libCEED: Efficient Extensible Discretization

Summary and Purpose

libCEED provides fast algebra for element-based discretizations, designed for performance portability, run-time flexibility, and clean embedding in higher level libraries and applications. It offers a C99 interface as well as bindings for Fortran, Python, Julia, and Rust. While 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 and API implementation portion of the documentation.

One 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. Thus, high-order methods require a new "format" that still represents a linear (or more generally non-linear) operator, but not through a sparse matrix.

The 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.). This new operator description is based on algebraically factored form, which is easy to incorporate in a wide variety of applications, without significant refactoring of their own discretization infrastructure.

The repository is part of the CEED software suite, a collection of software benchmarks, miniapps, libraries and APIs for efficient exascale discretizations based on high-order finite element and spectral element methods. See http://github.com/ceed for more information and source code availability.

The CEED research is supported by the 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, including software, applications, hardware, advanced system engineering and early testbed platforms, in support of the nation’s exascale computing imperative.

For more details on the CEED API see the user manual.

Building

The CEED library, libceed, is a C99 library with no required dependencies, and with Fortran, Python, Julia, and Rust interfaces. It can be built using:

console $ make

or, with optimization flags:

console $ make OPT='-O3 -march=skylake-avx512 -ffp-contract=fast'

These optimization flags are used by all languages (C, C++, Fortran) and this makefile variable can also be set for testing and examples (below).

The library attempts to automatically detect support for the AVX instruction set using gcc-style compiler options for the host. Support may need to be manually specified via:

console $ make AVX=1

or:

console $ make AVX=0

if your compiler does not support gcc-style options, if you are cross compiling, etc.

To enable CUDA support, add CUDA_DIR=/opt/cuda or an appropriate directory to your make invocation. To enable HIP support, add ROCM_DIR=/opt/rocm or an appropriate directory. To enable SYCL support, add SYCL_DIR=/opt/sycl or an appropriate directory. Note that SYCL backends require building with oneAPI compilers as well:

console $ . /opt/intel/oneapi/setvars.sh $ make SYCL_DIR=/opt/intel/oneapi/compiler/latest/linux SYCLCXX=icpx CC=icx CXX=icpx

The library can be configured for host applications which use OpenMP paralellism via:

console $ make OPENMP=1

which will allow operators created and applied from different threads inside an omp parallel region.

To store these or other arguments as defaults for future invocations of make, use:

console $ make configure CUDA_DIR=/usr/local/cuda ROCM_DIR=/opt/rocm OPT='-O3 -march=znver2'

which stores these variables in config.mk.

WebAssembly

libCEED can be built for WASM using Emscripten. For example, one can build the library and run a standalone WASM executable using

console $ emmake make build/ex2-surface.wasm $ wasmer build/ex2-surface.wasm -- -s 200000

Additional Language Interfaces

The Fortran interface is built alongside the library automatically.

Python users can install using:

console $ pip install libceed

or in a clone of the repository via pip install ..

Julia users can install using:

console $ julia julia> ] pkg> add LibCEED

See the LibCEED.jl documentation for more information.

Rust users can include libCEED via Cargo.toml:

toml [dependencies] libceed = "0.12.0"

See the Cargo documentation for details.

Testing

The test suite produces TAP output and is run by:

console $ make test

or, using the prove tool distributed with Perl (recommended):

console $ make prove

Backends

There are multiple supported backends, which can be selected at runtime in the examples:

| CEED resource | Backend | Deterministic Capable | | :--- | :--- | :---: | || | CPU Native | | /cpu/self/ref/serial | Serial reference implementation | Yes | | /cpu/self/ref/blocked | Blocked reference implementation | Yes | | /cpu/self/opt/serial | Serial optimized C implementation | Yes | | /cpu/self/opt/blocked | Blocked optimized C implementation | Yes | | /cpu/self/avx/serial | Serial AVX implementation | Yes | | /cpu/self/avx/blocked | Blocked AVX implementation | Yes | || | CPU Valgrind | | /cpu/self/memcheck/* | Memcheck backends, undefined value checks | Yes | || | CPU LIBXSMM | | /cpu/self/xsmm/serial | Serial LIBXSMM implementation | Yes | | /cpu/self/xsmm/blocked | Blocked LIBXSMM implementation | Yes | || | CUDA Native | | /gpu/cuda/ref | Reference pure CUDA kernels | Yes | | /gpu/cuda/shared | Optimized pure CUDA kernels using shared memory | Yes | | /gpu/cuda/gen | Optimized pure CUDA kernels using code generation | No | || | HIP Native | | /gpu/hip/ref | Reference pure HIP kernels | Yes | | /gpu/hip/shared | Optimized pure HIP kernels using shared memory | Yes | | /gpu/hip/gen | Optimized pure HIP kernels using code generation | No | || | SYCL Native | | /gpu/sycl/ref | Reference pure SYCL kernels | Yes | | /gpu/sycl/shared | Optimized pure SYCL kernels using shared memory | Yes | || | MAGMA | | /gpu/cuda/magma | CUDA MAGMA kernels | No | | /gpu/cuda/magma/det | CUDA MAGMA kernels | Yes | | /gpu/hip/magma | HIP MAGMA kernels | No | | /gpu/hip/magma/det | HIP MAGMA kernels | Yes | || | OCCA | | /*/occa | Selects backend based on available OCCA modes | Yes | | /cpu/self/occa | OCCA backend with serial CPU kernels | Yes | | /cpu/openmp/occa | OCCA backend with OpenMP kernels | Yes | | /cpu/dpcpp/occa | OCCA backend with DPC++ kernels | Yes | | /gpu/cuda/occa | OCCA backend with CUDA kernels | Yes | | /gpu/hip/occa | OCCA backend with HIP kernels | Yes |

