MOLE: Mimetic Operators Library Enhanced

Description

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.

Installation

Platform and Compiler Compatibility

Refer to the table below for compiler support across different operating systems when building MOLE.

OS / Compiler	GCC 13.2.0	AppleClang	IntelLLVM (icpx)
Linux	Yes	No	Yes
macOS	No	Yes	Yes

Prerequisites

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.

Package Installation by OS

Ubuntu/Debian Systems

# Install all required packages
sudo apt install cmake libopenblas-dev libeigen3-dev

macOS Systems

Install Homebrew if you don't have it already, then run:

# Install all required packages
brew install cmake openblas eigen libomp lapack

Troubleshooting 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

RHEL/CentOS/Fedora Systems

# Install all required packages
sudo yum install cmake openblas-devel eigen3-devel lapack

Building and Installing

1. Clone the repository:

   git clone https://github.com/csrc-sdsu/mole.git
   cd mole

2. Build the library:

   mkdir build && cd build
   cmake ..
   make

3. Install the library:

   • For a custom location:

     cmake --install . --prefix /path/to/location

   • For a system location (requires privileges):

     sudo cmake --install .

     Or

     sudo cmake --install . --prefix /path/to/privileged/location

Note: Armadillo and SuperLU will be automatically installed in the build directory during the build process.

Testing

Run from the build directory:

C++

A suite of four automatic tests that verify MOLE's installation and dependencies. These tests run automatically during the C++ library construction.

make run_tests

MATLAB/Octave

MATLAB/Octave equivalent of the C++ test suite. We recommend running these tests before using MOLE to ensure proper setup.

make run_matlab_octave_tests

Examples

Many of the examples require 'gnuplot' to visualize the results. You can get gnuplot on macOSX with

brew install gnuplot

and on Windows downlaoding and running the file from here

C++

Four 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.

MATLAB/Octave Examples

A collection of over 30 examples showcasing various PDE solutions, from simple linear one-dimensional problems to complex nonlinear multidimensional scenarios.

Documentation

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.

Licensing

MOLE is distributed under a GNU General Public License; please refer to the LICENSE file for more details.

Community Guidelines

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.

How to Cite

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.

@article{Corbino2024, 
   doi = {10.21105/joss.06288}, 
   url = {https://doi.org/10.21105/joss.06288}, 
   year = {2024}, 
   publisher = {The Open Journal}, 
   volume = {9}, 
   number = {99}, 
   pages = {6288}, 
   author = {Corbino, Johnny and Dumett, Miguel A. and Castillo, Jose E.}, 
   title = {MOLE: Mimetic Operators Library Enhanced}, 
   journal = {Journal of Open Source Software} }

The archival copy of the MOLE User Manual is maintained on Zenodo. To cite the User Manual please use:

@misc{MOLE_user_manual,
   author       = {Barra, Valeria and
                  Boada, Angel and
                  Brzenski, Jared and
                  Castillo, Jose and
                  Chakalasiya, Prit and
                  Singh, Surinder Chhabra and
                  Corbino, Johnny Delgado and
                  Drummond, Tony and
                  Dumett, Miguel and
                  Hellmers, Joe and
                  Ilaty, Arshia and
                  Kaviani, Katayoon and
                  Nzerem, Oluchi and
                  Pagallo, Giulia and
                  Paolini, Christopher and
                  Rosano, Valentina and
                  Srinivas, Aneesh Murthy and
                  Srinivasan, Janani Priyadharshini and
                  Valera, Manuel},
   title        = {{MOLE User Manual}},
   month        = aug,
   year         = 2025,
   publisher    = {Zenodo},
   version      = {1.1.0},
   doi          = {10.5281/zenodo.16898575},
   url          = {https://doi.org/10.5281/zenodo.16898575},
}

Gallery

Now, some cool pictures obtained with MOLE: