Parallel adaptive solution of 3D boundary value problems by Hessian recovery

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 11-12, 2003, Pages 1495-1513

  Lipnikov, Konstantin ^a   Vassilevski, Yuri ^b  

^a University of Houston   (United States)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

Hessian recovery; Inertial bisection; Parallel iterative solvers; Parallel mesh generator; Quasi optimal meshes

Indexed keywords

BOUNDARY VALUE PROBLEMS; ITERATIVE METHODS; PROBLEM SOLVING;

MESH GENERATION;

ADAPTIVE SYSTEMS;

BOUNDARY CONDITIONS;

EID: 0037436459     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00654-0     Document Type: Article

References (27)

1. E. D'Azevedo, On optimal triangular meshes for minimizing the gradient error, Numerische Mathematik 59 (1991) 321-348.
2. S. Rippa, Long and thin triangles can be good for linear interpolation, SIAM J. Numer. Anal. 29 (1992) 257-270.
3. A. Agouzal, K. Lipnikov, Y. Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes, East-West J. Numer. Math. 7 (1999) 223-244.
4. H. Borouchaki, P.-L. George, F. Hecht, P. Laug, B. Mohammadi, E. Saltel, Mailleur bidimensionnel de Delaunay gouverne par une carte de metriques, Technical Report R2760, INRIA, 1995.
5. J. Dompierre, M.-G. Vallet, M. Fortin, W. Habashi, D. Ait-Ali-Yahia, A. Tam, Edge-based mesh adaptation for CFD, Technical Report R95-73, CERCA, 1995.
6. G. Buscaglia, E. Dari, Anisotropic mesh optimization and its application in adaptivity, Int. J. Numer. Meth. Engrg. 40 (1997) 4119-4136.
7. K. Stüben, Algebraic multigrid (AMG): experiences and comparisons, Appl. Math. Comput. 13 (1983) 419-452.
8. T. Grauschopf, M. Griebel, H. Regler, Additive multilevel preconditioners based on bilinear interpolation, matrix dependent geometric coarsening and algebraic multigrid coarsening for second order elliptic PDEs, Appl. Numer. Math. 23 (1997) 63-96.
9. K. Lipnikov, Y. Vassilevski, Optimal triangulations: existence, approximation and double differentiation of P1 finite element functions, in: Electronic Proceedings of the Second Workshop on Grid Generation, Moscow, June 2002. Available from http://www.ccas.ru/gridgen/ggta02/abstracts.html to appear in Comp. Math. Math. Phys. (2003).
10. P. Zavattieri, E. Dari, G. Buscaglia, Optimization strategies in unstructured mesh generation, Int. J. Numer. Meth. Engrg. 39 (1996) 2055-2071.
11. Y. Vassilevski, K. Lipnikov, Adaptive algorithm for generation of quasi-optimal meshes, Comp.Math. Math. Phys. 39 (1999) 1532-1551.
12. G. Buscaglia, A. Agouzal, P. Ramirez, E. Dari, On Hessian recovery and anisotropic adaptivity, in: Proceedings of ECCOMAS 98 (the 4th European CFD Conference), Athens, Greece, 1998, pp. 403-407.
13. 1 finite elements, East-West J. Numer. Math. 10 (1) (2002) 1-12.
14. I. Foster, Designing and building parallel programs. Addison-Wesley Publishing Company, New York, 1995.
15. A. Pothen, H. Simon, K. Liou, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Math. Anal. Appl. 11 (1990) 430-452.
16. R. Williams, Performance of dynamic load balancing algorithms for unstructured mesh calculations, Concurrency: Pract. Exp. 3 (1992) 457-481.
17. Y. Vassilevski, Iterative solvers for the implicit parallel accurate reservoir simulator (IPARS). II. Parallelization issues, Technical Report 00-33, TICAM, The University of Texas at Austin, 2000.
18. S. Brenner, Lower bounds for two-level additive Schwarz preconditioners with small overlap, SIAM J. Sci. Comp. 21 (2000) 1657-1669.
19. A. Quarteroni, A. Valli, Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford, 1999.
20. J. Mandel, Hybrid domain decomposition method with unstructured subdomains, Contemp. Math. 157 (1994) 103-112.
21. J. Mandel, M. Bresina, Balancing domain decomposition for problems with large jumps in coefficients, Math. Comp. 65 (1996) 1387-1401.
22. R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H.V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994.
23. D. Young, Iterative Solution of Large Linear Systems, Academic Press, New York 1971.
24. E. Jenkins, C. Kees, C. Kelley, C. Miller, An aggregation-based domain decomposition preconditioner for groundwater flow, SIAM J. Sci. Comput. 23 (2001) 430-441.
25. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Co, Boston, 1996.
26. D. Kincaid, J. Respess, D. Young, R. Grimes, Algorithm 586 ITPACK 2C: a fortran package for solving large sparse linear systems by adaptive accelerated iterative methods, ACM Trans. Math. Software 8 (1982) 302-322.
27. T. Apel, Anisotropic Finite Elements: Local Estimates and Applications, Teubner, Stutgart, 1999.