Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I - A framework for surface mesh optimization

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 3, 2000, Pages 401-420

  Knupp, Patrick M ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Finite element mesh; Mesh optimization; Mesh smoothing; Unstructured grid generation

Indexed keywords

MATRIX ALGEBRA; OPTIMIZATION; TENSORS;

JACOBIAN MATRIX; MESH SMOOTHING; UNSTRUCTURED GRID GENERATION;

FINITE ELEMENT METHOD;

EID: 0033686077     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000530)48:3<401::AID-NME880>3.0.CO;2-D     Document Type: Article

References (26)

1. Freitag L, Jones M, Plassman P. An efficient parallel algorithm for mesh smoothing. In Proceedings of the fourth International Meshing Round Table, Sandia National Laboratories, 1995; 47-58.
2. Pardhanani A, Carey G. Optimization of computational grids. Numerical Methods for Partial Differential Equations 1988; 4(2):95-117.
3. Zavattieri P. Optimization strategies in unstructured mesh generation. International Journal for Numerical Methods in Engineering 1996; 39:2055-2071.
4. Canann S, Tristano J, Staten M. An approach to combined laplacian and optimization-based smoothing for triangular, quadrilateral and quad-dominant meshes. Proceedings of the 7th International Meshing Round Table, Detroit, 1998; 479-494.
5. Barerra P, Perez A, Castellanos L. Curvilinear Coordinate System Generation over Plane Irregular Regions. Facultad de Cienas UNAM: Mexico, 1992.
6. Castillo J. On variational grid generation. Ph.D. Thesis, University of New Mexico, 1987.
7. Castillo J. A direct variational grid generation method: Orthogonality control. In Numerical Grid Generation in Computational Fluid Mechanics '88, Sengupta S, Hausser J, Eiseman P, Thompson J (eds). Pineridge Press: Swansea, U.K. 1988; 247-256.
8. Castillo J. An adaptive direct variational grid generation method. Computers and Mathematics with Applications 1990; 4(1):1-9.
9. Castillo J. A discrete variational method. SIAM Journal on Scientific and Statistical Computing 1991; 12(2): 454-468.
10. Kennon S, Dulikravitch G. Generation of computational grids using optimization. AIAA Journal 1986; 24(7): 1069-1073.
11. Kumar A, Kumar N. A new approach to grid generation based on a local optimisation. In Numerical Grid Generation in Computational Fluid Mechanics '88, Sengupta S, Hausser J, Eiseman P, Thompson J (eds). Pineridge Press: Swansea U.K. 1988; 177-184.
12. Knupp P, Steinberg S. The Fundamentals of Grid Generation. CRC Press: Boca Raton FL, 1993.
13. Knupp P, Robidoux N. A framework for variational grid generation: conditioning the Jacobian matrix with matrix norms, to appear in SIAM J. Sci. Comput. 2000.
14. Knupp P. Robust grid generation on curves and surfaces. Ph.D. Thesis, University of New Mexico, 1989.
15. Knupp P. The direct variational grid generation method extended to curves. Applied Mathematical Computations 1991; 43:65-78.
16. CUBIT Mesh Generation Environment. SAND94-1100, Sandia National Laboratories, Albuquerque, NM 87185.
17. Knupp P. Winslow smoothing on two-dimensional unstructured meshes. Engineering with Computers 1999; 15: 263-268. See also the Proceedings of the Seventh International Meshing Round Table, Detroit, MI, October 1998; 449-457.
18. Knupp P. Winslow smoothing on two-dimensional unstructured meshes. Engineering with Computers 1999; 15: 263-268. See also the Proceedings of the Seventh International Meshing Round Table, Detroit, MI, October 1998; 449-457.
19. Robinson J. CRE method of element testing and the Jacobian shape parameters. Engineering Computations 1987; 4:113-118.
20. Brackbill J, Saltzman J. Adaptive zoning for singular problems in two dimensions. Journal of Computational Physics 1982; 46:342-368.
21. Gill P, Murray W, Wright M. Practical Optimization. Academic Press: New York, 1981.
22. Liao G. Variational approach to grid generation. Numerical Methods for Partial Differential Equations 1992; 8: 143-147.
23. Knupp P. A robust elliptic grid generator. Journal of Computational Physics 1992; 100:409-418.
24. Winslow AM. Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. Journal of Computational Physics 1967; 2:149-172.
25. Golub G, Van Loan C. Matrix Computations. Johns Hopkins University Press: Baltimore, MD, 1983.
26. Oddy A, Goldak J, McDill M, Bibby M. A distortion metric for isoparametric finite elements. Transactions on CSME, No. 38-CSME-32, Accession No. 2161, 1988.