Smoothed Aggregation Spectral Element Agglomeration AMG: SA-ρAMGe

A two---level smoothed aggregation (or SA) scheme with tentative coarse space constructed by spectral element agglomeration method is shown to provide weak---approximation property in a weighted L2 ---norm. The resulting method utilizing efficient (e.g., polynomial) smoothers is shown to have convergence factor independent of both the coarse and fine---grid mesh---sizes, as well as, to be independent of the contrast (i.e., possible large jumps in the PDE coefficient) for second order elliptic problems discretized on general unstructured meshes. The method allows for multilevel extensions. Presented numerical experiments exhibit behavior in agreement with the developed theory.

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