Abstract
Preconditioned iterative methods of conjugate gradient type for solving elliptic and parabolic problems discretized on grids wth local refinement are considered. The sparsity pattern of the residuals computed throughout the iterative process is investigated. It turns out that they are nonzero only near the interface nodes between the coarse-and fine-grids. This observation is used to formulate the preconditioned CG, and when the matrix is not symmetric as in the parabolic case—the generalized CG and GMRES methods, thus substantially saving storage and computation.
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