Abstract
Algebraic multigrid (AMG) methods are based on algebraically defined multigrid components of which, in particular, a proper definition of interpolation is important for obtaining fast and robust convergence. This is because AMG convergence crucially depends on how well the range of interpolation approximates the range of the smoothing operator used. On the basis of various experiments, we will demonstrate the dependency of convergence on the interpolation operator. A simple improvement by means of a Jacobi relaxation step, applied to the interpolation, is shown to considerably enhance convergence and robustness. Relaxation of interpolation can also be used to improve the performance of algebraic multigrid approaches which are based on accelerated coarsening strategies. Finally, in a parallel environment, the use of local relaxation of interpolation (only along processor boundaries) may be used to stabilize convergence.
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Krechel, A., Stüben, K. (1998). Operator Dependent Interpolation in Algebraic Multigrid. In: Hackbusch, W., Wittum, G. (eds) Multigrid Methods V. Lecture Notes in Computational Science and Engineering, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58734-4_11
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DOI: https://doi.org/10.1007/978-3-642-58734-4_11
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