Summary
| Also known as
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| Model type
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| Model part of larger framework
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| Note on status model
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| Date note status model
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Technical specs
| Supported platforms
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Unix, Linux
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| Other platform
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| Programming language
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Python
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| Other program language
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| Code optimized
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Single Processor
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| Multiple processors implemented
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| Nr of distributed processors
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| Nr of shared processors
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| Start year development
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2010
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| Does model development still take place?
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Yes
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| If above answer is no, provide end year model development
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| Code development status
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| When did you indicate the 'code development status'?
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| Model availability
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As code, As teaching tool
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Source code availability
(Or provide future intension)
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Through owner"Through owner" is not in the list (Through web repository, Through CSDMS repository) of allowed values for the "Source code availability" property., Through CSDMS repository
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| Source web address
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| Source csdms web address
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| Program license type
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GPL v3
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| Program license type other
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| Memory requirements
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| Typical run time
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Minutes to populate cofactor matrix, ~1 second for solution
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In/Output
| Describe input parameters
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- Elastic thickness map (ASCII)
- Load map (ASCII)
- dx, dy
- Material properties
- Young's modulus
- Poisson's ratio
- density of load
- density of infilling material (optional; this can also be done via iteration for more complicated situations
Only the elastic thickness and load need to be actual input files. The rest (scalars) can be specified at the command line interface.
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| Input format
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ASCII
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| Other input format
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| Describe output parameters
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Cofactor matrix (*.mtx sparse matrix file; ASCII)
Flexural response map (ASCII)
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| Output format
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ASCII
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| Other output format
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| Pre-processing software needed?
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No
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| Describe pre-processing software
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| Post-processing software needed?
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No
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| Describe post-processing software
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| Visualization software needed?
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No
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| If above answer is yes
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| Other visualization software
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Process
| Describe processes represented by the model
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Response of a lithospheric plate, potentially with nonuniform elastic thickness, to an applied surface load
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| Describe key physical parameters and equations
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We solve the PDE for lithospheric flexure in 2 dimensions:
'"`UNIQ--math-00000000-QINU`"'
Here, $D$ is the flexural rigidity, $w$ is the vertical displacement at each $(x,y)$, $\Delta \rho$ is the mantle density minus the density of infilling material, $g$ is gravitational acceleration, and $q$ is the applied load. We follow Wees and Cloetingh (1994) in acknowledging that flexural rigidity is a tensor property:
'"`UNIQ--math-00000001-QINU`"'
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| Describe length scale and resolution constraints
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Insufficiently tested to know.
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| Describe time scale and resolution constraints
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Currently does not time-evolve. I would like to couple this to a 3D viscoelastic mantle at some point, but this hasn't happened yet.
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| Describe any numerical limitations and issues
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Insufficiently tested to know.
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Testing
| Describe available calibration data sets
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| Upload calibration data sets if available:
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| Describe available test data sets
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| Upload test data sets if available:
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| Describe ideal data for testing
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Other
| Do you have current or future plans for collaborating with other researchers?
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| Is there a manual available?
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No
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| Upload manual if available:
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| Model website if any
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| Model forum / discussion board
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Introduction
The model flexure computes a direct Thomas algorithm finite difference solution to the flexure equations for a lithospheric plate of nonuniform elastic thickness via a thin plate assumption. It consists of two modules, the first of which is used to generate the coefficient matrix for the Thomas algorithm solution and the second of which actually generates that solution (using the coefficient matrix produced by the first module as an input file). The first module is slow, but the second is very fast, making this a poor technique for a one-off equilibrium flexure calculation, but a good choice for situations in which flexural response needs to be calculated many times in a row. Such situations in which this model would excel include:
- Numerical models that require frequent updating of flexural deformations of the lithosphere
- Simulations with forcings that take place on a time-scale that is comparable to the time-scale of Earth response to loading and unloading (e.g., ice and water loading during glacial cycles)
- Calculations of mixed sediment and/or water loading, or water loading with onlap and offlap, such that a constant fill density cannot be assumed and solutions must be produced iteratively.
History
Flexure was developed first in MATLAB (Spring / early Summer 2010) and then in python (translated October 2010).
The next planned step in development is to make flexure be IRF- and CMT-compliant.
Planned development will proceed slowly through Spring 2011 (though this will go faster if I get a solid day or two to work on it). Because the program is based on a set of functions in a python module, we plan on adding additional functionality for 1D and 2D analytical solutions, a 1D Thomas algorithm solution, and a 2D alternating direction implicit (ADI) iterative solution. If all goes as planned, this should be a one-stop shop for flexure solutions.
Papers
Issues
Help
Email Andy Wickert (see contact info in box at top).
Input Files
The coefficient matrix for the 2D Thomas algorithm solution requires a map of elastic thicknesses in *.txt / ASCII format. This elastic thickness map must be two cells wider on each side than the map of loads; this is because the finite difference solution must "look" two cells in every direction. It also requires the specification of several parameters, including:
- Young's modulus (defaults to 1011 Pa)
- Poisson's ratio (defaults to 0.25)
- Mantle density (defaults to 3300 kg/m3)
- Density of infilling material (defaults to 0 kg/m3)
This outputs an ASCII sparse matrix file (Matrix Market *.mtx format).
The flexural solution requires the ASCII file for the sparse coefficient matrix generated above and an imposed array of loads (also ASCII), along with the specification of input and output file names.
Output Files
Download
Template:Download Model
Source
Command-Line Access
If you plan to make changes, use this command to check out the code as yourself using HTTPS:
# Project members authenticate over HTTPS to allow committing changes.
svn checkout https://csdms.colorado.edu/svn/flexure
When prompted, enter your CSDMS Subversion password.
Non-members may only check out a read-only working copy of the project source.
To obtain a CSDMS Subversion account or to become a member of this project, please email csdms@colorado.edu.
Need help with Subversion? Go to the subversion help page.
GUI and IDE Access
This project's Subversion repository may be accessed using many different client programs and plug-ins. See your client's documentation for more information.
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