The /cpu/self/*/serial backends process one element at a time and are intended for meshes with a smaller number of high order elements. The /cpu/self/*/blocked backends process blocked batches of eight interlaced elements and are intended for meshes with higher numbers of elements.

The /cpu/self/ref/* backends are written in pure C and provide basic functionality.

The /cpu/self/opt/* backends are written in pure C and use partial e-vectors to improve performance.

The /cpu/self/avx/* backends rely upon AVX instructions to provide vectorized CPU performance.

The /cpu/self/memcheck/* backends rely upon the Valgrind Memcheck tool to help verify that user QFunctions have no undefined values. To use, run your code with Valgrind and the Memcheck backends, e.g. valgrind ./build/ex1 -ceed /cpu/self/ref/memcheck. A 'development' or 'debugging' version of Valgrind with headers is required to use this backend. This 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.

The /cpu/self/xsmm/* backends rely upon the LIBXSMM package to provide vectorized CPU performance. If 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. The LIBXSMM main development branch from 7 April 2024 or newer is required.

The /gpu/cuda/* backends provide GPU performance strictly using CUDA.

The /gpu/hip/* backends provide GPU performance strictly using HIP. They are based on the /gpu/cuda/* backends. ROCm version 4.2 or newer is required.

The /gpu/sycl/* backends provide GPU performance strictly using SYCL. They are based on the /gpu/cuda/* and /gpu/hip/* backends.

The /gpu/*/magma/* backends rely upon the MAGMA package. To 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/. By 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. MAGMA version 2.5.0 or newer is required. Currently, each MAGMA library installation is only built for either CUDA or HIP. The 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.

Users can specify a device for all CUDA, HIP, and MAGMA backends through adding :device_id=# after the resource name. For example:

• /gpu/cuda/gen:device_id=1

The /*/occa backends rely upon the OCCA package to provide cross platform performance. To 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). OCCA version 1.6.0 or newer is required.

Users can pass specific OCCA device properties after setting the CEED resource. For example:

• "/*/occa:mode='CUDA',device_id=0"

Bit-for-bit reproducibility is important in some applications. However, some libCEED backends use non-deterministic operations, such as atomicAdd for increased performance. The backends which are capable of generating reproducible results, with the proper compilation options, are highlighted in the list above.

Examples

libCEED 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. Nek5000 v18.0 or greater is required.

To build the examples, set the MFEM_DIR, PETSC_DIR (and optionally PETSC_ARCH), and NEK5K_DIR variables and run:

