Solving initial - Value problems by explicit domain decomposition approximate inverses

European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000

Volumn , Issue , 2000, Pages

  Gravvanis, George A ^a  

^a UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

Approximate factorization procedures; Approximate inverse matrix techniques; Arrow type matrix; Domain decomposition method; Parallel iterative methods; Preconditioning

Indexed keywords

APPROXIMATE FACTORIZATION; APPROXIMATE INVERSE; FACTORIZATION TECHNIQUES; HETEROGENEOUS METHOD; PARALLEL ITERATIVE METHODS; PRECONDITIONED CONJUGATE GRADIENT; PRECONDITIONING; SOLUTION OF LINEAR SYSTEMS;

COMPUTATIONAL METHODS; DOMAIN DECOMPOSITION METHODS; INITIAL VALUE PROBLEMS; LINEAR SYSTEMS; NUMERICAL METHODS;

INVERSE PROBLEMS;

EID: 84893377723     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (38)

1. O. Axelsson, Iterative solution methods, Cambridge University Press, (1994).
2. D.J. Evans, Preconditioning Methods: Theory and Applications, Gordon and Breach Science Publishers, (1983).
3. Y. Saad, Iterative methods for sparse linear systems, PWS Publishing, (1996).
4. J.J. Dongarra, P. Messina, D.C. Sorensen and R.G. Voigt, Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing, SIAM, (1989).
5. D.J. Evans, Iterative methods for sparse systems, In Sparsity and its Applications, Evans D.J., ed., Cambridge University Press, (1985).
6. H.R. Schwarz, Finite Element Methods, Academic Press, (1989).
7. I.S. Duff, A.M. Erisman and J.K. Reid, Direct methods for sparse matrices, Oxford University Press, (1986).
8. P.E. Bjorstad and O. Widlund, Solving elliptic problems on regions partitioned into substructures, in Elliptic Problem Solver II, G. Birkhoff and A. Schoenstadt, eds., Academic Press, 245-256 (1984).
9. J.H. Bramble, J.G. Pasciak and A.H. Schatz, The construction of preconditioners for elliptic problems by substructuring I, Math. Comp. 47, 103-134 (1986).
10. J.H. Bramble, J.G. Pasciak and A.H. Schatz, An iterative method for elliptic problems on regions partitioned in substructures, Math. Comp. 46, 361-369 (1986).
11. T.F. Chan, Analysis of preconditioners for domain decomposition, SIAM J. Num. Anal. 24, 382-390 (1987).
12. M. Dryja, A finite element capacitance method for elliptic problems on regions partitioned into subregions, Num. Math. 44, 153-168 (1984).
13. M. Dryja, A capacitance matrix method for Dirichlet problem on polygonal region, Num. Math. 39, 51-64 (1982).
14. G.H. Golub and C. van Loan, Matrix Computations, The Johns Hopkins University Press, (1996).
15. G. Frank, E. Gallopoulos and U. Meier, Experiments with elliptic problem solvers on theCedar multicluster, Proc. of 4th SIAM Conf. on Parallel Processing for Scientific Computing, SIAM, (1989).
16. G.A. Gravvanis, An approximate inverse matrix technique for arrowhead matrices, I. J. Comp. Math. 70, 35-45 (1998).
17. D. O'Leary and G. Stewart, Computing the eigenproblem and eigenvectors of arrowhead matrices, J. Comp. Physics 90, 497-505 (1990).
18. G.A. Gravvanis and E.A. Lipitakis, A three dimensional explicit preconditioned solver, Comp. Math. with Appl. 32, 111-131 (1996).
19. J.J. Dongarra, I.S. Duff, D.C. Sorensen and H.A. van der Vorst, Solving linear systems on vector and shared memory computers, SIAM, (1991).
20. D.J. Evans and C. Sutti, Parallel Computing : Methods, Algorithms and Applications, Proceedings of the International Meeting on Parallel Computing, Adam Hilger, (1988).
21. G.A. Gravvanis, Explicit approximate inverse finite element preconditioning for solving biharmonic equations, Applications of High Performance Computing in Engineering VI, eds M. Ingber, H. Power and C.A. Brebbia, WIT Press, 411-420 (2000).
22. G.A. Gravvanis and E.A. Lipitakis, An explicit sparse unsymmetric finite element solver, Commun. Numer Meth. in Engin. 12, 21-29 (1996).
23. E.A. Lipitakis and G.A. Gravvanis, Explicit preconditioned iterative methods for solving large unsymmetric finite element systems, Computing 54, 167-183, (1995).
24. G.A. Gravvanis Solving 3D time-dependent problems by pseudoinverses, Proc. of the 10th Inter. Conf. on Numerical Methods in Thermal Problems, eds. R. W. Lewis and J.T. Cross, Pineridge Press, Vol X, 910-921 (1997).
25. E.A. Lipitakis and G.A. Gravvanis, Hybrid Implicit-Explicit schemes by approximate inverse finite element matrix techniques for solving parabolic partial differential equations, Proc. of the First Conf. on Mathematics and Informatics, ed. E.A. Lipitakis, Hellenic Mathematical Society, 345-356 (1993).
26. J.M. Ortega, Introduction to parallel and vector solution of linear systems, Plenum Press, (1988).
27. G.A. Gravvanis, Generalized approximate inverse finite element matrix techniques, accepted Journal Neural Parallel and Scientific Computation, (1999).
28. G.A. Gravvanis, On the numerical modelling and solution of non-linear boundary value problems, Proc. of the 10th Inter. Conf. on Numerical Methods in Thermal Problems, eds. R. W. Lewis and J.T. Cross, Pineridge Press, Vol X, 898-909 (1997).
29. E.A. Lipitakis and G.A. Gravvanis, A class of explicit preconditioned conjugate gradient methods for solving large finite element system, I. J. Comp. Math. 44, 189-206 (1992).
30. G.A. Gravvanis, Parallel matrix techniques, Computational Fluid Dynamics 98, eds. K.D. Papailiou, D. Tsahalis, J. Periaux, C. Hirsch and M. Pandolfi, Wiley, Vol. 1, 472-477 (1998).
31. G.A. Gravvanis, Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques, I. J. Comp. Math. 56, 77-93 (1995).
32. E.A. Lipitakis and G.A. Gravvanis, Explicit preconditioned methods for computing the inverse and pseudoinverse solutions of unsymmetric finite element systems of linear equations, I. J. Math. Modelling and Scientific Computing 4, 886-893 (1994).
33. G.A. Gravvanis, Banded approximate inverse matrix techniques, Engineering Computations 16(3), 337-346 (1999).
34. H.A. van der Vorst, BI-CGSTAB:A fast and smoothly converging variant BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 13, 631-644 (1992).
35. G.A. Gravvanis, The rate of convergence of explicit approximate inverse preconditioning, I. J. Comp. Math. 60, 77-89 (1996).
36. H.A. van der Vorst and C. Vuik, GMRESR: A family of nested GMRES methods, Numer. Linear Alg. Appl. 1(4), 369-386 (1994).
37. C. Vuik and H.A. van der Vorst, A comparison of some GMRES-like methods, Linear Alg. Appl. 160, 131-162 (1992).
38. D.R.J. Owen, Iterative and parallel equation solutions strategies, R News, Issue No. 4, Rockfield Software Ltd, (1998).