Optimal Complex Relaxation Parameters in Multigrid for Complex-Shifted Linear Systems

Robert Hocking and Chen Greif

Code for reproducing results from the paper:

1. dampingParameterStrategyExperiment.m: For reproducing the experiments in Sections 6.2 and 6.3.
2. constantCoefficient3DExperiment.m: For reproducing the Experiment in Section 6.4.
3. variableCoefficientExperiment.m: For reproducing the Experiment in Section 6.5.
4. MarmousiExperiment.m: For reproducing the Experiment in Section 6.6.
5. Multigrid.m: Main routine. Each experiment file works by creating a "setup" object which is then passed to this m-file.
6. ExploreUniversalTable.m: Allows the user to examine slices of the universal lookup table from Section 5.3. This file is purely for visualization purposes and is not needed for running the core multigrid code.
7. ColorWheelDemo.m: Explores the color wheel that we use for visualizing our complex damping parameters; see more here. This file is purely for visualization purposes and is not needed for running the core multigrid code.

To get started:

1. Click on this link to download the code.
2. Unzip the file.
3. If you run a variable coefficient problem using RB-SOR (items 3 or 4 above), you must download the universal lookup table and put it in the current directory.
4. Run a Matlab session from the main folder.
   
5. Type, for example, "help dampingParameterStrategyExperiment" to see a brief description of the code.
6. Type, for example, "dampingParameterStrategyExperiment" to run the code.
7. Edit the "setup" object parameters defined, for example, in "dampingParameterStrategyExperiment" to explore different scenarios (type "help Multigrid" for an explanation of what these parameters are and what they do).