Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 21-26, 2009, Pages 1691-1700

  Burstedde, Carsten ^a   Ghattas, Omar ^a,b   Stadler, Georg ^a   Tu, Tiankai ^a   Wilcox, Lucas C ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Adaptive mesh refinement; Adjoint error estimation; Algebraic multigrid; Octree algorithms; Parallel computing; Stokes equations

Indexed keywords

ADAPTIVE MESH REFINEMENT; ADJOINT ERROR ESTIMATION; ALGEBRAIC MULTIGRID; OCTREE ALGORITHMS; PARALLEL COMPUTING; STOKES EQUATIONS;

DATA STRUCTURES; ERROR ANALYSIS; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS; VISCOSITY;

ADAPTIVE ALGORITHMS;

EID: 63249129443     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.12.015     Document Type: Article

References (32)

1. Ainsworth M., and Oden J.T. A Posteriori Error Estimation in Finite Element Analysis. Pure and Applied Mathematics (New York) (2000), John Wiley & Sons, New York
2. S. Aluru, F.E. Sevilgen, Parallel domain decomposition and load balancing using space-filling curves, in: Proceedings of the Fourth IEEE Conference on High Performance Computing, 1997, pp. 230-235.
3. Babuška I., and Rheinboldt W. A posteriori error estimates for the finite element method. Int. J. Numer. Method Engrg. 12 (1978) 1597-1615
4. Bangerth W., Hartmann R., and Kanschat G. deal.II - a general-purpose object-oriented finite element library. ACM Trans. Math. Software 33 (2007)
5. Becker R., and Rannacher R. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1-102
6. Bochev P., Dohrmann C., and Gunzburger M. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal. 44 (2006) 82-101
7. Briggs W.L., Henson V.E., and McCormick S. A Multigrid Tutorial. second ed. (2000), SIAM
8. C. Burstedde, O. Ghattas, M. Gurnis, G. Stadler, E. Tan, T. Tu, L.C. Wilcox, S. Zhong, Scalable adaptive mantle convection simulation on petascale supercomputers, in: Proceedings of ACM/IEEE SC08, 2008.
9. A. Caglar, M. Griebel, M.A. Schweitzer, G. Zumbusch, Dynamic load-balancing of hierarchical tree algorithms on a cluster of multiprocessor PCs and on the Cray T3E, in: H.W. Meuer (Ed.), Proceedings 14th Supercomputer Conference, Mannheim, Mateo, 1999.
10. Center for Applied Scientific Computing, LLNL, Hypre. High performance preconditioners, User Manual, 2007. .
11. Demkowicz L., Kurtz J., Pardo D., Paszyński M., Rachowicz W., and Zdunek A. Computing with hp Finite Elements II. Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications (2007), CRC Press, Taylor and Francis
12. J.M. Dennis, Partitioning with space-filling curves on the cubed-sphere, in: IPDPS'03: Proceedings of the 17th International Symposium on Parallel and Distributed Processing, Washington, DC, USA, 2003, IEEE Computer Society, p. 269.1.
13. De Sterck H., Yang U.M., and Heys J.J. Reducing complexity in parallel algebraic multigrid preconditioners. SIAM J. Matrix Anal. Appl. 27 (2006) 1019-1039
14. Dohrmann C., and Bochev P. A stabilized finite element method for the Stokes problem based on polynomial pressure projections. Int. J. Numer. Methods Fluids 46 (2004) 183-201
15. Elman H.C., Silvester D.J., and Wathen A.J. Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics (2005), Oxford University Press, Oxford
16. Falgout R.D. An introduction to algebraic multigrid. Comput. Sci. Engrg. 8 (2006) 24-33
17. Hughes T.J.R. The Finite Element Method (2000), Dover, New York
18. Hutter K. Theoretical Glaciology. Mathematical Approaches to Geophysics (1983), D. Reidel Publishing Company, Dordrecht, Holland
19. Kirk B., Peterson J.W., Stogner R.H., and Carey G.F. libMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations. Engrg. Comput. 22 (2006) 237-254
20. Laszloffy A., Long J., and Patra A.K. Simple data management, scheduling and solution strategies for managing the irregularities in parallel adaptive hp finite element simulations. Parallel Comput. 26 (2000) 1765-1788
21. McKenzie D. The generation and compaction of partially molten rock. J. Petrol. 25 (1984) 713-765
22. Moresi L.N., Zhong S., and Gurnis M. The accuracy of finite element solutions of Stokes' flow with strongly varying viscosity. Phys. Earth Planet. Interiors 97 (1996) 83-94
23. Morgan J.P., and Forsyth D.W. Three-dimensional flow and temperature perturbations due to a transform offset: effects on oceanic crustal and upper mantle structure. J. Geophys. Res. 93 (1988) 2955-2966
24. Morgan J.P. Melt migration beneath mid-ocean spreading centers. Geophys. Res. Lett. 14 (1987) 1238-1241
25. Oden J.T., and Prudhomme S. Goal-oriented error estimation and adaptively for the finite element method. Comput. Method Appl. Mech. Engrg. 41 (2001) 735-756
26. Olshanskii M.A., Peters J., and Reusken A. Uniform preconditioners for a parameter dependent saddle point problem with application to generalized stokes interface equations. Numer. Math. 105 (2006) 159-191
27. Olshanskii M.A., and Reusken A. Analysis of a stokes interface problem. Numer. Math. 103 (2006) 129-149
28. Paige C.C., and Saunders M.A. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975) 617-629
29. M. Spiegelman, SpecRidge: a spectral ridge benchmark for pressure-velocity Stokes solvers, 2007. .
30. Sundar H., Sampath R.S., and Biros G. Bottom-up construction and 2:1 balance refinement of linear octrees in parallel. SIAM J. Sci. Comput. 30 (2008) 2675-2708
31. T. Tu, D.R. O'Hallaron, O. Ghattas, Scalable parallel octree meshing for terascale applications, in: Proceedings of ACM/IEEE SC05, 2005.
32. Zhong S., Yuen D.A., and Moresi L.N. Numerical Methods in Mantle Convection. Treatise on Geophysics (2007), Elsevier pp. 227-252, (Chapter 7)