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The idea is that the coarse solution procedure captures the fine-grid variations of the solution.
For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution.
Third, a fine-grid solution is computed on each subdomain using boundary conditions set with the global coarse solution, corrected locally with fine-grid information from nearby subdomains.
The coarse solution can be obtained in the coarse approximation space, and refined by adding details in the detail spaces over several levels till the equation is resolved to the desired accuracy.
In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage.
The method projects the original pressure problem onto a second coarser grid, on which it is less expensive to solve, and then prolongates the approximated coarse solution back to the fine-scale grid.
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With an auxiliary point, the linear method for the special case of four coplanar points is extended to find the coarse solutions for the general P3P problem.
The individual and coarse solutions can deviate slightly, as only a finite number of PC coefficients are used during the computations, but the difference is practically unnoticeable in the "eye norm" (Fig. 11).
The coarse solutions are employed to make initial populations for the subsequent GAs.
The search is performed by various crossover methods, resulting in obtaining local solutions around the coarse solutions.
At this stage, it is important to find the coarse solutions showing some oscillations because GAs cannot evolve non-oscillatory solutions into stable oscillators.
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