Design and data structure of fully adaptive, multigrid, finite-element software

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Design and data structure of fully adaptive, multigrid, finite-element software

Full text

Pdf (1.40 MB)

Source

ACM Transactions on Mathematical Software (TOMS) archive
Volume 10 , Issue 3 (September 1984) table of contents

Pages: 242 - 264

Year of Publication: 1984

ISSN:0098-3500

Author

Maria-Cecilia Rivara

Catholic University, Leuven, Belgium

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 70, Citation Count: 6

Additional Information:

references cited by index terms review collaborative colleagues

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/1271.1274 What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BABUSKA, I., The self-adaptive approach in the finite element method. In The Mathematics of Finite Element and Applications, J.R. Whiteman, Ed. Academic Press, New York 1976, pp. 125-143
	2	BABUSKA, I., AND RHEINROLDT, W.C. Computational aspects of finite element method. In Mathematical Software III, J.R. Rice, Ed. Academic Press, New York, 1977, pp. 225-255.
	3	BABUSKA, I., AND RHEINBOLDT, W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978), 736-754.
	4	BABUSKA, I., AND RHEINEOLDT, W.C. Reliable error estimation and mesh adaptation for the finite element method. In Computational Methods m Nonlinear Mechanics, J.T. Oden, Ed. Elsevier North Holland, Amsterdam, 1980. 67-108.
	5	BANK, R.E. PLTMG Users' Guide. Dept. of Mathematics, Univ. of California, San Diego, June, 1981 version.
	6	BANK, R.E., AND DUPONT, T. An optimal order process for solving finite element equations. Math Comput., 36 (1981), 35-51.
	7	BANK, R.E., AND SHERMAN, A.H. The use of adaptive grid refinement for badly behaved elliptic partial differential equations. In Mathematics and Computers in Simulation XXII, North Holland, Amsterdam, 1980. 18-24.
	8	BRANDT, A. Multilevel adaptive solutions to boundary value problems. Math. Comput. 31 (1977), 390.
	9	John Alan George, Computer implementation of the finite element method, 1971
	10	Alan George , Joseph W. Liu, Computer Solution of Large Sparse Positive Definite, Prentice Hall Professional Technical Reference, 1981
	11	HACKBUSCH, W. On the convergence of multigrid iterations, Beitrage. Numer. Math 9 (1981), 239.
	12	HACKBUSCH, W. Multi-grid convergence theory. In Multigrid Methods, Lecture Notes in Mathemattcs 960, W. Hackbusch and U. Trottenberg, Eds. Springer-Verlag, New York, 1982, pp. 177-219
	13	David R. Kincaid , John R. Respess , David M. Young , Rober R. Grimes, Algorithm 586: ITPACK 2C: A FORTRAN Package for Solving Large Sparse Linear Systems by Adaptive Accelerated Iterative Methods, ACM Transactions on Mathematical Software (TOMS), v.8 n.3, p.302-322, Sept. 1982 [doi>10.1145/356004.356009]
	14	Donald E. Knuth, The art of computer programming, volume 1 (3rd ed.): fundamental algorithms, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1997
	15	NICOLAIDES, R.A. On some theoretical and practical aspects of multigrid methods. Math of Comput. 33 (1979), 933-952.
	16	Werner C. Rheinboldt , Charles K. Mesztenyi, On a Data Structure for Adaptive Finite Element Mesh Refinements, ACM Transactions on Mathematical Software (TOMS), v.6 n.2, p.166-187, June 1980 [doi>10.1145/355887.355891]
	17	RICE, J.R, HOUSTiS, E.N., AND DYKSEN, W.R. A population of hnear second order elliptic partial differentml equations on rectangular domains. Part I. Math. Comput. 36 (1981), 475-484.
	18	RIVAl{A, M.C. Adaptive multigrid software for the finite element method, Ph.D. dissertation Leuven, Belgium. 1984.
	19	RI VARA, M.C. Algorithms for refining triangular grids suitable for adaptive and multigrid techniques. Int. J. Numer. Methods Eng. 20 (1984), 745-756.
	20	RIVARA, M.C. Mesh refinement processes based on the generalized bisection of simplices. SIAM Numer. Anal. To be published.
	21	SEWELL, G. A finite element program with automatic, user-controlled mesh grading. In Advances in Computer Methods {or Partial Differential Equations III, R. Vichnevetsky and R.S. Stepleman, Eds. IMACS, Rutgers Univ., New Brunswick, N.J., 1979, pp. 8-10.
	22	STUBEN, K. NDTROTTENBERGU. Multigrldmethods: Fundamentalalgorlthms, modelproblem analysis and apphcations. In Multigrwl Methods, Lecture Notes m Math. 960, W. Hackbusch and Trottenberg Eds Springer-Verlag, New York, 1982, pp. 1-176.
	23	WEISI{R, A. Local-mesh, local-order, adaptive finite element methods with a posteriori error estimators for elliptlc partial differential equations. Tech. Rep. 213. Dept. of Computer Science, Umv., New Haven, CT., 1981.
	24	YOUNG, D.M. Iterative solutmn of linear systems arising from finite element techniques. In Mathematics of Finite Elements and Applications, J.R. Whiteman Ed. Academic Press, New York, 1976, pp. 439-464.
	25	Pamela Zave , Werner C. Rheinboldt, Design of an Adaptive, Parallel Finite-Element System, ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.1-17, March 1979 [doi>10.1145/355815.355816]

CITED BY 6

	R. D. Williams, DIME: a programming environment for unstructured triangular meshes on a distributed-memory parallel processor, Proceedings of the third conference on Hypercube concurrent computers and applications, p.1770-1787, January 1989, Pasadena, California, United States
	William F. Mitchell, A comparison of adaptive refinement techniques for elliptic problems, ACM Transactions on Mathematical Software (TOMS), v.15 n.4, p.326-347, Dec. 1989
	Pankaj Kumar, Language support for data parallelism in pointer based dynamic data structures, Proceedings of the 1993 conference of the Centre for Advanced Studies on Collaborative research: distributed computing, October 24-28, 1993, Toronto, Ontario, Canada
	Angel Plaza, The eight-tetrahedra longest-edge partition and Kuhn triangulations, Computers & Mathematics with Applications, v.54 n.3, p.427-433, August, 2007
	Peter Bastian , Christian Wieners, Multigrid Methods on Adaptively Refined Grids, Computing in Science and Engineering, v.8 n.6, p.44-54, November 2006
	Maria-Cecilia Rivara, Lepp-bisection algorithms, applications and mathematical properties, Applied Numerical Mathematics, v.59 n.9, p.2218-2235, September, 2009

INDEX TERMS

Classification:
E. Data

F. Theory of Computation
F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
F.2.1 Numerical Algorithms and Problems
Subjects: Computations on matrices

G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.3 Numerical Linear Algebra
Subjects: Sparse, structured, and very large systems (direct and iterative methods); Linear systems (direct and iterative methods)
G.1.8 Partial Differential Equations
Subjects: Elliptic equations; Finite element methods

General Terms:
Algorithms, Design

REVIEW

"R. Bruce Simpson : Reviewer"

The major feature of this paper for the reviewer was the discussion of a data structure for representing a nested series of general triangular grids generated by essentially arbitrary (conforming) refinement strategies; that is an alternative to more...

Collaborative Colleagues:

Maria-Cecilia Rivara: colleagues

Adobe Acrobat

QuickTime

Windows Media Player

Real Player