1# Changes/Release Notes 2 3On this page we provide a summary of the main API changes, new features and examples 4for each release of libCEED. 5 6(main)= 7 8## Current `main` branch 9 10### Interface changes 11 12- Update {c:func} `CeedQFunctionGetFields` and {c:func} `CeedOperatorGetFields` to include number of fields. 13 14### Maintainability 15 16- Refactored preconditioner support internally to facilitate future development and improve GPU completeness/test coverage. 17 18(v0-9)= 19 20## v0.9 (Jul 6, 2021) 21 22### Interface changes 23 24- Minor modification in error handling macro to silence pedantic warnings when compiling with Clang, but no functional impact. 25 26### New features 27 28- Add {c:func}`CeedVectorAXPY` and {c:func}`CeedVectorPointwiseMult` as a convenience for stand-alone testing and internal use. 29- Add `CEED_QFUNCTION_HELPER` macro to properly annotate QFunction helper functions for code generation backends. 30- Add `CeedPragmaOptimizeOff` macro for code that is sensitive to floating point errors from fast math optimizations. 31- Rust support: split `libceed-sys` crate out of `libceed` and [publish both on crates.io](https://crates.io/crates/libceed). 32 33### Performance improvements 34 35### Examples 36 37- Solid mechanics mini-app updated to explore the performance impacts of various formulations in the initial and current configurations. 38- Fluid mechanics example adds GPU support and improves modularity. 39 40### Deprecated backends 41 42- The `/cpu/self/tmpl` and `/cpu/self/tmpl/sub` backends have been removed. These backends were intially added to test the backend inheritance mechanism, but this mechanism is now widely used and tested in multiple backends. 43 44(v0-8)= 45 46## v0.8 (Mar 31, 2021) 47 48### Interface changes 49 50- Error handling improved to include enumerated error codes for C interface return values. 51- Installed headers that will follow semantic versioning were moved to {code}`include/ceed` directory. These headers have been renamed from {code}`ceed-*.h` to {code}`ceed/*.h`. Placeholder headers with the old naming schema are currently provided, but these headers will be removed in the libCEED v0.9 release. 52 53### New features 54 55- Julia and Rust interfaces added, providing a nearly 1-1 correspondence with the C interface, plus some convenience features. 56- Static libraries can be built with `make STATIC=1` and the pkg-config file is installed accordingly. 57- Add {c:func}`CeedOperatorLinearAssembleSymbolic` and {c:func}`CeedOperatorLinearAssemble` to support full assembly of libCEED operators. 58 59### Performance improvements 60 61- New HIP MAGMA backends for hipMAGMA library users: `/gpu/hip/magma` and `/gpu/hip/magma/det`. 62- New HIP backends for improved tensor basis performance: `/gpu/hip/shared` and `/gpu/hip/gen`. 63 64### Examples 65 66- {ref}`example-petsc-elasticity` example updated with traction boundary conditions and improved Dirichlet boundary conditions. 67- {ref}`example-petsc-elasticity` example updated with Neo-Hookean hyperelasticity in current configuration as well as improved Neo-Hookean hyperelasticity exploring storage vs computation tradeoffs. 68- {ref}`example-petsc-navier-stokes` example updated with isentropic traveling vortex test case, an analytical solution to the Euler equations that is useful for testing boundary conditions, discretization stability, and order of accuracy. 69- {ref}`example-petsc-navier-stokes` example updated with support for performing convergence study and plotting order of convergence by polynomial degree. 70 71(v0-7)= 72 73## v0.7 (Sep 29, 2020) 74 75### Interface changes 76 77- Replace limited {code}`CeedInterlaceMode` with more flexible component stride {code}`compstride` in {code}`CeedElemRestriction` constructors. 78 As a result, the {code}`indices` parameter has been replaced with {code}`offsets` and the {code}`nnodes` parameter has been replaced with {code}`lsize`. 79 These changes improve support for mixed finite element methods. 80- Replace various uses of {code}`Ceed*Get*Status` with {code}`Ceed*Is*` in the backend API to match common nomenclature. 81- Replace {code}`CeedOperatorAssembleLinearDiagonal` with {c:func}`CeedOperatorLinearAssembleDiagonal` for clarity. 82- Linear Operators can be assembled as point-block diagonal matrices with {c:func}`CeedOperatorLinearAssemblePointBlockDiagonal`, provided in row-major form in a {code}`ncomp` by {code}`ncomp` block per node. 83- Diagonal assemble interface changed to accept a {ref}`CeedVector` instead of a pointer to a {ref}`CeedVector` to reduce memory movement when interfacing with calling code. 84- Added {c:func}`CeedOperatorLinearAssembleAddDiagonal` and {c:func}`CeedOperatorLinearAssembleAddPointBlockDiagonal` for improved future integration with codes such as MFEM that compose the action of {ref}`CeedOperator`s external to libCEED. 