Multigrid method: Difference between revisions

Revision as of 09:06, 20 September 2007

Revision as of 09:09, 20 September 2007

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Combining these two expressions (and using <math>N_{k+1} = \rho N_k</math>) gives

:<math>W_1 = K N_1 \sum_{p=0}^n \rho^p </math>

Using the [[geometric series]], we then find (for tfinite <math>n</math>)

or

:<math>W_1 =< W_3K +N_1 \rho^2frac{1}{1 K N_1 +- \rho K N_1}</math>

:<math>W_1 / (K N_1) + 1 = 1 + \sum_p \rho^p </math>

:<math>W_1 / (K N_1) + 1 = 1 / (1 - \rho)</math>

:<math>W_1 = (K N_1) (1 / (1 - \rho) - 1),</math>

that is, a solution may be obtained in <math>O(N)</math> time.

Using the [[geometric series]], we then find for t

== See also ==