An algorithm for adaptive refinement of triangular element meshes

Nambiar, R.V.; Valera, R. S.; Lawrence, K. L.; Morgan, Robert B.; Amil, David

doi:10.1002/nme.1620360308

Cited by 42 publications

(17 citation statements)

References 10 publications

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“…The algorithms have been successfully used to implement adaptive (and adaptive multigrid) software in two dimensions [8,10,13,14], and have been generalized and used in the 3-dimensional context [5,7,18]. Derefinement algorithms, suitable to refine and derefine the mesh in the course of adaptive computations, such as needed in complex time-dependent problems (which require moving regions of refinement) have also been developed [16].…”

Section: Introduction: the Triangulation Refinement Problemmentioning

confidence: 99%

The 4-triangles longest-side partition of triangles and linear refinement algorithms

Rivara

Iribarren

1996

Math. Comp.

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Abstract. In this paper we study geometrical properties of the iterative 4-triangles longest-side partition of triangles (and of a 3-triangles partition), as well as practical algorithms based on these partitions, used both directly for the triangulation refinement problem, and as a basis for point insertion strategies in Delaunay refinement algorithms. The 4-triangles partition is obtained by joining the midpoint of the longest side with the opposite vertex and the midpoints of the two remaining sides. By means of simple geometrical arguments we show that the iterative partition of obtuse triangles systematically improves the triangles (while they remain obtuse) in the following sense: the sequence of smallest angles monotonically increases while the sequence of largest angles monotonically decreases in an amount (at least) equal to the smallest angle of each iteration. This allows us to improve the known bound on the smallest angle (without making use of previous results), and to obtain a better a priori bound on the number of similarly distinct triangles, as a function of the geometry of the initial triangle. Numerical evidence, showing that the practical behavior of the 4-triangles partition is in complete agreement with this theory, is included. A 4-triangles refinement algorithm is also discussed and illustrated. Furthermore, we show that the time cost of the algorithm is linear independently of the size of the triangulation.

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Section: Introduction: the Triangulation Refinement Problemmentioning

confidence: 99%

The 4-triangles longest-side partition of triangles and linear refinement algorithms

Rivara

Iribarren

1996

Math. Comp.

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“…See e.g. the applications of Nambiar et al [31], Muthukrishnan et al [30]. Based on the longest edge idea over Delaunay meshes, Lepp-Delaunay algorithms for triangulation improvement have been also developed [39,41,44] 2.…”

Section: Introductionmentioning

confidence: 99%

Multithread parallelization of Lepp-bisection algorithms

Rivara

Rodríguez

Montenegro

et al. 2012

Applied Numerical Mathematics

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Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained. Multithread parallelization of lepp-bisection algorithms AbstractLongest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained.

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“…triangular elements and quadrilateral elements. The triangular elements have distinct advantages over the quadrilateral elements for mesh discretization because they are convenient for local mesh re"nement and automatic mesh generation and thus facilitate the modeling of arbitrary geometry [1,2].…”

Section: Introductionmentioning

confidence: 99%

An assumed strain formulation of efficient solid triangular element for general shell analysis

Kim

Lee

2000

Int. J. Numer. Meth. Engng.

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SUMMARYAn e$cient assumed strain triangular solid element is developed for the analysis of plate and shell structures. The "nite element formulation is based on the two-"eld assumed strain formulation with two independent "elds of assumed displacement and assumed strain. The assumed strain "eld is carefully selected to alleviate the shear locking e!ect without triggering undesirable spurious kinematic modes. The curvilinear surface of shell structures is modelled with #at facet elements to obviate the membrane locking e!ect. The patch tests are successfully passed, and numerical test involving various example problems demonstrates the validity and e$ciency of the present element.

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An algorithm for adaptive refinement of triangular element meshes

Cited by 42 publications

References 10 publications

The 4-triangles longest-side partition of triangles and linear refinement algorithms

The 4-triangles longest-side partition of triangles and linear refinement algorithms

Multithread parallelization of Lepp-bisection algorithms

An assumed strain formulation of efficient solid triangular element for general shell analysis

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