console $ cd examples/

```console

libCEED examples on CPU and GPU

$ cd ceed/ $ make $ ./ex1-volume -ceed /cpu/self $ ./ex1-volume -ceed /gpu/cuda $ ./ex2-surface -ceed /cpu/self $ ./ex2-surface -ceed /gpu/cuda $ cd ..

MFEM+libCEED examples on CPU and GPU

$ cd mfem/ $ make $ ./bp1 -ceed /cpu/self -no-vis $ ./bp3 -ceed /gpu/cuda -no-vis $ cd ..

Nek5000+libCEED examples on CPU and GPU

$ cd nek/ $ make $ ./nek-examples.sh -e bp1 -ceed /cpu/self -b 3 $ ./nek-examples.sh -e bp3 -ceed /gpu/cuda -b 3 $ cd ..

PETSc+libCEED examples on CPU and GPU

$ cd petsc/ $ make $ ./bps -problem bp1 -ceed /cpu/self $ ./bps -problem bp2 -ceed /gpu/cuda $ ./bps -problem bp3 -ceed /cpu/self $ ./bps -problem bp4 -ceed /gpu/cuda $ ./bps -problem bp5 -ceed /cpu/self $ ./bps -problem bp6 -ceed /gpu/cuda $ cd ..

$ cd petsc/ $ make $ ./bpsraw -problem bp1 -ceed /cpu/self $ ./bpsraw -problem bp2 -ceed /gpu/cuda $ ./bpsraw -problem bp3 -ceed /cpu/self $ ./bpsraw -problem bp4 -ceed /gpu/cuda $ ./bpsraw -problem bp5 -ceed /cpu/self $ ./bpsraw -problem bp6 -ceed /gpu/cuda $ cd ..

$ cd petsc/ $ make $ ./bpssphere -problem bp1 -ceed /cpu/self $ ./bpssphere -problem bp2 -ceed /gpu/cuda $ ./bpssphere -problem bp3 -ceed /cpu/self $ ./bpssphere -problem bp4 -ceed /gpu/cuda $ ./bpssphere -problem bp5 -ceed /cpu/self $ ./bpssphere -problem bp6 -ceed /gpu/cuda $ cd ..

$ cd petsc/ $ make $ ./area -problem cube -ceed /cpu/self -degree 3 $ ./area -problem cube -ceed /gpu/cuda -degree 3 $ ./area -problem sphere -ceed /cpu/self -degree 3 -dmrefine 2 $ ./area -problem sphere -ceed /gpu/cuda -degree 3 -dmrefine 2

$ cd fluids/ $ make $ ./navierstokes -ceed /cpu/self -degree 1 $ ./navierstokes -ceed /gpu/cuda -degree 1 $ cd ..

$ cd solids/ $ make $ ./elasticity -ceed /cpu/self -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -problem Linear -forcing mms $ ./elasticity -ceed /gpu/cuda -mesh [.exo file] -degree 2 -E 1 -nu 0.3 -problem Linear -forcing mms $ cd .. ```

For the last example shown, sample meshes to be used in place of [.exo file] can be found at https://github.com/jeremylt/ceedSampleMeshes

The above code assumes a GPU-capable machine with the CUDA backends enabled. Depending on the available backends, other CEED resource specifiers can be provided with the -ceed option. Other command line arguments can be found in examples/petsc.

Benchmarks

A sequence of benchmarks for all enabled backends can be run using:

console $ make benchmarks

The results from the benchmarks are stored inside the benchmarks/ directory and they can be viewed using the commands (requires python with matplotlib):

console $ cd benchmarks $ python postprocess-plot.py petsc-bps-bp1-*-output.txt $ python postprocess-plot.py petsc-bps-bp3-*-output.txt

Using the benchmarks target runs a comprehensive set of benchmarks which may take some time to run. Subsets of the benchmarks can be run using the scripts in the benchmarks folder.

For more details about the benchmarks, see the benchmarks/README.md file.

Install

To install libCEED, run:

console $ make install prefix=/path/to/install/dir

or (e.g., if creating packages):

console $ make install prefix=/usr DESTDIR=/packaging/path

To build and install in separate steps, run:

console $ make for_install=1 prefix=/path/to/install/dir $ make install prefix=/path/to/install/dir

The 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'. Use STATIC=1 to build static libraries (libceed.a).

To install libCEED for Python, run:

console $ pip install libceed

with the desired setuptools options, such as --user.

pkg-config

In addition to library and header, libCEED provides a pkg-config file that can be used to easily compile and link. For example, if $prefix is a standard location or you set the environment variable PKG_CONFIG_PATH:

console $ cc `pkg-config --cflags --libs ceed` -o myapp myapp.c

will build myapp with libCEED. This can be used with the source or installed directories. Most build systems have support for pkg-config.

Contact

You can reach the libCEED team by emailing ceed-users@llnl.gov or by leaving a comment in the issue tracker.

How to Cite

If you utilize libCEED please cite:

bibtex @article{libceed-joss-paper, 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}, title = {{libCEED}: Fast algebra for high-order element-based discretizations}, journal = {Journal of Open Source Software}, year = {2021}, publisher = {The Open Journal}, volume = {6}, number = {63}, pages = {2945}, doi = {10.21105/joss.02945} }

The archival copy of the libCEED user manual is maintained on Zenodo. To cite the user manual:

bibtex @misc{libceed-user-manual, author = {Abdelfattah, Ahmad and Barra, Valeria and Beams, Natalie and Brown, Jed and Camier, Jean-Sylvain and Dobrev, Veselin and Dudouit, Yohann and Ghaffari, Leila and Grimberg, Sebastian and Kolev, Tzanio and Medina, David and Pazner, Will and Ratnayaka, Thilina and Shakeri, Rezgar and Thompson, Jeremy L and Tomov, Stanimire and Wright III, James}, title = {{libCEED} User Manual}, month = nov, year = 2023, publisher = {Zenodo}, version = {0.12.0}, doi = {10.5281/zenodo.10062388} }

For libCEED's Python interface please cite:

bibtex @InProceedings{libceed-paper-proc-scipy-2020, author = {{V}aleria {B}arra and {J}ed {B}rown and {J}eremy {T}hompson and {Y}ohann {D}udouit}, title = {{H}igh-performance operator evaluations with ease of use: lib{C}{E}{E}{D}'s {P}ython interface}, booktitle = {{P}roceedings of the 19th {P}ython in {S}cience {C}onference}, pages = {85 - 90}, year = {2020}, editor = {{M}eghann {A}garwal and {C}hris {C}alloway and {D}illon {N}iederhut and {D}avid {S}hupe}, doi = {10.25080/Majora-342d178e-00c} }

The BibTeX entries for these references can be found in the doc/bib/references.bib file.

Copyright

The following copyright applies to each file in the CEED software suite, unless otherwise stated in the file:

Copyright (c) 2017-2025, Lawrence Livermore National Security, LLC and other CEED contributors. All rights reserved.

See files LICENSE and NOTICE for details.