Comparative analysis of PCG solvers for voxel FEM systems

Proceedings of the International Multiconference on Computer Science and Information Technology, IMCSIT

Volumn 1, Issue , 2006, Pages 591-598

  Margenov, S ^a   Vutov, Y ^a  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

AMG; FEM; MIC(0); Parallel algorithms; PCG

Indexed keywords

ALGEBRAIC MULTIGRIDS; AMG; BENCH-MARK PROBLEMS; CHOLESKY FACTORIZATIONS; COMPARATIVE ANALYSIS; DISCRETIZATIONS; ELLIPTIC PROBLEM; FEM SIMULATIONS; FINITE ELEMENT; HETEROGENEOUS STRUCTURES; HIGH RESOLUTION COMPUTER TOMOGRAPHIES; HUMAN BONES; ITERATIVE SOLVERS; LARGE-SCALE LINEAR SYSTEMS; LARGE-SCALE PROBLEM; MIC(0); NUMBER OF ITERATIONS; NUMERICAL TESTS; PCG; POSITIVE-DEFINITE MATRICES; PRECONDITIONED CONJUGATE GRADIENT METHOD; PRECONDITIONERS; SYMMETRIC SYSTEMS; VOXEL DATA;

BONE; CODES (SYMBOLS); COMPUTER SCIENCE; DATA PROCESSING; FINITE ELEMENT METHOD; INFORMATION TECHNOLOGY; LINEAR SYSTEMS; PARALLEL ALGORITHMS;

CONJUGATE GRADIENT METHOD;

EID: 81355128204     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. ABAQUS, Nonlinear Micro Finite Element Analysis of Human Trabecular Bone, ABAQUS Technology Brief, TB-03-HTB-1, 2004.
2. P. Arbenz, S. Margenov: Parallel MIC(0) preconditioning of 3D nonconforming FEM systems, Iterative Methods, Preconditioning and Numerical PDEs, Proceedings of IMET Conference, Prague, 2004, pp. 12-15.
3. P. Arbenz, S. Margenov, Y. Vutov: Parallel MIC(0) Preconditioning of 3D Elliptic Problems Discretized by Rannacher-Turek Finite Elements, Comput. Math. Appl. (to appear).
4. D. N. Arnold, F. Brezzi: Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Model. Math. Anal. Numer. 19 (1985), pp. 7-32.
5. O. Axelsson: Iterative Solution Methods. Cambridge University Press, Cambridge, 1994.
6. G. Bencheva, S. Margenov: Parallel incomplete factorization preconditioning of rotated linear FEM systems, J. Comput. Appl. Mech., V.4(2) (2003), pp. 105-117.
7. R. Blaheta: Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems, Numer. Linear Algebra Appl. 1 (1994), pp. 107-126.
8. D. Braess: Finite elements. Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, 1997.
9. I. Gustafsson: Modified incomplete Cholesky (MIC) factorization, In: D.J. Evans (ed.): Preconditioning Methods; Theory and Applications, Gordon and Breach, 1983, pp. 265-293.
10. I. Gustafsson, G. Lindskog: On parallel solution of linear elasticity problems: Part I: Theory, Numer. Linear Algebra Appl. 5(2) (1998), pp. 123-139.
11. I. Gustafsson: Stability and rate of convergence of modified incomplete Cholesky factorization methods, Chalmers University of Technology, Report Nr. 79.02R, 1979.
12. V. E. Henson and U. M. Yang. BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics, 41(5):155-177, 2002. Also available as LLNL technical report UCRL-JC-141495.
13. R. A. Horn, C. R. Johnson: Matrix Analysis, Cambridge University Press, Cambridge, 1985.
14. R. D. Lazarov, S. Margenov: On a two-level parallel MIC(0) preconditioning of Crouzeix-Raviart non-conforming FEM systems, In: I. Dimov, I. Lirkov, S. Margenov, Z. Zlatev (eds.): Numerical Methods and Applications, Springer LNCS 2542, 2003, pp. 192-201.
15. R. Rannacher, S. Turek: Simple nonconforming quadrilateral Stokes Element, Numer. Methods Partial Differential Equations 8(2) (1992), pp. 97-112.
16. J. W. Ruge and K. Stüben. Algebraic multigrid (AMG). In S. F. McCormick, editor, Multigrid Methods, volume 3 of Frontiers in Applied Mathematics, pages 73-130. SIAM, Philadelphia, PA, 1987.
17. Y. Vutov: Parallel Incomplete Factorization of 3D NC FEM Elliptic Systems, Proceedings of 5th Conference on Numerical Methods and Applications, Borovets, Bulgaria, 2006, to appear.
18. U. M. Yang. Parallel algebraic multigrid methods - high performance preconditioners. In: A. M. Bruaset and A. Tveito, editors, Numerical Solution of Partial Differential Equations on Parallel Computers, pages 209-236. Springer-Verlag, 2005. Also available as LLNL technical report UCRL-BOOK-208032.