Alternating-direction line-relaxation methods on multicomputers

SIAM Journal on Scientific Computing

Volumn 17, Issue 2, 1996, Pages 454-478

  Hofhaus, Jörn ^a   Van De Velde, Eric F ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

ADI; Alternating directions; Block tridiagonal systems; Concurrency; Navier Stokes equations; Parallelism; Tridiagonal systems

Indexed keywords

EID: 0010247235     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827593253872     Document Type: Article

References (16)

1. W. ALTHAUS, E. KRAUSE, J. HOFHAUS, AND M. WEIMER, Bubble- and spiral-type breakdown of slender vortices, Exp. Thermal Fluid Sci., (1995), to appear.
2. S. BONDELI, Divide and conquer: A parallel algorithm for the solution of a tridiagonal system of equations, Parallel Comput., 17 (1991), pp. 419-434.
3. M. BREUER, Numerische Lösung der Navier-Stokes Gleichungen für dreidimensionale inkompressible instationäre Strömungen zur Simulation des Wirbelaufplatzens, Ph.D. thesis, Aerodynamisches Institut der RWTH Aachen, Germany, 1991.
4. M. BREUER AND D. HÄNEL, A dual time-stepping method for 3-D, viscous, incompressible vortex flows, Comput. & Fluids, 22 (1993), pp. 467-484.
5. INTEL SUPERCOMPUTING SYSTEMS DIVISION, Touchstone Delta System User's Guide, Beaverton, Oregon, 1991.
6. _, The Intel Paragon Supercomputer - an Overview, Beaverton, Oregon, 1992.
7. A. FROMMER, Lösung linearer Gleichungssysteme auf Parallelrechnern, Vieweg-Verlag, Braunschweig, Germany, 1990.
8. C. HO AND S. JOHNSSON, Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors, SIAM J. Sci. Staust. Comput., 11 (1990), pp. 563-592.
9. R. HOCKNEY, A fast and direct solution of Poisson's equation using Fourier analysis, J. Assoc. Comput. Mach., 1 (1965), pp. 95-113.
10. R. HOCKNEY AND C. JESSHOPE, Parallel Computers, Adam Hilger, Bristol, 1981.
11. E. ISAACSON AND H. KELLER, Analysis of Numerical Methods, John Wiley and Sons, New York, 1966.
12. S. JOHNSSON, Y. SAAD, AND M. SCHULTZ, Alternating direction methods on multiprocessors, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 686-700.
13. W. JULING AND K. KREMER, The massively parallel computer system of the DFG priority research program "flow simulation on supercomputers", in Notes on Numerical Fluid Mechanics, Vol. 38, Vieweg-Verlag, Braunschweig, Germany, 1993.
14. A. KRECHEL, H.-J. PLUM, AND K. STÜBEN, Parallelization and vectorization aspects of the solution of tridiagonal linear systems, Parallel Comput., 14 (1990), pp. 31-49.
15. H. STONE, An efficient parallel algorithm for the solution of a tridiagonal linear system of equations, J. Assoc. Comput. Mach., 20 (1973), pp. 27-38.
16. H. WANG, A parallel method for tridiagonal equations, ACM Trans. Math. Software, 7 (1981), pp. 170-183.