85- Added {c:func}`CeedVectorTakeAray` to sync and remove libCEED read/write access to an allocated array and pass ownership of the array to the caller. 86 This function is recommended over {c:func}`CeedVectorSyncArray` when the {code}`CeedVector` has an array owned by the caller that was set by {c:func}`CeedVectorSetArray`. 87- Added {code}`CeedQFunctionContext` object to manage user QFunction context data and reduce copies between device and host memory. 88- Added {c:func}`CeedOperatorMultigridLevelCreate`, {c:func}`CeedOperatorMultigridLevelCreateTensorH1`, and {c:func}`CeedOperatorMultigridLevelCreateH1` to facilitate creation of multigrid prolongation, restriction, and coarse grid operators using a common quadrature space. 89 90### New features 91 92- New HIP backend: `/gpu/hip/ref`. 93- CeedQFunction support for user `CUfunction`s in some backends 94 95### Performance improvements 96 97- OCCA backend rebuilt to facilitate future performance enhancements. 98- Petsc BPs suite improved to reduce noise due to multiple calls to {code}`mpiexec`. 99 100### Examples 101 102- {ref}`example-petsc-elasticity` example updated with strain energy computation and more flexible boundary conditions. 103 104### Deprecated backends 105 106- The `/gpu/cuda/reg` backend has been removed, with its core features moved into `/gpu/cuda/ref` and `/gpu/cuda/shared`. 107 108(v0-6)= 109 110## v0.6 (Mar 29, 2020) 111 112libCEED v0.6 contains numerous new features and examples, as well as expanded 113documentation in [this new website](https://libceed.readthedocs.io). 114 115### New features 116 117- New Python interface using [CFFI](https://cffi.readthedocs.io/) provides a nearly 118 1-1 correspondence with the C interface, plus some convenience features. For instance, 119 data stored in the {cpp:type}`CeedVector` structure are available without copy as 120 {py:class}`numpy.ndarray`. Short tutorials are provided in 121 [Binder](https://mybinder.org/v2/gh/CEED/libCEED/main?urlpath=lab/tree/examples/tutorials/). 122- Linear QFunctions can be assembled as block-diagonal matrices (per quadrature point, 123 {c:func}`CeedOperatorAssembleLinearQFunction`) or to evaluate the diagonal 124 ({c:func}`CeedOperatorAssembleLinearDiagonal`). These operations are useful for 125 preconditioning ingredients and are used in the libCEED's multigrid examples. 126- The inverse of separable operators can be obtained using 127 {c:func}`CeedOperatorCreateFDMElementInverse` and applied with 128 {c:func}`CeedOperatorApply`. This is a useful preconditioning ingredient, 129 especially for Laplacians and related operators. 130- New functions: {c:func}`CeedVectorNorm`, {c:func}`CeedOperatorApplyAdd`, 131 {c:func}`CeedQFunctionView`, {c:func}`CeedOperatorView`. 132- Make public accessors for various attributes to facilitate writing composable code. 133- New backend: `/cpu/self/memcheck/serial`. 134- QFunctions using variable-length array (VLA) pointer constructs can be used with CUDA 135 backends. (Single source is coming soon for OCCA backends.) 136- Fix some missing edge cases in CUDA backend. 137 138### Performance Improvements 139 140- MAGMA backend performance optimization and non-tensor bases. 141- No-copy optimization in {c:func}`CeedOperatorApply`. 142 143### Interface changes 144 145- Replace {code}`CeedElemRestrictionCreateIdentity` and 146 {code}`CeedElemRestrictionCreateBlocked` with more flexible 147 {c:func}`CeedElemRestrictionCreateStrided` and 148 {c:func}`CeedElemRestrictionCreateBlockedStrided`. 149- Add arguments to {c:func}`CeedQFunctionCreateIdentity`. 150- Replace ambiguous uses of {cpp:enum}`CeedTransposeMode` for L-vector identification 151 with {cpp:enum}`CeedInterlaceMode`. This is now an attribute of the 152 {cpp:type}`CeedElemRestriction` (see {c:func}`CeedElemRestrictionCreate`) and no 153 longer passed as `lmode` arguments to {c:func}`CeedOperatorSetField` and 154 {c:func}`CeedElemRestrictionApply`. 155 156### Examples 157 158libCEED-0.6 contains greatly expanded examples with {ref}`new documentation <Examples>`. 159Notable additions include: 160 161- Standalone {ref}`ex2-surface` ({file}`examples/ceed/ex2-surface`): compute the area of 162 a domain in 1, 2, and 3 dimensions by applying a Laplacian. 163 164- PETSc {ref}`example-petsc-area` ({file}`examples/petsc/area.c`): computes surface area 165 of domains (like the cube and sphere) by direct integration on a surface mesh; 166 demonstrates geometric dimension different from topological dimension. 167 168- PETSc {ref}`example-petsc-bps`: 169 170 - {file}`examples/petsc/bpsraw.c` (formerly `bps.c`): transparent CUDA support. 171 - {file}`examples/petsc/bps.c` (formerly `bpsdmplex.c`): performance improvements 172 and transparent CUDA support. 