Automatic p-version mesh generation for curved domains
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To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.
Keywordsp-version method Curved meshes Graded meshes
This work was supported by the National Science Foundation through SBIR grant number DMI-0132742.
- 1.Anderson B, Falk U, Babuska I, Petersdorff TV (1995) Reliable stress and fracture mechanics analysis of complex components using a hp version of FEM. Int J Numer Methods Eng 38:2135–2163Google Scholar
- 6.Dey S, Shephard MS, Flaherty JE (1997) Geometry representation issues associated with p-version finite element computations. Comput Methods Appl Mech Eng 150(1–4):39–55Google Scholar
- 10.Garimella R, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations in complex geometric domains. Int J Numer Methods Eng 49(1–2):193–218Google Scholar
- 11.Harber R, Shephard MS, Abel JF, Gallagher RH, Greenberg DP (1981) A general two-dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings. Int J Numer Methods Eng 17:1015–1044Google Scholar
- 12.Li X, Shephard MS, Beall MW (2003) 3-D anisotropic mesh adaptation by mesh modifications. Comput Methods Appl Mech Eng (submitted)Google Scholar
- 13.Luo XJ, Shephard MS, Remacle JF, O’Bara RM, Beall MW, Szabo BA, Actis R (2002) p-version mesh generation issues. In: Proceedings of the 11th international meshing roundtable, Ithaca, New York, September 2002. Sandia National Laboratories, pp 343–354Google Scholar
- 16.Szabo BA, Babuska I (1991) Finite element analysis. Wiley, New YorkGoogle Scholar