms are presented which reduce the computational complexity of the adaptive proc...

Low-distortion parameterization of 3D meshes is a fundamental problem in computer graphics. Several widely used approaches have been presented for triangular meshes. But no direct parameterization techniques are available for quadrilateral meshes yet. In this paper, we present a parameterization technique for non-closed quadrilateral meshes based on mesh simplification. The parameterization is ...

In this paper we present an efficient face-based connectivity coding technique for the special class of quadrilateral and the hybrid triangular-quadrilateral meshes. This work extends the main ideas of non-split encoding presented by the first contribution of the authors (Khattab, Abd El-Latif, Abdel Wahab and Tolba, 2007) for triangle meshes and improves over the compression results provided s...

Abstract: A graph G with p vertices is said to be strongly multiplicative if the vertices of G can be labeled with p consecutive positive integers 1, 2, ..., p such that label induced on the edges by the product of labels of end vertices are all distinct. In this paper we investigate strongly multiplicative labeling of some snake related graphs. We prove that alternate triangular snake and alte...

A non–oscillatory, high resolution reconstruction method on quadrilateral meshes in 2D is presented. It is a two–dimensional extension of Marquina’s hyperbolic method. The generalization to quadrilateral meshes allows the method to simulate realistic flow problems in complex domains. An essential point in the construction of the method is a second order accurate approximation of gradients on an...