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Elements"],"sub_categories":[],"readme":"# libCEED: Efficient Extensible Discretization\n\n[![GitHub Actions][github-badge]][github-link]\n[![GitLab-CI][gitlab-badge]][gitlab-link]\n[![Code coverage][codecov-badge]][codecov-link]\n[![BSD-2-Clause][license-badge]][license-link]\n[![Documentation][doc-badge]][doc-link]\n[![JOSS paper][joss-badge]][joss-link]\n[![Binder][binder-badge]][binder-link]\n\n## Summary and Purpose\n\nlibCEED provides fast algebra for element-based discretizations, designed for performance portability, run-time flexibility, and clean embedding in higher level libraries and applications.\nIt offers a C99 interface as well as bindings for Fortran, Python, Julia, and Rust.\nWhile our focus is on high-order finite elements, the approach is mostly algebraic and thus applicable to other discretizations in factored form, as explained in the [user manual](https://libceed.org/en/latest/) and API implementation portion of the [documentation](https://libceed.org/en/latest/api/).\n\nOne of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec.\nThus, high-order methods require a new \"format\" that still represents a linear (or more generally non-linear) operator, but not through a sparse matrix.\n\nThe goal of libCEED is to propose such a format, as well as supporting implementations and data structures, that enable efficient operator evaluation on a variety of computational device types (CPUs, GPUs, etc.).\nThis new operator description is based on algebraically [factored form](https://libceed.org/en/latest/libCEEDapi/#finite-element-operator-decomposition), which is easy to incorporate in a wide variety of applications, without significant refactoring of their own discretization infrastructure.\n\nThe repository is part of the [CEED software suite](http://ceed.exascaleproject.org/software/), a collection of software benchmarks, miniapps, libraries and APIs for efficient exascale discretizations based on high-order finite element and spectral element methods.\nSee \u003chttp://github.com/ceed\u003e for more information and source code availability.\n\nThe CEED research is supported by the [Exascale Computing Project](https://exascaleproject.org/exascale-computing-project) (17-SC-20-SC), a collaborative effort of two U.S. Department of Energy organizations (Office of Science and the National Nuclear Security Administration) responsible for the planning and preparation of a [capable exascale ecosystem](https://exascaleproject.org/what-is-exascale), including software, applications, hardware, advanced system engineering and early testbed platforms, in support of the nation’s exascale computing imperative.\n\nFor more details on the CEED API see the [user manual](https://libceed.org/en/latest/).\n\n% gettingstarted-inclusion-marker\n\n## Building\n\nThe CEED library, `libceed`, is a C99 library with no required dependencies, and with Fortran, Python, Julia, and Rust interfaces.\nIt can be built using:\n\n```console\n$ make\n```\n\nor, with optimization flags:\n\n```console\n$ make OPT='-O3 -march=skylake-avx512 -ffp-contract=fast'\n```\n\nThese optimization flags are used by all languages (C, C++, Fortran) and this makefile variable can also be set for testing and examples (below).\n\nThe library attempts to automatically detect support for the AVX instruction set using gcc-style compiler options for the host.\nSupport may need to be manually specified via:\n\n```console\n$ make AVX=1\n```\n\nor:\n\n```console\n$ make AVX=0\n```\n\nif your compiler does not support gcc-style options, if you are cross compiling, etc.\n\nTo enable CUDA support, add `CUDA_DIR=/opt/cuda` or an appropriate directory to your `make` invocation.