Longest-edge n-section algorithms: Properties and open problems

被引：6

作者：

Korotov, Sergey ^{[1
]}

Plaza, Angel ^{[2
]}

Suarez, Jose P. ^{[2
]}

机构：

[1] Bergen Univ Coll, Dept Comp Math & Phys, N-5020 Bergen, Norway

[2] Univ Las Palmas Gran Canaria, Div Math Graph & Computat MAGiC, IUMA, Informat & Commun Syst, Canary Islands, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 293卷

关键词：

Longest-edge n-section algorithm; Simplicial partition; Angle conditions; Finite element method; Mesh refinement; Mesh regularity; BISECTION METHOD; REFINEMENT ALGORITHM; FASTER CONVERGENCE; TRIANGULAR GRIDS; LOCAL REFINEMENT; ANGLE CONDITION; NON-DEGENERACY; REGULARITY; PROPAGATION; PARTITION;

D O I：

10.1016/j.cam.2015.03.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we survey all known (including own recent results) properties of the longest-edge n-section algorithms. These algorithms (in classical and recently designed conforming form) are nowadays used in many applications, including finite element simulations, computer graphics, etc. as a reliable tool for controllable mesh generation. In addition, we present a list of open problems arising in and around this topic. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：139 / 146

页数：8

共 10 条

[1] Properties of the longest-edge n-section refinement scheme for triangular meshes
Suarez, Jose P.
MorenoB, Tania
Abad, Pilar
Plaza, Angel
APPLIED MATHEMATICS LETTERS, 2012, 25 (12) : 2037 - 2039
[2] On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n
Korotov, Sergey
Plaza, Angel
Suarez, Jose P.
COMPUTER AIDED GEOMETRIC DESIGN, 2015, 32 : 69 - 73
[3] A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes
Perdomo, Francisco
Plaza, Angel
APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (04) : 2342 - 2344
[4] A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes (vol 219, pg 2342, 2012)
Perdomo, Francisco
Plaza, Angel
APPLIED MATHEMATICS AND COMPUTATION, 2015, 260 : 412 - 413
[5] Properties of triangulations obtained by the longest-edge bisection
Perdomo, Francisco
Plaza, Angel
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2014, 12 (12): : 1796 - 1810
[6] New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations
Rivara, MC
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1997, 40 (18) : 3313 - 3324
[7] Longest-edge algorithms for size-optimal refinement of triangulations
Bedregal, Carlos
Rivara, Maria-Cecilia
COMPUTER-AIDED DESIGN, 2014, 46 : 246 - 251
[8] New Longest-Edge algorithms for the refinement and/or improvement of unstructured triangulations
Rivara, Maria-Cecilia
John Wiley & Sons Ltd, Chichester, United Kingdom (40):
[9] Two-sided estimation of diameters reduction rate for the longest edge n-section of triangles with n ≥ 4
Suarez, Jose P.
Moreno, Tania
Plaza, Angel
Abad, Pilar
APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 492 - 500
[10] Mesh quality improvement and other properties in the four-triangles longest-edge partition
Plaza, A
Suárez, JP
Padrón, MA
Falcón, S
Amieiro, D
COMPUTER AIDED GEOMETRIC DESIGN, 2004, 21 (04) : 353 - 369

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