Iterative solution of elliptic collocation systems on a cognitive parallel computer

Computers and Mathematics with Applications

Volumn 48, Issue 5-6, 2004, Pages 951-970

  Mathioudakis, E N ^a   Papadopoulou, E P ^a   Saridakis, Y G ^a  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Cognitive computers; Collocation; Distributed memory parallel computers; MIMD; Red black orderings; SPMD; Successive overrelaxation (SOR)

Indexed keywords

COGNITIVE SYSTEMS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DISTRIBUTED COMPUTER SYSTEMS; FUNCTIONS; ITERATIVE METHODS; LINEAR SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; PARALLEL ALGORITHMS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

COGNITIVE COMPUTERS; COLLOCATION; DISTRIBUTED MEMORY PARALLEL COMPUTERS; MIMD; RED-BLACK ORDERINGS; SPMD; SUCCESSIVE OVERRELAXATION (SOR);

PARALLEL PROCESSING SYSTEMS;

EID: 14644437105     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2003.01.017     Document Type: Article

References (20)

1. B.P. Bertsekas, and J.N. Tsitsiklis Parallel and Distributed Computation 1989 Prentice-Hall Berlin
2. J.M. Ortega, and R.G. Voigt Solution of partial differential equations on vector and parallel computers SIAM Review 27 2 1985 149 240
3. G. Birkhoff, M.H. Schultz, and R.S. Varga Piecewise Hermite in one and two variables with applications to partial differential equations Numer. Math. 11 1968 232 256
4. C. de Boor, and B. Swartz Collocation at Gaussian points SIAM J. Numer. Anal. 10 1973 582 606
5. J. Douglas, and T. Dupont Collocation Methods for Parabolic Equations in a Single Space Variable Lecture Notes vol. 385 1974 Springer-Verlag Englewood Cliffs, NJ
6. E.N. Houstis Application of the method of collocation on lines for solving nonlinear hyperbolic problems Math. Comp. 31 1977 443 456
7. E.N. Houstis, W. Mitchell, and J.R. Rice Collocation software for second order elliptic partial differential equations ACM Trans. Math. Software 11 1985 379 412
8. E.N. Houstis, R.E. Lynch, T.S. Papatheodorou, and J.R. Rice Evaluation of numerical methods for elliptic partial differential equations J. Comp. Phys. 27 1978 323 350
9. T.S. Papatheodorou Block AOR iteration for nonsymmetric matrices Math. Comp. 41 164 1983 511 525
10. T.S. Papatheodorou Inverses for a class of banded matrices and applications to piecewise cubic approximation J. Comp. Appl. Math. 8 4 1982 285 288
11. A. Hadjidimos, T.S. Papatheodorou, and Y.G. Saxidakis Optimal block iterative schemes for certain large sparse and non-symmetric linear systems Linear Algebra Appl. 110 1988 285 318
12. Y.G. Saridakis Parallelism, applicability and optimality of modern iterative methods Ph.D. Thesis 1985 Clarkson University Berlin
13. Dallas E. Papadopoulou, Y.G. Saridakis, and T.S. Papatheodorou Orderings and partitions of PDE computations on a fixed size VLSI architecture Procs. of IEEE-ACM Fall Joint Computer Science Conference 1987 366 374
14. T.S. Papatheodorou, and Y.G. Saridakis Parallel algorithms and architectures for multisplitting iterative methods Parallel Computing 12 1989 171 182
15. nd Hellenic Conference on Mathematics and Informatics (HERMIS '94) 1994 441 448
16. E.N. Mathioudakis, E.P. Papadopoulou, and Y.G. Saridakis Mapping parallel iterative algorithms for PDE computations on a distributed memory computer Parallel Algorithms and Applications 8 34 1996 141 154
17. Y.-L. Lai, A. Hadjidimos, E.N. Houstis, and J.R. Rice On the iterative solution of Hermite collocation equations SIAM J Matrix Anal. 16 1 1995 254 277
18. R.S. Varga Matrix Iterative Analysis 1962 Prentice-Hall Englewood Cliffs, NJ
19. nd Hellenic Conference on Mathematics and Informatics (HERMIS '94) 1994 449 456
20. D.M. Young Iterative Solution of Large Linear Systems 1981 Academic Press Englewood Cliffs, NJ