MOLE is a high-quality (C++ & MATLAB/Octave) library that implements high-order mimetic operators to solve partial differential equations. It provides discrete analogs of the most common vector calculus operators: Gradient, Divergence, Laplacian, Bilaplacian, and Curl. These operators (highly sparse matrices) act on staggered grids (uniform, non-uniform, curvilinear) and satisfy local and global conservation laws.
Mathematics is based on the work of Corbino and Castillo. However, the user may find helpful previous publications, such as Castillo and Grone, in which similar operators were derived using a matrix analysis approach.
To install the MOLE library, you'll need the following packages:
- CMake (Minimum version 3.10)
- OpenBLAS (Minimum version 0.3.10)
- Eigen3
- LAPACK (Mac only)
- libomp (Mac only)
For documentation build requirements, please refer to the Documentation Guide.
# Install all required packages
sudo apt install cmake libopenblas-dev libeigen3-devInstall Homebrew if you don't have it already, then run:
# Install all required packages
brew install cmake openblas eigen libomp lapackTroubleshooting Homebrew: If you encounter installation errors, try these steps:
# Fix permissions issues sudo chown -R $(whoami) /usr/local/Cellar # Fix shallow clone issues git -C /usr/local/Homebrew/Library/Taps/homebrew/homebrew-core fetch --unshallow # Remove Java dependencies if they cause conflicts brew uninstall --ignore-dependencies java brew update
# Install all required packages
sudo yum install cmake openblas-devel eigen3-devel-
Clone the repository:
git clone https://github.com/csrc-sdsu/mole.git cd mole -
Build the library:
mkdir build && cd build cmake .. make
-
Install the library:
- For a custom location:
cmake --install . --prefix /path/to/location - For a system location (requires privileges):
Or
sudo cmake --install .sudo cmake --install . --prefix /path/to/privileged/location
- For a custom location:
Note: Armadillo and SuperLU will be automatically installed in the build directory during the build process.
A suite of four automatic tests that verify MOLE's installation and dependencies. These tests run automatically during the C++ library construction.
Run from the build directory:
make run_testsMATLAB/Octave equivalent of the C++ test suite. We recommend running these tests before using MOLE to ensure proper setup.
Run from the tests/matlab:
run_testsFour self-contained, well-documented examples demonstrating typical PDE solutions. These are automatically built with make and serve as an excellent starting point for C++ users.
A collection of over 30 examples showcasing various PDE solutions, from simple linear one-dimensional problems to complex nonlinear multidimensional scenarios.
MOLE comes with comprehensive documentation:
- API Reference & User Guide: Access our online Documentation
- Building Documentation: To build documentation locally, follow our Documentation Guide.
Important Note: Performing non-unary operations involving operands constructed over different grids may lead to unexpected results. While MOLE allows such operations without throwing errors, users must exercise caution when manipulating operators across different grids.
MOLE is distributed under a GNU General Public License; please refer to the LICENSE file for more details.
We welcome contributions to MOLE, including:
- Adding new functionalities
- Providing examples
- Addressing existing issues
- Reporting bugs
- Requesting new features
Please refer to our Contribution Guidelines for more details.
Please cite our work if you use MOLE in your research or software. Citations are helpful for the continued development and maintenance of the library.
Now, some cool pictures obtained with MOLE:
