TY - JOUR
T1 - Projection techniques for iterative solution of Ax = b with successive right-hand sides
AU - Fischer, Paul F.
N1 - Funding Information:
The author would like to thank Catherine Mavriplis, Anthony Patera,a nd Einar Ronquist for useful comments in the course of this work. This work was supportedb y the NSF under Grant #ASC-9405403, and in part by NASA Contract No. NASl-19480 while the author was in residencea t the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA.
PY - 1998/9/21
Y1 - 1998/9/21
N2 - Projection techniques are developed for computing approximate solutions to linear systems of the form Axn = bn, for a sequence n = 1, 2,..., e.g. arising from time discretization of a partial differential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in significantly reduced computational expense. Examples of two-and three-dimensional incompressible Navier-Stokes calculations are presented in which xn represents the pressure at time level tn, and A is a consistent discrete Poisson operator. In flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time.
AB - Projection techniques are developed for computing approximate solutions to linear systems of the form Axn = bn, for a sequence n = 1, 2,..., e.g. arising from time discretization of a partial differential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in significantly reduced computational expense. Examples of two-and three-dimensional incompressible Navier-Stokes calculations are presented in which xn represents the pressure at time level tn, and A is a consistent discrete Poisson operator. In flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time.
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U2 - 10.1016/S0045-7825(98)00012-7
DO - 10.1016/S0045-7825(98)00012-7
M3 - Article
AN - SCOPUS:0039776178
SN - 0045-7825
VL - 163
SP - 193
EP - 204
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 1-4
ER -