Hessian-based anisotropic mesh adaptation in domains with discrete boundaries

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 20, Issue 4, 2005, Pages 391-402

  Vassilevski, Yu V ^a   Dyadechko, V G ^b   Lipnikov, K N ^b  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; DIFFUSION; MATHEMATICAL MODELS; PERFORMANCE; PROBLEM SOLVING;

BLACK-BOX METHODOLOGY; HESSIAN-BASED ANISOTROPY; HIGH-ORDER RECONSTRUCTION METHOD; SURFACE MESHES;

BOUNDARY CONDITIONS;

EID: 24344480543     PISSN: 09276467     EISSN: None     Source Type: Journal    
DOI: 10.1163/156939805775122307     Document Type: Article

References (15)

1. A. Agouzal, K. Lipnikov, and Yu. Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes. East-West J. Numer. Math. (1999) 7, No. 4, 223-244.
2. J. F. Bonnans, C. Gilbert, C. Lemarécha, and C. A. Sagastizábal, Numerical Optimization. Theoretical and Practical Aspects. Springer-Verlag, Berlin, 2003.
3. H. Borouchaki, F. Hecht, and P. J. Frey, Mesh gradation control. Inter. J. Numer. Meth. Engrg. (1998) 43, 1143-1165.
4. G. C. Buscaglia and E. A. Dari, Anisotropic mesh optimization and its application in adaptivity. Inter. J. Numer. Meth. Engrg. (1997) 40, 4119-4136.
5. P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.
6. J. Dompierre, M.-G. Vallet, M. Fortin, W. G. Habashi, D. Ait-Ali-Yahia, and A. Tam, Edge-based mesh adaptation for CFD. CERCA Report No. 95-73, 1995.
7. R. V. Garimella and B. K. Swartz, Curvature estimation for unstructured triangulations of surfaces. Los Alamos Report No. LA-UR-03-8240, Los Alamos, NM, http://math.lanl.gov/Research/Publications/Docs/garimella-2003-curvature.pdf.
8. R. Garimella, P. Knupp, and M. Shashkov, Triangular and quadrilateral surface mesh quality optimization using local parameterization. Comp. Meth. Appl. Mech. Engrg. (2004) 193, No. 9-11, 913-928.
9. K. Lipnikov and Yu. Vassilevski, Parallel adaptive solution of 3D boundary value problems by Hessian recovery. Comp. Meth. Appl. Mech. Engrg. (2003) 192, 1495-1513.
10. A. M. McIvor and R. J. Valkenburg, A comparison of local surface geometry estimation methods. Machine Vision and Appl. (1997) 10, 17-26.
11. M. Meyer, H. Lee, A. H. Barr, and M. Desbrun, Generalized barycentric coordinates on irregular polygons. J. Graphics Tools (2002) 7, No. 1, 13-22.
12. F. Mokhtarian, N. Khalili, and P. Yuen, Curvature computation of free-form 3-D meshes at multiple scales. Comp. Vision and Image Understanding (2001) 83, 118-139.
13. J. Nocedal and S. J. Wright, Numerical Optimization. Springer-Verlag, New York, 1999.
14. S. Petitjean, A survey of methods for recovering quadrics in triangle meshes. ACM Comp. Surveys (2002) 32, 211-262.
15. Yu. Vassilevski and K. Lipnikov, Optimal triangulations: existence, approximation and double differentiation of PI finite element functions. Comp. Math. Math. Phys. (2003) 43, 827-835.