\nTo enable HIP support, add `ROCM_DIR=/opt/rocm` or an appropriate directory.\nTo enable SYCL support, add `SYCL_DIR=/opt/sycl` or an appropriate directory.\nNote that SYCL backends require building with oneAPI compilers as well:\n\n```console\n$ . /opt/intel/oneapi/setvars.sh\n$ make SYCL_DIR=/opt/intel/oneapi/compiler/latest/linux SYCLCXX=icpx CC=icx CXX=icpx\n```\n\nThe library can be configured for host applications which use OpenMP paralellism via:\n\n```console\n$ make OPENMP=1\n```\n\nwhich will allow operators created and applied from different threads inside an `omp parallel` region.\n\nTo store these or other arguments as defaults for future invocations of `make`, use:\n\n```console\n$ make configure CUDA_DIR=/usr/local/cuda ROCM_DIR=/opt/rocm OPT='-O3 -march=znver2'\n```\n\nwhich stores these variables in `config.mk`.\n\n### WebAssembly\n\nlibCEED can be built for WASM using [Emscripten](https://emscripten.org). For example, one can build the library and run a standalone WASM executable using\n\n``` console\n$ emmake make build/ex2-surface.wasm\n$ wasmer build/ex2-surface.wasm -- -s 200000\n```\n\n## Additional Language Interfaces\n\nThe Fortran interface is built alongside the library automatically.\n\nPython users can install using:\n\n```console\n$ pip install libceed\n```\n\nor in a clone of the repository via `pip install .`.\n\nJulia users can install using:\n\n```console\n$ julia\njulia\u003e ]\npkg\u003e add LibCEED\n```\n\nSee the [LibCEED.jl documentation](http://ceed.exascaleproject.org/libCEED-julia-docs/dev/) for more information.\n\nRust users can include libCEED via `Cargo.toml`:\n\n```toml\n[dependencies]\nlibceed = \"0.12.0\"\n```\n\nSee the [Cargo documentation](https://doc.rust-lang.org/cargo/reference/specifying-dependencies.html#specifying-dependencies-from-git-repositories) for details.\n\n## Testing\n\nThe test suite produces [TAP](https://testanything.org) output and is run by:\n\n```console\n$ make test\n```\n\nor, using the `prove` tool distributed with Perl (recommended):\n\n```console\n$ make prove\n```\n\n## Backends\n\nThere are multiple supported backends, which can be selected at runtime in the examples:\n\n| CEED resource              | Backend                                           | Deterministic Capable |\n| :---                       | :---                                              | :---:                 |\n||\n| **CPU Native**             |\n| `/cpu/self/ref/serial`     | Serial reference implementation                   | Yes                   |\n| `/cpu/self/ref/blocked`    | Blocked reference implementation                  | Yes                   |\n| `/cpu/self/opt/serial`     | Serial optimized C implementation                 | Yes                   |\n| `/cpu/self/opt/blocked`    | Blocked optimized C implementation                | Yes                   |\n| `/cpu/self/avx/serial`     | Serial AVX implementation                         | Yes                   |\n| `/cpu/self/avx/blocked`    | Blocked AVX implementation                        | Yes                   |\n||\n| **CPU Valgrind**           |\n| `/cpu/self/memcheck/*`     | Memcheck backends, undefined value checks         | Yes                   |\n||\n| **CPU LIBXSMM**            |\n| `/cpu/self/xsmm/serial`    | Serial LIBXSMM implementation                     | Yes                   |\n| `/cpu/self/xsmm/blocked`   | Blocked LIBXSMM implementation                    | Yes                   |\n||\n| **CUDA Native**            |\n| `/gpu/cuda/ref`            | Reference pure CUDA kernels                       | Yes                   |\n| `/gpu/cuda/shared`         | Optimized pure CUDA kernels using shared memory   | Yes                   |\n| `/gpu/cuda/gen`            | Optimized pure CUDA kernels using code generation | No                    |\n||\n| **HIP Native**             |\n| `/gpu/hip/ref`             | Reference pure HIP kernels                        | Yes                   |\n| `/gpu/hip/shared`          | Optimized pure HIP kernels using shared memory    | Yes                   |\n| `/gpu/hip/gen`             | Optimized pure HIP kernels using code generation  | No                    |\n||\n| **SYCL Native**            |\n| `/gpu/sycl/ref`            | Reference pure SYCL kernels                       | Yes                   |\n| `/gpu/sycl/shared`         | Optimized pure SYCL kernels using shared memory   | Yes                   |\n||\n| **MAGMA**                  |\n| `/gpu/cuda/magma`          | CUDA MAGMA kernels                                | No                    |\n| `/gpu/cuda/magma/det`      | CUDA MAGMA kernels                                | Yes                   |\n| `/gpu/hip/magma`           | HIP MAGMA kernels                                 | No                    |\n| `/gpu/hip/magma/det`       | HIP MAGMA kernels                                 | Yes                   |\n||\n| **OCCA**                   |\n| `/*/occa`                  | Selects backend based on available OCCA modes     | Yes                   |\n| `/cpu/self/occa`           | OCCA backend with serial CPU kernels              | Yes                   |\n| `/cpu/openmp/occa`         | OCCA backend with OpenMP kernels                  | Yes                   |\n| `/cpu/dpcpp/occa`          | OCCA backend with DPC++ kernels                   | Yes                   |\n| `/gpu/cuda/occa`           | OCCA backend with CUDA kernels                    | Yes                   |\n| `/gpu/hip/occa`            | OCCA backend with HIP kernels                     | Yes                   |\n\nThe `/cpu/self/*/serial` backends process one element at a time and are intended for meshes with a smaller number of high order elements.\nThe `/cpu/self/*/blocked` backends process blocked batches of eight interlaced elements and are intended for meshes with higher numbers of elements.\n\nThe `/cpu/self/ref/*` backends are written in pure C and provide basic functionality.\n\nThe `/cpu/self/opt/*` backends are written in pure C and use partial e-vectors to improve performance.\n\nThe `/cpu/self/avx/*` backends rely upon AVX instructions to provide vectorized CPU performance.\n\nThe `/cpu/self/memcheck/*` backends rely upon the [Valgrind](https://valgrind.org/) Memcheck tool to help verify that user QFunctions have no undefined values.\nTo use, run your code with Valgrind and the Memcheck backends, e.g. `valgrind ./build/ex1 -ceed /cpu/self/ref/memcheck`.\nA 'development' or 'debugging' version of Valgrind with headers is required to use this backend.\nThis backend can be run in serial or blocked mode and defaults to running in the serial mode if `/cpu/self/memcheck` is selected at runtime.\n\nThe `/cpu/self/xsmm/*` backends rely upon the [LIBXSMM](https://github.com/libxsmm/libxsmm) package to provide vectorized CPU performance.\nIf linking MKL and LIBXSMM is desired but the Makefile is not detecting `MKLROOT`, linking libCEED against MKL can be forced by setting the environment variable `MKL=1`.\nThe LIBXSMM `main` development branch from 7 April 2024 or newer is required.\n\nThe `/gpu/cuda/*` backends provide GPU performance strictly using CUDA.\n\nThe `/gpu/hip/*` backends provide GPU performance strictly using HIP.\nThey are based on the `/gpu/cuda/*` backends.\nROCm version 4.2 or newer is required.