TY - JOUR
T1 - Parallelism across time in ODEs
AU - Gear, C. W.
AU - Xuhai, Xu
N1 - Funding Information:
Correspondence to: C.W. Gear, NEC Research Institute, 4 Independence Telephone: (609) 951-2700. Fax: (609) 951-2481. * Work done while at University of Illinois, Department of Computer Science, grant DOE DEFG02-87ER25026 and by NSF under grant DMS 87-03226.
PY - 1993/1
Y1 - 1993/1
N2 - There is no natural parallelism across time in ODEs, so to exploit massive parallelism for a small system of equations it is necessary to use iterative techniques in time, such as waveform. The Picard method, for example, allows each integration to be performed in O(log N) time over N time steps but its convergence is poor for any but almost quadrature problems (∂f∂y small). Generalized Picard, or waveform, may have much faster convergence but less parallelism. This paper considers parallelism across time, explores a proposal made in an earlier paper [2], and reports on some tests made on that method.
AB - There is no natural parallelism across time in ODEs, so to exploit massive parallelism for a small system of equations it is necessary to use iterative techniques in time, such as waveform. The Picard method, for example, allows each integration to be performed in O(log N) time over N time steps but its convergence is poor for any but almost quadrature problems (∂f∂y small). Generalized Picard, or waveform, may have much faster convergence but less parallelism. This paper considers parallelism across time, explores a proposal made in an earlier paper [2], and reports on some tests made on that method.
KW - Differential equations
KW - initial value problems
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U2 - 10.1016/0168-9274(93)90039-T
DO - 10.1016/0168-9274(93)90039-T
M3 - Article
AN - SCOPUS:0027189438
VL - 11
SP - 45
EP - 68
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 1-3
ER -