Some Domain Decomposition And Iterative Refinement Algorithms for Elliptic Finit
Some Domain Decomposition And Iterative Refinement Algorithms for Elliptic Finit
Olof B Widlund
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, 2, 1, 2, ... K-1, k. In [23], we establish the following result. Theorem 2 The multiplicative iterative refinement algorithm has a condi- tion number which is independent of k and the number of degrees of freedom. When we now turn to additive algorithms, we note that the most natu- ral algorithm would amount to using the projections P-, defined above, in equation 2. However, it is relatively easy to show that the condition num- ber of that algorithm grows linearly with k. A very promising met...hod, for which to our knowledge the optimality has only been established in a quite special model case cf. [14], is based on using P- - P-^.^, i
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