\n\nThe `/gpu/sycl/*` backends provide GPU performance strictly using SYCL.\nThey are based on the `/gpu/cuda/*` and `/gpu/hip/*` backends.\n\nThe `/gpu/*/magma/*` backends rely upon the [MAGMA](https://bitbucket.org/icl/magma) package.\nTo enable the MAGMA backends, the environment variable `MAGMA_DIR` must point to the top-level MAGMA directory, with the MAGMA library located in `$(MAGMA_DIR)/lib/`.\nBy default, `MAGMA_DIR` is set to `../magma`; to build the MAGMA backends with a MAGMA installation located elsewhere, create a link to `magma/` in libCEED's parent directory, or set `MAGMA_DIR` to the proper location.\nMAGMA version 2.5.0 or newer is required.\nCurrently, each MAGMA library installation is only built for either CUDA or HIP.\nThe corresponding set of libCEED backends (`/gpu/cuda/magma/*` or `/gpu/hip/magma/*`) will automatically be built for the version of the MAGMA library found in `MAGMA_DIR`.\n\nUsers can specify a device for all CUDA, HIP, and MAGMA backends through adding `:device_id=#` after the resource name.\nFor example:\n\n\u003e - `/gpu/cuda/gen:device_id=1`\n\nThe `/*/occa` backends rely upon the [OCCA](http://github.com/libocca/occa) package to provide cross platform performance.\nTo enable the OCCA backend, the environment variable `OCCA_DIR` must point to the top-level OCCA directory, with the OCCA library located in the `${OCCA_DIR}/lib` (By default, `OCCA_DIR` is set to `../occa`).\nOCCA version 1.4.0 or newer is required.\n\nUsers can pass specific OCCA device properties after setting the CEED resource.\nFor example:\n\n\u003e - `\"/*/occa:mode='CUDA',device_id=0\"`\n\nBit-for-bit reproducibility is important in some applications.\nHowever, some libCEED backends use non-deterministic operations, such as `atomicAdd` for increased performance.\nThe backends which are capable of generating reproducible results, with the proper compilation options, are highlighted in the list above.\n\n## Examples\n\nlibCEED comes with several examples of its usage, ranging from standalone C codes in the `/examples/ceed` directory to examples based on external packages, such as MFEM, PETSc, and Nek5000.\nNek5000 v18.0 or greater is required.\n\nTo build the examples, set the `MFEM_DIR`, `PETSC_DIR` (and optionally `PETSC_ARCH`), and `NEK5K_DIR` variables and run:\n\n```console\n$ cd examples/\n```\n\n% running-examples-inclusion-marker\n\n```console\n# libCEED examples on CPU and GPU\n$ cd ceed/\n$ make\n$ ./ex1-volume -ceed /cpu/self\n$ ./ex1-volume -ceed /gpu/cuda\n$ ./ex2-surface -ceed /cpu/self\n$ ./ex2-surface -ceed /gpu/cuda\n$ cd ..\n\n# MFEM+libCEED examples on CPU and GPU\n$ cd mfem/\n$ make\n$ ./bp1 -ceed /cpu/self -no-vis\n$ ./bp3 -ceed /gpu/cuda -no-vis\n$ cd ..\n\n# Nek5000+libCEED examples on CPU and GPU\n$ cd nek/\n$ make\n$ ./nek-examples.sh -e bp1 -ceed /cpu/self -b 3\n$ ./nek-examples.sh -e bp3 -ceed /gpu/cuda -b 3\n$ cd ..\n\n# PETSc+libCEED examples on CPU and GPU\n$ cd petsc/\n$ make\n$ ./bps -problem bp1 -ceed /cpu/self\n$ ./bps -problem bp2 -ceed /gpu/cuda\n$ ./bps -problem bp3 -ceed /cpu/self\n$ ./bps -problem bp4 -ceed /gpu/cuda\n$ ./bps -problem bp5 -ceed /cpu/self\n$ ./bps -problem bp6 -ceed /gpu/cuda\n$ cd ..\n\n$ cd petsc/\n$ make\n$ ./bpsraw -problem bp1 -ceed /cpu/self\n$ ./bpsraw -problem bp2 -ceed /gpu/cuda\n$ ./bpsraw -problem bp3 -ceed /cpu/self\n$ ./bpsraw -problem bp4 -ceed /gpu/cuda\n$ ./bpsraw -problem bp5 -ceed /cpu/self\n$ ./bpsraw -problem bp6 -ceed /gpu/cuda\n$ cd ..\n\n$ cd petsc/\n$ make\n$ ./bpssphere -problem bp1 -ceed /cpu/self\n$ ./bpssphere -problem bp2 -ceed /gpu/cuda\n$ ./bpssphere -problem bp3 -ceed /cpu/self\n$ ./bpssphere -problem bp4 -ceed /gpu/cuda\n$ ./bpssphere -problem bp5 -ceed /cpu/self\n$ ./bpssphere -problem bp6 -ceed /gpu/cuda\n$ cd ..