Exasim is an open-source software for generating high-order discontinuous Galerkin (DG) codes to numerically solve parametrized partial differential equations (PDEs) on different computing platforms with distributed memory. It combines high-level languages and low-level languages to easily construct parametrized PDE models and automatically produce high-performance C++ codes. The construction of parametrized PDE models and the generation of the stand-alone C++ production code are handled by high-level languages, while the production code itself can run on various machines, from laptops to the largest supercomputers, with AMD and Nvidia GPU processors. Exasim has the following capabilities:
- Solve a wide variety of PDEs in fluid mechanics, solid mechanics, electromagnetism, and multi-physics models, in 1D, 2D, and 3D
- Generate stand-alone C++ production code via the mathematical expressions of the PDEs
- Implement local DG and hybridized DG methods for spatial discretization
- Implement diagonally implicit Runge-Kutta methods for temporal discretization
- Implement parallel Newton-GMRES solvers and scalable preconditioners using reduced basis method, additive Schwarz method, block ILU, and polynomial preconditioners
- Implement monolithic multi-physics solvers for the HDG discretization
- Employ Kokkos to provide full GPU functionality for all code components from discretization schemes to iterative solvers
- Provide auto-gen tools to calculate thermodynamic, transport, chemistry, and energy transfer properties for chemically-reacting flows
- Provide application interfaces to Julia, Python, and Matlab.
Full documentation is published at https://mit-psaap-iv.github.io/Exasim
(source under docs/, built with MkDocs —
pip install -r requirements-docs.txt && mkdocs serve):
- Quickstart — build and run a built-in solve
- Installation — local (macOS, Linux CPU/NVIDIA/AMD) and HPC (Frontier, Tuolumne, generic)
- Usage modes — built-in, external built-in, shared library
- Frontends — author models in Python / Julia / MATLAB
- Model contract,
pdeapp.txt,pdemodel.txt, and CMake references - Driving the solver (C++ API) — embed Exasim in your own program
- Theory — the LDG formulation and Jacobian the contract maps to
- Internals — architecture, test harness, baselines
One command builds the whole stack — vendored dependencies (Kokkos, METIS/ParMETIS, SymEngine) are found on the system or built from source, then text2code, the solver libraries, the built-in model library, and the language frontends are built and installed:
# build directories must be OUTSIDE the source tree (the repo stays pristine)
cmake -S Exasim -B Exasim-build # add -DEXASIM_CUDA=ON or -DEXASIM_HIP=ON for GPUs
cmake --build Exasim-build -j
cmake --install Exasim-build --prefix /path/to/prefixAfter downloading the source code, make sure the folder is named Exasim and
that the path to it contains no whitespace (Kokkos will not compile otherwise).
See the installation docs for prerequisites, all
configure options, and HPC instructions (Frontier, Tuolumne, generic clusters),
and Testing / tests/README.md for the test suite.
[1] Vila-Pérez, J., Van Heyningen, R. L., Nguyen, N.-C., & Peraire, J. (2022). Exasim: Generating discontinuous Galerkin codes for numerical solutions of partial differential equations on graphics processors. SoftwareX, 20, 101212. https://doi.org/10.1016/j.softx.2022.101212
[2] Hoskin, D. S., Van Heyningen, R. L., Nguyen, N. C., Vila-Pérez, J., Harris, W. L., & Peraire, J. (2024). Discontinuous Galerkin methods for hypersonic flows. Progress in Aerospace Sciences, 146, 100999. https://doi.org/10.1016/j.paerosci.2024.100999
[3] Nguyen, N. C., Terrana, S., & Peraire, J. (2022). Large-Eddy Simulation of Transonic Buffet Using Matrix-Free Discontinuous Galerkin Method. AIAA Journal, 60(5), 3060–3077. https://doi.org/10.2514/1.j060459
[4] Nguyen, N. C., & Peraire, J. (2012). Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics. Journal of Computational Physics, 231(18), 5955–5988. https://doi.org/10.1016/j.jcp.2012.02.033