Electronic Resource
New York, NY [u.a.]
:
Wiley-Blackwell
Numerical Methods for Partial Differential Equations
14 (1998), S. 27-46
ISSN:
0749-159X
Keywords:
Parallel
;
domain decomposition
;
parabolic equation
;
space decomposition
;
Mathematics and Statistics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27-46, 1998
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
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