\n\n$ cd petsc/\n$ make\n$ ./area -problem cube -ceed /cpu/self -degree 3\n$ ./area -problem cube -ceed /gpu/cuda -degree 3\n$ ./area -problem sphere -ceed /cpu/self -degree 3 -dm_refine 2\n$ ./area -problem sphere -ceed /gpu/cuda -degree 3 -dm_refine 2\n\n$ cd fluids/\n$ make\n$ ./navierstokes -ceed /cpu/self -degree 1\n$ ./navierstokes -ceed /gpu/cuda -degree 1\n$ cd ..\n\n$ cd solids/\n$ make\n$ ./elasticity -ceed /cpu/self -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -problem Linear -forcing mms\n$ ./elasticity -ceed /gpu/cuda -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -problem Linear -forcing mms\n$ cd ..\n```\n\nFor the last example shown, sample meshes to be used in place of `[.exo file]` can be found at \u003chttps://github.com/jeremylt/ceedSampleMeshes\u003e\n\nThe above code assumes a GPU-capable machine with the CUDA backends enabled.\nDepending on the available backends, other CEED resource specifiers can be provided with the `-ceed` option.\nOther command line arguments can be found in [examples/petsc](https://github.com/CEED/libCEED/blob/main/examples/petsc/README.md).\n\n% benchmarks-marker\n\n## Benchmarks\n\nA sequence of benchmarks for all enabled backends can be run using:\n\n```console\n$ make benchmarks\n```\n\nThe results from the benchmarks are stored inside the `benchmarks/` directory and they can be viewed using the commands (requires python with matplotlib):\n\n```console\n$ cd benchmarks\n$ python postprocess-plot.py petsc-bps-bp1-*-output.txt\n$ python postprocess-plot.py petsc-bps-bp3-*-output.txt\n```\n\nUsing the `benchmarks` target runs a comprehensive set of benchmarks which may take some time to run.\nSubsets of the benchmarks can be run using the scripts in the `benchmarks` folder.\n\nFor more details about the benchmarks, see the `benchmarks/README.md` file.\n\n## Install\n\nTo install libCEED, run:\n\n```console\n$ make install prefix=/path/to/install/dir\n```\n\nor (e.g., if creating packages):\n\n```console\n$ make install prefix=/usr DESTDIR=/packaging/path\n```\n\nTo build and install in separate steps, run:\n\n```console\n$ make for_install=1 prefix=/path/to/install/dir\n$ make install prefix=/path/to/install/dir\n```\n\nThe usual variables like `CC` and `CFLAGS` are used, and optimization flags for all languages can be set using the likes of `OPT='-O3 -march=native'`.\nUse `STATIC=1` to build static libraries (`libceed.a`).\n\nTo install libCEED for Python, run:\n\n```console\n$ pip install libceed\n```\n\nwith the desired setuptools options, such as `--user`.\n\n### pkg-config\n\nIn addition to library and header, libCEED provides a [pkg-config](https://en.wikipedia.org/wiki/Pkg-config) file that can be used to easily compile and link.\n[For example](https://people.freedesktop.org/~dbn/pkg-config-guide.html#faq), if `$prefix` is a standard location or you set the environment variable `PKG_CONFIG_PATH`:\n\n```console\n$ cc `pkg-config --cflags --libs ceed` -o myapp myapp.c\n```\n\nwill build `myapp` with libCEED.\nThis can be used with the source or installed directories.\nMost build systems have support for pkg-config.\n\n## Contact\n\nYou can reach the libCEED team by emailing [ceed-users@llnl.gov](mailto:ceed-users@llnl.gov) or by leaving a comment in the [issue tracker](https://github.com/CEED/libCEED/issues).