A particle-partition of unity method part VI: A p-robust multilevel solver

Lecture Notes in Computational Science and Engineering

Volumn 43, Issue , 2005, Pages 71-92

  Griebel, Michael ^a   Oswald, Peter ^b   Schweitzer, Marc Alexander ^a  

^a UNIVERSITY OF BONN   (Germany)

^b JACOBS UNIVERSITY BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DOMAIN DECOMPOSITION METHODS; LINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

APPROXIMATION ORDERS; CONVERGENCE RATES; HIGHER ORDER DISCRETIZATION; LOCAL POLYNOMIALS; MULTILEVEL SOLUTIONS; NUMERICAL EXPERIMENTS; PARTITION OF UNITY METHODS; SECOND-ORDER PARTIAL DIFFERENTIAL EQUATION;

ITERATIVE METHODS;

EID: 84880366322     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-27099-x_5     Document Type: Article

References (22)

1. I. Babuška and J. M. Melenk. The Partition of Unity Finite Element Method: Basic Theory and Applications. Comput. Meth. Appl. Mech. Engrg., 139:289-314,1996. Special Issue on Meshless Methods.
2. I. Babuška and J. M. Melenk. The Partition of Unity Method. Int. J. Numer. Meth. Engrg., 40:727-758, 1997.
3. J. H. Bramble and X. Zhang. Handbook of Numerical Analysis. In P. G. Ciarlet and J. L. Lions, editors, The Analysis of Multigrid Methods, volume VII, pages 173-416. Elsevier, 2000.
4. W. Dahmen. Multiscale Analysis, Approximation, and Interpolation Spaces. In C. K. Chui and L. L. Schumaker, editors, Approximation Theory VIII, volume 2, pages 47-88. World Scientific, 1995.
5. J. A. George. Nested Dissection of a Regular Finite Element Mesh. SIAM J. Num. Anal., 10:345-363, 1973.
6. T. Gerstner and M. Griebel. Numerical Integration using Sparse Grids. Numer. Alg., 18:209-232, 1998.
7. M. Griebel and M. A. Schweitzer. A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic and Hyperbolic PDE. SIAM J. Sci. Comput., 22(3):853-890, 2000.
8. M. Griebel and M. A. Schweitzer. A Particle-Partition of Unity Method-Part II: Efficient Cover Construction and Reliable Integration. SIAM J. Sci. Comput., 23(5):1655-1682, 2002.
9. M. Griebel and M. A. Schweitzer. A Particle-Partition of Unity Method-Part III: A Multilevel Solver. SIAM J. Sci. Comput., 24(2):377-409, 2002.
10. M. Griebel and M. A. Schweitzer. A Particle-Partition of Unity Method-Part IV: Parallelization. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations, volume 26 of Lecture Notes in Computational Science and Engineering, pages 161-192. Springer, 2002.
11. M. Griebel and M. A. Schweitzer. A Particle-Partition of Unity Method-Part V: Boundary Conditions. In S. Hildebrandt and H. Karcher, editors, Geometric Analysis and Nonlinear Partial Differential Equations, pages 517-540. Springer, 2002.
12. W. Hackbusch. Multi-Grid Methods and Applications, volume 4 of Springer Series in Computational Mathematics. Springer, 1985.
13. W. Hackbusch. Iterative Solution of Large Sparse Linear Systems of Equations. Springer, 1994.
14. J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg, 36:9-15, 1970-1971.
15. P. Oswald. Multilevel Finite Element Approximation. Teubner Skripten zur Numerik. Teubner, 1994.
16. T. N. L. Patterson. The Optimum Addition of Points to Quadrature Formulae. Math. Comp., 22:847-856, 1968.
17. L. F. Pavarino. Additive Schwarz Methods for the p-Version Finite Element Method. Numer. Math., 66:493-515, 1994.
18. M. A. Schweitzer. A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, volume 29 of Lecture Notes in Computational Science and Engineering. Springer, 2003.
19. T. Strouboulis, I. Babuška, and K. Copps. The Design and Analysis of the Generalized Finite Element Method. Comput. Meth. Appl. Mech. Engrg., 181(I 3):43-69, 2000.
20. T. Strouboulis, K. Copps, and I. Babuška. The Generalized Finite Element Method. Comput. Meth. Appl. Mech. Engrg., 190:4081-4193, 2001.
21. J. Xu. Iterative Methods by Space Decomposition and Subspace Correction. SIAM Review, 34(4):581-613, 1992.
22. H. Yserentant. Old and New Convergence Proofs for Multigrid Methods. Acta Numerica 93, pages 285-326, 1993.