The smoothing properties of the alternating direction implicit method in multigrid iterations |
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| Institution: | 1. Institute of Electronic Structure and Laser, Foundation for Research and Technology - Hellas, Heraklion, 71110, Crete, Greece;2. Department of Physics, University of Crete, 70013, Heraklion, Greece;3. Bundesanstalt für Materialforschung und −prüfung (BAM), 12205, Berlin, Germany;4. Institute of Applied Physics, Johannes Kepler University Linz, 4040, Linz, Austria;5. Laser Processing Group, Instituto de Optica (IO-CSIC), Consejo Superior de Investigaciones Científicas, CSIC, 28006, Madrid, Spain;6. Department of Materials Science and Technology, University of Crete, 70013, Heraklion, Greece;7. Institute for Zoology, RWTH Aachen University, 52074, Aachen, Germany;8. Institute of Biomedical Mechatronics, Johannes Kepler University Linz, 4040, Linz, Austria;1. Institute for Software Convergence, Hanyang University, Seoul, Republic of Korea;2. Department of Emergency Medicine, College of Medicine, Hanyang University, Seoul, Republic of Korea |
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| Abstract: | The performance of the alternating direction implicit (ADI) method within the multigrid context is examined. Local mode analysis is used to predict the smoothing properties of ADI for the Laplace problem and the biharmonic equation. The smoothing rate of ADI is shown to compare favourably with that of the Gauss-Seidel method. As a result, fewer iterations are required when ADI is used as the relaxation process in the multigrid method. |
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