\n\n## How to Cite\n\nIf you utilize libCEED please cite:\n\n```bibtex\n@article{libceed-joss-paper,\n  author       = {Jed Brown and Ahmad Abdelfattah and Valeria Barra and Natalie Beams and Jean Sylvain Camier and Veselin Dobrev and Yohann Dudouit and Leila Ghaffari and Tzanio Kolev and David Medina and Will Pazner and Thilina Ratnayaka and Jeremy Thompson and Stan Tomov},\n  title        = {{libCEED}: Fast algebra for high-order element-based discretizations},\n  journal      = {Journal of Open Source Software},\n  year         = {2021},\n  publisher    = {The Open Journal},\n  volume       = {6},\n  number       = {63},\n  pages        = {2945},\n  doi          = {10.21105/joss.02945}\n}\n```\n\nThe archival copy of the libCEED user manual is maintained on [Zenodo](https://doi.org/10.5281/zenodo.4302736).\nTo cite the user manual:\n\n```bibtex\n@misc{libceed-user-manual,\n  author       = {Abdelfattah, Ahmad and\n                  Barra, Valeria and\n                  Beams, Natalie and\n                  Brown, Jed and\n                  Camier, Jean-Sylvain and\n                  Dobrev, Veselin and\n                  Dudouit, Yohann and\n                  Ghaffari, Leila and\n                  Grimberg, Sebastian and\n                  Kolev, Tzanio and\n                  Medina, David and\n                  Pazner, Will and\n                  Ratnayaka, Thilina and\n                  Shakeri, Rezgar and\n                  Thompson, Jeremy L and\n                  Tomov, Stanimire and\n                  Wright III, James},\n  title        = {{libCEED} User Manual},\n  month        = nov,\n  year         = 2023,\n  publisher    = {Zenodo},\n  version      = {0.12.0},\n  doi          = {10.5281/zenodo.10062388}\n}\n```\n\nFor libCEED's Python interface please cite:\n\n```bibtex\n@InProceedings{libceed-paper-proc-scipy-2020,\n  author    = {{V}aleria {B}arra and {J}ed {B}rown and {J}eremy {T}hompson and {Y}ohann {D}udouit},\n  title     = {{H}igh-performance operator evaluations with ease of use: lib{C}{E}{E}{D}'s {P}ython interface},\n  booktitle = {{P}roceedings of the 19th {P}ython in {S}cience {C}onference},\n  pages     = {85 - 90},\n  year      = {2020},\n  editor    = {{M}eghann {A}garwal and {C}hris {C}alloway and {D}illon {N}iederhut and {D}avid {S}hupe},\n  doi       = {10.25080/Majora-342d178e-00c}\n}\n```\n\nThe BibTeX entries for these references can be found in the `doc/bib/references.bib` file.\n\n## Copyright\n\nThe following copyright applies to each file in the CEED software suite, unless otherwise stated in the file:\n\n\u003e Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors.\n\u003e All rights reserved.\n\nSee files LICENSE and NOTICE for details.\n\n[github-badge]: https://github.com/CEED/libCEED/workflows/C/Fortran/badge.svg\n[github-link]: https://github.com/CEED/libCEED/actions\n[gitlab-badge]: https://gitlab.com/libceed/libCEED/badges/main/pipeline.svg?key_text=GitLab-CI\n[gitlab-link]: https://gitlab.com/libceed/libCEED/-/pipelines?page=1\u0026scope=all\u0026ref=main\n[codecov-badge]: https://codecov.io/gh/CEED/libCEED/branch/main/graphs/badge.svg\n[codecov-link]: https://codecov.io/gh/CEED/libCEED/\n[license-badge]: https://img.shields.io/badge/License-BSD%202--Clause-orange.svg\n[license-link]: https://opensource.org/licenses/BSD-2-Clause\n[doc-badge]: https://readthedocs.org/projects/libceed/badge/?version=latest\n[doc-link]: https://libceed.org/en/latest/?badge=latest\n[joss-badge]: https://joss.theoj.org/papers/10.21105/joss.02945/status.svg\n[joss-link]: https://doi.org/10.21105/joss.02945\n[binder-badge]: http://mybinder.org/badge_logo.svg\n[binder-link]: https://mybinder.org/v2/gh/CEED/libCEED/main?urlpath=lab/tree/examples/python/tutorial-0-ceed.ipynb\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FCEED%2FlibCEED","html_url":"https://awesome.ecosyste.ms/projects/github.com%2FCEED%2FlibCEED","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FCEED%2FlibCEED/lists"}