A COARSENING ALGORITHM ON ADAPTIVE GRIDS BY NEWEST VERTEX BISECTION AND ITS APPLICATIONS

被引：34

作者：

Chen, Long ^{[1
]}

Zhang, Chensong ^{[2
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 06期

关键词：

Adaptive finite element method; Coarsening; Newest vertex bisection; Multilevel preconditioning; FINITE-ELEMENT-METHOD; POSTERIORI ERROR ESTIMATION; LINEAR PARABOLIC PROBLEMS; ELLIPTIC RECONSTRUCTION; ITERATIVE METHODS; REFINEMENT; PRECONDITIONERS; EQUATIONS; SPACES;

D O I：

10.4208/jcm.1004-m3172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

引用

页码：767 / 789

页数：23

共 36 条

[1] An odyssey into local refinement and multilevel preconditioning III: Implementation and numerical experiments
Aksoylu, B
Bond, S
Holst, M
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 25 (02) : 478 - 498
[2] THE POST-PROCESSING APPROACH IN THE FINITE-ELEMENT METHOD .3. A POSTERIORI ERROR-ESTIMATES AND ADAPTIVE MESH SELECTION
BABUSKA, I
MILLER, A
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1984, 20 (12) : 2311 - 2324
[3] deal. II - A general-purpose object-oriented finite element library
Bangerth, W.
Hartmann, R.
Kanschat, G.
[J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2007, 33 (04):
[4] THE HIERARCHICAL BASIS MULTIGRID METHOD
BANK, RE
DUPONT, TF
YSERENTANT, H
[J]. NUMERISCHE MATHEMATIK, 1988, 52 (04) : 427 - 458
[5] Efficient algorithms for Petersen's matching theorem
Biedl, TC
Bose, P
Demaine, ED
Lubiw, A
[J]. JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, 2001, 38 (01): : 110 - 134
[6] THE FINITE-ELEMENT METHOD FOR PARABOLIC EQUATIONS .2. A POSTERIORI ERROR ESTIMATION AND ADAPTIVE APPROACH
BIETERMAN, M
BABUSKA, I
[J]. NUMERISCHE MATHEMATIK, 1982, 40 (03) : 373 - 406
[7] THE FINITE-ELEMENT METHOD FOR PARABOLIC EQUATIONS .1. A POSTERIORI ERROR ESTIMATION
BIETERMAN, M
BABUSKA, I
[J]. NUMERISCHE MATHEMATIK, 1982, 40 (03) : 339 - 371
[8] Adaptive finite element methods with convergence rates
Binev, P
Dahmen, W
DeVore, R
[J]. NUMERISCHE MATHEMATIK, 2004, 97 (02) : 219 - 268
[9] A BASIC NORM EQUIVALENCE FOR THE THEORY OF MULTILEVEL METHODS
BORNEMANN, F
YSERENTANT, H
[J]. NUMERISCHE MATHEMATIK, 1993, 64 (04) : 455 - 476
[10] BRAMBLE JH, 1990, MATH COMPUT, V55, P1, DOI 10.1090/S0025-5718-1990-1023042-6

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