10.59 It is well-known that the linear systems arising from spatial discretizations of fluid mechanics problems grow rapidly as the size of the problem increases. The solution process involves the inversion of a Laplacian in each spatial direction.

The larger number of iterations involved lead to longer solution times. Zsaki et al. (International Journal for Numerical Methods in Fluids, 2003)

studied how to effectively solve the vector Laplacian system by applying finite-element tearing and interconnecting (FETI) method. In this method, the total number of inner iterations changes depending on the mesh size used.

They performed numerical tests for different mesh sizes with and without the reconjugation method and the inner FTEI iterations were recorded for each case.

Is the inner FETI significantly higher without reconjugation than that with reconjugation? Justify your answer using a 5% level of significance.

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Inner FETI Mesh size (w/o) Inner FETI (with Reconj) 1/8 217 95 1/12 252 107 1/16 269 109 1/20 271 113 1/28 291 115 1/32 291 118 1/38 291 118 1/40 293 119 1/48 311 119