Adaptive mesh generation for curved domains

Applied Numerical Mathematics

Volumn 52, Issue 2-3 SPEC. ISS., 2005, Pages 251-271

  Shephard, Mark S ^a   Flaherty, Joseph E ^a   Jansen, Kenneth E ^a   Li, Xiangrong ^a   Luo, Xiaojuan ^a   Chevaugeon, Nicolas ^a   Remacle, Jean François ^b   Beall, Mark W ^c   O'Bara, Robert M ^c  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c Simmetrix Inc   (United States)

Author keywords

Adaptive meshes; Anisotropic meshes; Curved meshes

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; FINITE ELEMENT METHOD; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SET THEORY;

ADAPTIVE MESHES; ANISOTROPIC MESHES; CURVED MESHES; MESH METRIC;

COMPUTER AIDED DESIGN;

EID: 10444248225     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.08.040     Document Type: Conference Paper

References (29)

1. S. Adjerid, K.D. Devine, J.E. Flaherty, L. Krivodonova, A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 191 (2002) 1097-1112.
2. B. Andersson, U. Falk, I. Babuska, T. V. Petersdorff, Reliable stress and fracture mechanics analysis of complex components using a h-p version of fern, Internat. J. Numer. Methods Engrg. 38 (1995) 2135-2163.
3. I. Babuska, Uncertainties in engineering design: Mathematical theory and numerical practice, in: J. A. Bennett, M.E. Botkin (Eds.), The Optimum Shape: Automated Structural Design, Plenum, 1986, pp. 171-197.
4. I. Babuska, M. Suri, The p and h-p versions of the finite element method, basic principles and properties, SIAM Rev. 36 (4) (1994) 578-632.
5. I. Babuska, B. Anderson, B. Guo, J.M. Melenk, H.S. Oh, Finite element method for solving problems with singular solutions, J. Comput. Appl. Math. 74 (1996) 51-70.
6. I. Babuska, T.V. Petersdorff, B. Anderson, Numerical treatment of vertex singularities and intensity factors for mixed boundary value problems for the Laplace equation, SIAM J. Numer. Anal. 31 (5) (1994) 1265-1288.
7. M.W. Beall, J. Walsh, M.S. Shephard, Accessing CAD geometry for mesh generation, in: 12th International Meshing Roundtable, Sandia National Laboratories, SAND-2003-3030P, 2003, pp. 33-42.
8. M.W. Beall, M.S. Shephard, A general topology-based mesh data structure, Internat. J. Numer. Methods Engrg. 40 (1997) 1573-1596.
9. H. Borouchaki, P.L. George, F. Hecht, P. Laug, Saltel, Delaunay mesh generation governed by metric specifications, part I: algorithms, and part II: applications, Finite Elem. Anal. Des. 25 (1997) 61-109.
10. H.L. de Cougny, M.S. Shephard, Parallel refinement and coarsening of tetrahedral meshes, Internat. J. Numer. Methods Engrg. 46 (1999) 1101-1125.
11. S. Dey, R.M. O'Bara, M.S. Shephard, Curvilinear mesh generation in 3D, Computer Aided Geom. Design 33 (2001) 199-209.
12. R. Garimella, M. S. Shephard, Boundary layer mesh generation for viscous flow simulations in complex geometric domains, Internat. J. Numer. Methods Engrg. 49 (1-2) (2000) 193-218.
13. P.L. George, F. Hecht, Non isotropic grids, in: J. Thompson, B.K. Soni, N.P. Weatherill (Eds.), CRC Handbook of Grid Generation, CRC Press, Boca Raton, 1999, pp. 20.1-20.29.
14. M.K. Georges, M.S. Shephard, Automated adaptive two-dimensional system for the hp-version of the finite element method, Internat. J. Numer. Methods Engrg. 32 (1991) 867-893.
15. G. Kunert, Toward anisotropic mesh construction and error estimation in the finite element method, Numer. Methods Partial Differential Equations 18 (2002) 625-648.
16. X. Li, M.S. Shephard, M.W. Beall, Accounting for curved domains in mesh adaptation, Internat. J. Numer. Methods Engrg. 58 (2003) 246-276.
17. X. Li, M.S. Shephard, M.W. Beall, 3D anisotropic mesh adaptation by mesh modifications, Comput. Methods Appl. Mech. Engrg., 2005, in press.
18. A. Liu, B. Joe, Relationship between tetrahedron shape measures, BIT 34 (1994) 268-287.
19. X.J. Luo, M.S. Shephard, J.F. Remacle, R.M. O'Bara, M.W. Beall, B.A. Szabo, R. Actis, p-version mesh generation issues, in: 11th International Meshing Roundtable, Sandia National Laboratories, 2002, pp. 343-354.
20. R.M. O'Bara, M.W. Beall, M.S. Shephard, Attribute management system for engineering analysis, Engrg. Comput. 18 (4) (2002) 339-351.
21. S. Prudhomme, J.T. Oden, T. Westermann, J. Bass, M.E. Botkin, Practical methods for a posteriori error estimation in engineering applications, Internat. J. Numer. Methods Engrg. 56 (2003) 1193-1224.
22. E. Rank, I. Babuska, An expert system for the optimal mesh design in the hp-version of finite element method, Internat. J. Numer. Methods Engrg. 24 (1987) 2087-2106.
23. J.-F. Remacle, M.S. Shephard, An algorithm oriented mesh database, Internat. J. Numer. Methods Engrg. 58 (2003) 349-374.
24. J.-F. Remacle, X. Li, M.S. Shephard, J.E. Flaherty, Anisotropic adaptive simulation of transient flows, Internat. J. Numer. Methods Engrg., submitted for publication.
25. M.S. Shephard, Meshing environment for geometry-based analysis, Internat. J. Numer. Methods Engrg. 47 (1-3) (2000) 169-190.
26. M.S. Shephard, M.K. Georges, Reliability of automatic 3D mesh generation, Comput. Methods Appl. Mech. Engrg. 101 (1992) 443-462.
27. B.A. Szabo, I. Babuska, Finite Element Analysis, Wiley, New York, 1991.
28. K. Weiler, The radial edge structure: a topological representation for non-manifold geometric modeling, in: M.J. Wozny, H. McLaughlin, J. Encarnacao (Eds.), Geometric Modeling for CAD Applications, IFIP WG5.2 Working Conference, Rensselaerville, NY, May 12-14, 1986,1988, pp. 3-36.
29. C.H. Whiting, K.E. Jansen, A stabilized finite element method for incompressible Navier-Stokes equations using a hierarchical basis, Internat. J. Numer. Methods Fluids 35 (2001) 93-116.