Currently supports FEniCS 2019.1.0 on Python 3.6.8
Gryphon is intended to serve as a tool for solving systems of time dependent partial differential equations in FEniCS. It achieves this by solving the semidiscretized system of ordinary differential equations arising by applying a finite element method with a Runge-Kutta method. Gryphon currently supports singly diagonally implicit Runge-Kutta methods with an explicit first stage (ESDIRKs) of order 2, 3 and 4, developed by Anne Kværnø at the Norwegian University of Science and Technology.
Gryphon is delivered with some (hopefully) easy-to-follow code examples intended to help you on your way to solving your own problems. The examples included are:
- The heat equation
- The Gray-Scott equations
- The Cahn-Hilliard equations
- The Aliev-Panfilov model (thanks to Vladimir Zverev)
Gryphon came about as a result of my masters thesis. It is available by following this link: http://bit.ly/gryphon-thesis
Each branch contains roughly the following folders:
documentation/
This folder contains the documentation for Gryphon. To start, open the Gryphon.html file in any web browser (Firefox/Chrome looks good).
source/
This folder contains the source code for the Gryphon module. In order to use Gryphon, this folder must be included in your Python-path.
examplecode/
This folder contains the Python code for the examples found in the Gryphon user manual. This is a good place to start.
Gryphon requires that FEniCS is installed. Currently only Linux is supported (Ubuntu/Mint tested). Once you have downloaded the desired branch, make sure that the folder source is present in your $PYTHONPATH variable. When this is in place, you should be able to run the example scripts found in the examplecode folder.
From here on, Gryphon will be hosted on Github. I've also attempted to make the code run on FEniCS 2019.1.0 / Python 3.6.8.
From here on, Gryphon will be hosted on Bitbucket. Also, I have done some preliminary testing with Gryphon on FEniCS 1.4.0, it looks like it should perform as it used to. If you encounter any quirks, let me know. I have also added some small updates to the parameters. The updates include:
- User can specify absolute path for output data
- User can specify which img format the plot of the time steps should have (eps/png/jpg)
- User is prompted when a script is about to reuse an already existing path for storing output data. This is to prevent output data being overwritten (statistics, plots, etc). A parameter has been added to always allow for reuse if desirable.
Michael J. Welland has recently published an article in the journal Physical Review E, where he used FEniCS and Gryphon to simulate a "Multicomponent phase-field model for extremely large partition coefficients". His article can be found on his website (http://www.mikewelland.com/publications/journalarticle-3) where he has also published the code used for the simulations (http://www.mikewelland.com/publications/code).
Congratulations, Mike!
Once an ESDIRK Python object (here denoted as ESDIRK_Object) has been created, you can modify the following parameters:
ESDIRK_Object.parameters["drawplot"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | If this value is set to True, a plot of the current time step will be displayed. This can be useful when doing initial testing on a problem. |
ESDIRK_Object.parameters["verbose"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | This parameter will cause extra information to be printed to the terminal as the script is running. |
ESDIRK_Object.parameters["method"]
| Possible values | string, "ESDIRK32a"/"ESDIRK32b"/"ESDIRK43a"/"ESDIRK43b" |
| Default value | "ESDIRK43b" |
| Effect | This parameter selects which ESDIRK method that should be used for the time integration. The default set method "ESDIRK43b" has the highest order and is generally a good place to start. |
ESDIRK_Object.parameters["output"]["statistics"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | If set to True, runtime statistics will be saved to a sub-folder to where the script was run from. The name of the folder will be on the format
The user can specify an own path by using the parameter "path" (to be defined). |
ESDIRK_Object.parameters["output"]["imgformat"]
| Possible values | string, "eps"/"jpg"/"png" |
| Default value | "png" |
| Effect | Sets the image format for the plot of the selected time steps by the time stepping algorithm. Note that output statistics must be set to True in order for this to have any effect. |
