The computation of simplicial approximations of implicitly defined p-dimensional manifolds

Computers and Mathematics with Applications

Volumn 36, Issue 6, 1998, Pages 93-113

  Brodzik, M L ^a,b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b NONE   (United States)

Author keywords

Delaunay triangulation; Nonlinear equations; Simplex overlap; Simplicial approximation; Solution manifolds

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; NONLINEAR EQUATIONS; SET THEORY;

DELAUNAY TRIANGULATION; SIMPLEX OVERLAP; SIMPLICIAL APPROXIMATION;

COMPUTATIONAL METHODS;

EID: 0032166207     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00164-3     Document Type: Article

References (18)

1. L.P. Chew, Guaranteed-quality mesh generation for curved surfaces, In Proceedings of the Ninth Annual ACM Symposium on Computational Geometry, San Diego, CA, May 19-21, 1993, ACM Press, New York, (1993).
2. M. Bern and D. Eppstein, Mesh generation and optimal triangulation, In Computing in Euclidean Geometry, (Edited by F.K. Hwang and D.Z. Du), World Scientific, Singapore, (1992).
3. E.L. Allgower and P.H. Schmidt, Piecewise-linear approximation of solution manifolds for nonlinear systems of equations, In Lecture Notes in Econ. and Math. Systems, Volume 226, Springer-Verlag, Heidelberg, (1984).
4. E.L. Allgower and P.H. Schmidt, An algorithm for piecewise-linear approximation of an implicitly defined manifold, SIAM J. Num. Anal. 22, 322-346, (1985).
5. E.L. Allgower and S. Gnutzmann, An algorithm for piecewise-linear approximation of implicitly defined two-dimensional surfaces, SIAM J. Num. Anal. 24, 452-469, (1987).
6. W.C. Rheinboldt, On a moving frame algorithm and the triangulation of equilibrium manifolds, In Bifurcations: Analysis, Algorithms, Applications, (Edited by T. Kuepper, R. Seydel and R. Troger) ISNM Volume 79, pp. 256-267, Birkhäuser, Basel, (1987).
7. W.C. Rheinboldt, On the computation of multi-dimensional solution manifolds of parametrized equations, Numer. Math. 53, 165-181, (1988).
8. M.L. Brodzik and W.C. Rheinboldt, The computation of simplicial approximations of implicitly defined two-dimensional manifolds, Computers Math. Applic. 28 (9), 9-21, (1994).
9. D.S. Mackey and R. Melville, A new algorithm for two-dimensional numerical continuation, Computers Math. Applic. 30 (1), 31-46, (1995).
10. M.E. Henderson, Computing implicitly defined surfaces: Two parameter continuation, Research Report RC 18777 (82115), IBM T. J. Watson Research Center, Yorktown Heights, NY, (March 1993).
11. M.L. Brodzik, Numerical approximation of manifolds, and applications, Ph.D. Thesis, Applied Mathematics, University of Pittsburgh, Pittsburgh, PA, (1996).
12. E.L. Allgower and K. Georg, Triangulations by reflections with applications to approximation, In Numerische Methoden der Approximationstheorie, Volume 4, ISNM 42, (Edited by L. Collatz, G. Meinardus and H. Werner), Birkhäuser-Verlag, Basel, (1978).
13. M.L. Brodzik, An algorithm for the numerical detection of simplex overlap, Appl. Math. Lett. 8 (4), 13-18, (1995).
14. P.J. Rabier and W.C. Rheinboldt, Submanifolds in finite-dimensional spaces, University of Pittsburgh, Pittsburgh, PA, (unpublished note).
15. M.L. Brodzik, An algorithm for computing simplicial approximations of implicitly defined p-dimensional manifolds, Technical Report ICMA-97-202, Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, (December 1997).
16. B. Joe, Construction of k-dimensional Delaunay triangulations using local transformations, SIAM J. Sci. Comput 14, 1415-1436, (1993).
17. G.W. Stewart, An iterative method for solving nonlinear inequalities, Research Report TR-1833, Department of Computer Science and Institute for Physical Science and Technology, University of Maryland, College Park, MD, (April 1987).
18. J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, (1983).