Abstract
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 L 2–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.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
This work of the first author was sponsored by the Department of Energy under grant numbers DE-FG02-03ER25574 and DE-FC02-06ER25784, Lawrence Livermore National Laboratory under contract numbers B568677, and the National Science Foundation under grant numbers DMS-0621199, DMS-0749317, and DMS-0811275.
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Brezina, M., Vassilevski, P.S. (2012). Smoothed Aggregation Spectral Element Agglomeration AMG: SA-ρAMGe. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_1
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DOI: https://doi.org/10.1007/978-3-642-29843-1_1
Publisher Name: Springer, Berlin, Heidelberg
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