ESDIRK_Object.parameters["output"]["path"]
| Default value | "" |
| Effect | Sets the path where Gryphon output data will be stored. If the path does not start with a slash (/), the folder will be relative to the current working directory. If the path does start with a slash, the path will be absolute. As an example, consider a FEniCS/Gryphon script stored in the folder "/home/user/my_numerical_test/test.py". If the "path" parameter is set to "my_output", the output will be stored in "/home/user/my_numerical_test/my_output/" if the script "test.py" is run from "/home/user/my_numerical_test/". If "path" is set to "/tmp/foo/", the output will be stored in that folder regardless. Gryphon will inform the user if the specified path is unavailable for writing. |
ESDIRK_Object.parameters["output"]["plot"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | If this parameter is set to True, a plot of each of the time steps will be stored to a sub folder named "plot" below the path specified by the "path" parameter. The plots will be stored in VTK format. |
ESDIRK_Object.parameters["output"]["reuseoutputfolder"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | If the same script is executed twice, any runtime statistics or saved plots are at risk of being overwritten. Because of this, the user must explicitly acknowledge that they want to reuse the specified path whenever a Gryphon script is executed. If this parameter is set to True, Gryphon will reuse the specified path without asking. |
ESDIRK_Object.parameters["timestepping"]["dt"]
| Possible values | double, positive |
| Default value | One thousandth of the specified time integration domain. |
| Effect | Initial time step used when doing the time integration. If the parameter "adaptive" is set to False, this time step will be used for the entire time integration (fixed time stepping). |
ESDIRK_Object.parameters["timestepping"]["dtmax"]
| Possible values | double, positive |
| Default value | 0.1 |
| Effect | Largest allowable time stepping value that Gryphon can use when doing adaptive time stepping. |
ESDIRK_Object.parameters["timestepping"]["dtmin"]
| Possible values | double, positive |
| Default value | 1e-14 |
| Effect | Smallest allowable time stepping value that Gryphon can use when doing adaptive time stepping. |
ESDIRK_Object.parameters["timestepping"]["adaptive"]
| Possible values | boolean, True/False |
| Default value | True |
| Effect | Turn on/off adaptive time stepping. Setting this to False implies fixed time stepping. |
ESDIRK_Object.parameters["timestepping"]["convergence_criterion"]
| Possible values | string, "absolute"/"relative" |
| Default value | "absolute" |
| Effect | Set absolute or relative as convergence criterion when doing adaptive time integration. |
ESDIRK_Object.parameters["timestepping"]["absolute_tolerance"]
| Possible values | double, positive |
| Default value | 1e-07 |
| Effect | Set the magnitude of the absolute convergence criterion. |
ESDIRK_Object.parameters["timestepping"]["relative_tolerance"]
| Possible values | double, positive |
| Default value | 1e-06 |
| Effect | Set the magnitude of the relative convergence criterion. |
ESDIRK_Object.parameters["timestepping"]["inconsistent_initialdata"]
| Possible values | boolean, True/False |
| Default value | False |
| Effect | If you are using Gryphon to solve an index 1 DAE problem and the initial data is inconsistent, setting this parameter to True will cause Gryphon to take a very small first time step in order to arrive at a better set of initial data before starting the time integration. Note that this might not work if the initial data is too far off. |
ESDIRK_Object.parameters["timestepping"]["stepsizeselector"]
| Possible values | String, "gustafsson"/"standard" |
| Default value | "standard" |
| Effect | Select algorithm for calculating the adaptive step sizes. The standard algorithm only use the previous time step to calculate the next while the Gustafsson algorithm uses the two previous time steps. |
ESDIRK_Object.parameters["timestepping"]["pessimistic_factor"]
| Possible values | double, [0,1] |
| Default value | 0.8 |
| Effect | The pessimistic factor determines how confident Gryphon is in the derived estimate for the next time step. A value of 1.0 is perfect confidence while 0.0 is no confidence (meaningless as the time stepping process will not proceed). This can be tweaked if you are having trouble with too many time steps being rejected. |