Unstructured grid generation and a simple triangulation algorithm for arbitrary 2-D geometries using object oriented programming

Date

1997-01-30

Author

Karamete, BK
Tokdemir, Turgut
Ger, M

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

168
views

0
downloads

This paper describes the logic of a dynamic algorithm for a general 2D Delaunay triangulation of arbitrarily prescribed interior and boundary nodes. The complexity of the geometry is completely arbitrary. The scheme is free of specific restrictions on the input of the geometrical data. The scheme generates triangles whose associated circumcircles contain 'no nodal points except their vertices. There is no predefined limit for the number of points and the boundaries. The direction of generation of the triangles cannot be determined a priori as opposed to the moving front techniques. An automatic node placement scheme reflecting the initial boundary point spacings is used. The successive refinement scheme results in such a point distribution that the triangulation algorithm need not perform any geometric intersection check for overlapped triangles and penetrated boundaries. Further computational saving is provided by using a special binary tree (ADT) in which the points are ordered such that contiguous points in the list are neighbours in physical space. The method consists of a set of simple rules to understand. The dynamic nature of the Object Oriented Programming (OOP) of the algorithms provides efficient memory management on the insertion, deletion and searching processes. The computational effort bears a linear relationship between the CPU time and the total number of nodes. Some of the existing methods in the literature regarding triangular mesh generation are discussed in context.

Subject Keywords

General Engineering, Applied Mathematics, Numerical Analysis

URI

https://hdl.handle.net/11511/39504

Journal

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

DOI

https://doi.org/10.1002/(sici)1097-0207(19970130)40:2<251::aid-nme62>3.0.co;2-u

Collections

Department of Engineering Sciences, Article

Suggestions

OpenMETU
Core

Intelligent analysis of chaos roughness in regularity of walk for a two legged robot Kaygisiz, BH; Erkmen, İsmet; Erkmen, Aydan Müşerref (Elsevier BV, 2006-07-01) We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being ...
NONCOMMUTATIVE MACKEY THEOREM Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01) In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
A quasi-incompressible and quasi-inextensible element formulation for transversely isotropic materials Dal, Hüsnü (Wiley, 2019-01-06) The contribution presents a new finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelastic behavior of transeversely isotropic materials and addresses its computational aspects. The material formulation is presented in purely Eulerian setting and based on the additive decomposition of the free energy function into isotropic and anisotropic parts, where the former is further decomposed into isochoric and volumetric parts. For the quasi-incompressible response, the Q1P0 ele...
AN OPTIMAL-CONTROL PROBLEM WITH NONLINEAR ELLIPTIC STATE-EQUATIONS Leblebicioğlu, Mehmet Kemal (Elsevier BV, 1992-02-01) In this article some of the results for optimal control of linear systems have been generalized to a nonlinear case. This is achieved by employing standard techniques of the nonlinear theory. After demonstrating the existence of optimal controls, finite element method is used to discretize the problem. The resulting finite dimensional problem is solved by a special algorithm. The theoretical discussions are completed by proving that approximate solutions are reduced to exact solutions as the element size te...

Citation Formats

B. Karamete, T. Tokdemir, and M. Ger, “Unstructured grid generation and a simple triangulation algorithm for arbitrary 2-D geometries using object oriented programming,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, pp. 251–268, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39504.