A numerical method for computing minimal surfaces in arbitrary dimension

Journal of Computational Physics

Volumn 206, Issue 2, 2005, Pages 650-660

  Cecil, Thomas ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DROP BREAKUP; IMAGE PROCESSING; LEVEL MEASUREMENT;

ARBITRARY DIMENSION; CODIMENSION; CURVATURE FLOW; FIXED BOUNDARIES; IMAGES PROCESSING; LEVEL SET; LEVEL SET METHOD; MATERIAL SCIENCE; MEAN CURVATURE FLOW; MINIMAL SURFACES;

NUMERICAL METHODS;

EID: 18144376994     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.12.022     Document Type: Article

References (30)

1. S. Andersson S.T. Hyde K. Larsson S. Lidin Minimal surfaces and structures: From inorganic and metal crystals to cell membranes and biopolymers Chem. Rev. 1988 88
2. K.A. Brakke The surface evolver Exp. Math. 1 2 1992 141-165
3. T. Cecil J.L. Qian S. Osher Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions J. Comput. Phys. 196 2004 327-347
4. B. Chen M. Eddaoudi S.T. Hyde M. O'Keeffe O.M. Yaghi Interwoven metal-organic framework on a periodic minimal surface with extra-large pores Science 2001 291
5. L.-T. Cheng. The level set method applied to geometrically based motion, materials science, and image processing. UCLA CAM Report, 00-20
6. D.L. Chopp Computing minimal surfaces via level set curvature flow J. Comput. Phys. 106 1 1993 77-91
7. C. Coppin D. Greenspan A contribution to the particle modeling of soap films Appl. Math. Comput. 26 4 1988 315-331
8. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab, Minimal Surfaces, I,II, volume 295,296 of Grundlehren der Mathematis-chen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1992, Boundary regularity
9. J. Douglas A method of numerical solution of the problem of Plateau Ann. Math. (2) 29 1-4 1927/28 180-188
10. G. Dziuk An algorithm for evolutionary surfaces Numer. Math. 58 6 1991 603-611
11. G. Dziuk J.E. Hutchinson On the approximation of unstable parametric minimal surfaces Calc. Var. Partial Dif. 4 1 1996 27-58
12. G. Dziuk J.E. Hutchinson The discrete Plateau problem: Algorithm and numerics Math. Comp. 68 225 1999 1-23
13. D. Greenspan On approximating extremals of functionals. I. The method and examples for boundary value problems ICC Bull. 4 1965 99-120
14. M. Hinze On the numerical approximation of unstable minimal surfaces with polygonal boundaries Numer. Math. 73 1 1996 95-118
15. R.H.W. Hoppe Multigrid algorithms for variational inequalities SIAM J. Numer. Anal. 24 5 1987 1046-1065
16. S. Hyde S. Andersson K. Larsson Z. Blum T. Landh S. Lidin B.W. Ninham The Language of Shape: The Role of Curvature in Con- densed Matter: Physics, Chemistry, and Biology 1997 Elsevier Amsterdam 383 pp
17. S.T. Hyde S. Andersson A systematic net description of saddle polyhedra and periodic minimal surfaces Z. Krist. 168 1-4 1984 221-254
18. A. Iske T. Sonar On the structure of function spaces in optimal recovery of point functionals for ENO-schemes by radial basis functions Numer. Math. 74 2 1996 177-201
19. R.D. Kamien T.C. Lubensky Minimal surfaces, screw dislocations and twist grain boundaries Phys. Rev. Lett. 1999 82
20. Chohong Min Local level set method in high dimension and codimension J. Comput. Phys. 200 1 2004 368-382
21. H.U. Nissen Crystal orientation and plate structure in echinoderm plates Science 1969 166
22. J.C.C. Nitsche Lectures on Minimal Surfaces, vol. 1. Introduction, Fundamentals, Geometry and Basic Boundary Value Problems (Trans. Jerry M. Feinberg, with a German foreword) 1989 Cambridge University Press Cambridge
23. S.J. Osher J.A. Sethian Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 1988 12-49
24. S. Osher R.P. Fedkiw Level Set Methods and Dynamic Implicit Surfaces 2002 Oxford University Press
25. Harold R. Parks, Explicit determination of area minimizing hypersurfaces. II, Mem. Am. Math. Soc. 60(342) (1986) iv+90
26. Danping Peng B. Merriman S. Osher Hongkai Zhao Myungjoo Kang A PDE-based fast local level set method J. Comput. Phys. 155 2 1999 410-438
27. J. Strain Fast tree-based redistancing for level set computations J. Comput. Phys. 152 2 1999 664-686
28. L. Vese T. Chan A multiphase level set framework for image segmentation using the Mumford and Shah model Int. J. Comput. Vision 50 3 2002 271-293
29. H.G. von Schnering, R. Nesper, The curvature of chemical structures, in: International Workshop on Geometry and Interfaces, Aussois, 1990, J. Phys. 51(23, Suppl. Colloq. C7) (1990) 383-396
30. H.-J. Wagner A contribution to the numerical approximation of minimal surfaces Computing 19 1 1977/78 35-58