Adaptive solver for the p-version of finite element method

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 10, 1997, Pages 1767-1784

  Fish, Jacob ^a   Guttal, Ravi ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Adaptive solver; Conditioning; Conjugate gradient; Multigrid; Sparse direct solver; Sparsity

Indexed keywords

ADAPTIVE SYSTEMS; DEGREES OF FREEDOM (MECHANICS); HIERARCHICAL SYSTEMS; LARGE SCALE SYSTEMS; PROBLEM SOLVING; SHELLS (STRUCTURES); THREE DIMENSIONAL;

MEMORY TRAFFIC;

FINITE ELEMENT METHOD;

EID: 0031143977     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19970530)40:10<1767::AID-NME136>3.0.CO;2-G     Document Type: Article

References (14)

1. R. B. Morris, Y. Tsuji and P. Carnevali, 'Adaptive solution strategy for solving large systems of p-type finite element equations', Int. j. numer. methods eng., 33, 2059-2071 (1992).
2. J. Mandel, 'Adaptive iterative solvers in finite elements', in M. Papadrakakis (ed.), Solving Large-scale Problems in Mechanics, Wiley, New York, 1993, pp. 65-88.
3. W. Hackbusch, Iterative Solution of Large Sparse System of Equations, Springer, New York, 1994.
4. A. Brandt, 'Multi-level adaptive solutions to boundary-value problems', Math. Comp., 31, 333-390 (1977).
5. J. Fish and R. Guttal, 'The p-version of finite element method for shell analysis', Comput. Mech. Int. J., 16, 328-340 (1995).
6. R. E. Bank, T. F. Dupont and H. Yserentant, 'The hierarchical basis multigrid method', Numer. Math., 52, 427-458 (1988).
7. O. Axelsson, 'Analysis of incomplete matrix factorizations as multigrid smoothers for vector and parallel computers', Appl. Math. Comp., 19, 3-22 (1986).
8. D. S. Kershaw, 'The incomplete Choleski-conjugate gradient method for the iterative solution of systems of linear equations', J. Comp. Phys., 26, 43-65 (1968).
9. M. A. Ajiz and A. Jennings, 'A robust incomplete Choleski-conjugate gradient algorithm', Int. j. numer. methods eng., 20, 949-966 (1984).
10. O. Axelsson and I. Gustafsson, 'Preconditioning and two-level multigrid methods of arbitrary degree of approximation', Math. Comp., 40, 219-242 (1983).
11. I. Babuska, A. Craig, J. Mandel and J. Pitkaranta, 'Efficient preconditioning for the p-version finite element method in two dimensions', SIAM J. Numer. Anal., 28, 624-661 (1991).
12. VSS - Sparse Direct Solver, NASA Langley, Hamplou, VA, 1996.
13. W. F. Tinney, Comments on using sparsity techniques for power system problems. Sparse Matrix Proceedings, IBM Research Rept. RAI 3-12-69.
14. C. J. Huberty, Applied Discriminant Analysis. Wiley, New York, 1994.