The mixed-cell-complex partition-of-unity method

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 13-14, 2009, Pages 1235-1248

  Riker, Carsten ^a   Holzer, Stefan M ^a  

^a BUNDESWEHR UNIVERSITY MUNICH   (Germany)

Author keywords

Finite element method (FEM); Galerkin method; Generalized finite element method (GFEM); h Version; Meshless methods; Mixed cell complex; p Version; Partition of unity method (PUM)

Indexed keywords

COMPUTATIONAL MECHANICS; GALERKIN METHODS; POISSON EQUATION;

FINITE ELEMENT METHOD (FEM); GALERKIN METHOD; GENERALIZED FINITE ELEMENT METHOD (GFEM); H-VERSION; MESHLESS METHODS; MIXED CELL COMPLEX; P-VERSION; PARTITION OF UNITY METHOD (PUM);

FINITE ELEMENT METHOD;

EID: 60249103753     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.04.026     Document Type: Article

References (21)

1. J.M. Melenk, On generalized finite element methods, PhD Thesis, Department of Mathematics, University of Maryland, 1995.
2. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Engrg. 139 1 (1996) 3-47
3. Li S., and Liu W.K. Meshfree and particle methods and their applications. Appl. Mech. Rev. 55 1 (2002) 1-34
4. Liszka T., Duarte C., and Tworzydlo W. hp-Meshless cloud method. Comput. Methods Appl. Mech. Engrg. 139 (1996) 263-288
5. Griebel M., and Schweitzer M.A. A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs. SIAM J. Sci. Comput. 22 (2000) 853-890
6. Griebel M., and Schweitzer M.A. A particle-partition of unity method-Part II: Efficient cover construction and reliable integration. SIAM J. Sci. Comput. 23 (2002) 1665-1682
7. Griebel M., and Schweitzer M.A. A particle-partition of unity method-Part III: A multilevel solver. SIAM J. Sci. Comput. 24 (2002) 377-409
8. Shepard D. A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 1968 23rd ACM National Conference (1968), ACM Press 517-524
9. Babuška I., Banerjee U., and Osborne J.E. Meshless and generalized finite element methods: a survey of some major results. In: Griebel M., and Schweitzer M.A. (Eds). Meshfree Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering vol. 26 (2002), Springer-Verlag 1-20
10. Fernández-Méndez S., and Huerta A. Imposing essential boundary conditions in meshfree methods. Comput. Methods Appl. Mech. Engrg. 193 12-14 (2004) 1257-1275
11. Griebel M., and Schweitzer M.A. A particle-partition of unity method-Part V: Boundary conditions. In: Hildebrandt S., and Karcher H. (Eds). Geometric Analysis and Nonlinear Partial Differential Equations (2002), Springer-Verlag 517-540
12. Schwebke K., and Holzer S. Some remarks on generalized finite element methods (GFEM) in solid mechanics. In: Mang H.A., Rammerstorfer F.G., and Eberhardsteiner F.G. (Eds). Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V) (2002), Vienna University of Technology, Austria
13. H. Edelsbrunner, Lecture Notes in Geometry and Topology of Grid Generation, VII. Smooth Surfaces, Mixed Complex , (1999).
14. Edelsbrunner H. Deformable smooth surface design. Discrete Comput. Geom. 21 (1999) 87-115
15. Ruppert J. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms 18 3 (1995) 548-585
16. J.M. Melenk, Finite element methods with harmonic shape functions for solving Laplace's equation, Master Thesis, University of Maryland, 1992.
17. Klaas O., and Shepard M.S. Automatic generation of octree-based three-dimensional discretizations of partition of unity methods. Comput. Mech. 25 2-3 (2000) 296-304
18. Karutz H., and Krätzig W. A quadtree data structure for the coupled finite element/element free galerkin method. Int. J. Numer. Methods Engrg. 53 (2002) 375-391
19. Du Q., Gunzburger M., and Ju L. Meshfree, probabilistic determination of point sets and support regions for meshless computing. Comput. Methods Appl. Mech. Engrg. 191 13-14 (2002) 1349-1366
20. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abhandlungen Mathematisches Seminar Universität Hamburg, vol. 36, 1970-1971, pp. 9-15.
21. Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., and Sorensen D. LAPACK Users' Guide. third ed. (1999), Society for Industrial and Applied Mathematics, Philadelphia, PA