CASL-HJX

CASL-HJX is a C++ library for solving Hamilton-Jacobi equations and related partial differential equations using high-order numerical methods.

Features

• Hamilton-Jacobi-Bellman equations for optimal control problems
• Linear quadratic regulator (LQR) with SIMD optimization
• Level-set methods for interface tracking
• High-order WENO and ENO spatial discretization
• TVD Runge-Kutta time integration
• IMEX methods for stiff problems
• MPI and OpenMP parallelization

The library supports various PDE types including advection, diffusion, Burgers equation, and advection-diffusion systems.

Example: LQR Optimal Control

Example: Advection in Normal Direction

Installation

git clone https://github.com/UCSB-CASL/CASL-HJX.git
cd CASL-HJX
mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j

Requirements: C++17 compiler, CMake 3.15+, OpenMP 4.0+

Quick Start

# Run LQR example
cd CASLProjects/projectLQR2D
./projectLQR2D 80 160

# Run other examples
cd ../projectAdvection && ./projectAdvection
cd ../projectBurgers && ./projectBurgers

Documentation

• User Manual Paper: https://arxiv.org/abs/2505.11527
• Examples: examples/ directory

Authors

Faranak Rajabi, Jacob Fingerman, Andrew Wang, Jeff Moehlis, Frederic Gibou

Computational Applied Systems Laboratory (CASL)
Department of Mechanical Engineering
University of California, Santa Barbara
https://sites.engineering.ucsb.edu/~fgibou/index.html

Citation

@article{rajabi2025caslhjx,
  title={CASL-HJX: A Comprehensive Guide to Solving Deterministic and 
         Stochastic Hamilton-Jacobi Equations},
  author={Rajabi, Faranak and Fingerman, Jacob and Wang, Andrew and 
          Moehlis, Jeff and Gibou, Frederic},
  journal={Computer Physics Communications},
  year={2025},
  note={Submitted}
}

License

Academic research license. See LICENSE file for details.