173 - {ref}`example-petsc-bps-sphere` ({file}`examples/petsc/bpssphere.c`): 174 generalizations of all CEED BPs to the surface of the sphere; demonstrates geometric 175 dimension different from topological dimension. 176 177- {ref}`example-petsc-multigrid` ({file}`examples/petsc/multigrid.c`): new p-multigrid 178 solver with algebraic multigrid coarse solve. 179 180- {ref}`example-petsc-navier-stokes` ({file}`examples/fluids/navierstokes.c`; formerly 181 `examples/navier-stokes`): unstructured grid support (using PETSc's `DMPlex`), 182 implicit time integration, SU/SUPG stabilization, free-slip boundary conditions, and 183 quasi-2D computational domain support. 184 185- {ref}`example-petsc-elasticity` ({file}`examples/solids/elasticity.c`): new solver for 186 linear elasticity, small-strain hyperelasticity, and globalized finite-strain 187 hyperelasticity using p-multigrid with algebraic multigrid coarse solve. 188 189(v0-5)= 190 191## v0.5 (Sep 18, 2019) 192 193For this release, several improvements were made. Two new CUDA backends were added to 194the family of backends, of which, the new `cuda-gen` backend achieves state-of-the-art 195performance using single-source {ref}`CeedQFunction`. From this release, users 196can define Q-Functions in a single source code independently of the targeted backend 197with the aid of a new macro `CEED QFUNCTION` to support JIT (Just-In-Time) and CPU 198compilation of the user provided {ref}`CeedQFunction` code. To allow a unified 199declaration, the {ref}`CeedQFunction` API has undergone a slight change: 200the `QFunctionField` parameter `ncomp` has been changed to `size`. This change 201requires setting the previous value of `ncomp` to `ncomp*dim` when adding a 202`QFunctionField` with eval mode `CEED EVAL GRAD`. 203 204Additionally, new CPU backends 205were included in this release, such as the `/cpu/self/opt/*` backends (which are 206written in pure C and use partial **E-vectors** to improve performance) and the 207`/cpu/self/ref/memcheck` backend (which relies upon the 208[Valgrind](http://valgrind.org/) Memcheck tool to help verify that user 209{ref}`CeedQFunction` have no undefined values). 210This release also included various performance improvements, bug fixes, new examples, 211and improved tests. Among these improvements, vectorized instructions for 212{ref}`CeedQFunction` code compiled for CPU were enhanced by using `CeedPragmaSIMD` 213instead of `CeedPragmaOMP`, implementation of a {ref}`CeedQFunction` gallery and 214identity Q-Functions were introduced, and the PETSc benchmark problems were expanded 215to include unstructured meshes handling were. For this expansion, the prior version of 216the PETSc BPs, which only included data associated with structured geometries, were 217renamed `bpsraw`, and the new version of the BPs, which can handle data associated 218with any unstructured geometry, were called `bps`. Additionally, other benchmark 219problems, namely BP2 and BP4 (the vector-valued versions of BP1 and BP3, respectively), 220and BP5 and BP6 (the collocated versions---for which the quadrature points are the same 221as the Gauss Lobatto nodes---of BP3 and BP4 respectively) were added to the PETSc 222examples. Furthermoew, another standalone libCEED example, called `ex2`, which 223computes the surface area of a given mesh was added to this release. 224 225Backends available in this release: 226 227| CEED resource (`-ceed`) | Backend | 228|--------------------------|-----------------------------------------------------| 229| `/cpu/self/ref/serial` | Serial reference implementation | 230| `/cpu/self/ref/blocked` | Blocked reference implementation | 231| `/cpu/self/ref/memcheck` | Memcheck backend, undefined value checks | 232| `/cpu/self/opt/serial` | Serial optimized C implementation | 233| `/cpu/self/opt/blocked` | Blocked optimized C implementation | 234| `/cpu/self/avx/serial` | Serial AVX implementation | 235| `/cpu/self/avx/blocked` | Blocked AVX implementation | 236| `/cpu/self/xsmm/serial` | Serial LIBXSMM implementation | 237| `/cpu/self/xsmm/blocked` | Blocked LIBXSMM implementation | 238| `/cpu/occa` | Serial OCCA kernels | 239| `/gpu/occa` | CUDA OCCA kernels | 240| `/omp/occa` | OpenMP OCCA kernels | 241| `/ocl/occa` | OpenCL OCCA kernels | 242| `/gpu/cuda/ref` | Reference pure CUDA kernels | 243| `/gpu/cuda/reg` | Pure CUDA kernels using one thread per element | 244| `/gpu/cuda/shared` | Optimized pure CUDA kernels using shared memory | 245| `/gpu/cuda/gen` | Optimized pure CUDA kernels using code generation | 246| `/gpu/magma` | CUDA MAGMA kernels | 247 248Examples available in this release: 249 250:::{list-table} 251:header-rows: 1 252:widths: auto 253* - User code 254 - Example 255* - `ceed` 256 - * ex1 (volume) 257 * ex2 (surface) 258* - `mfem` 259 - * BP1 (scalar mass operator) 260 * BP3 (scalar Laplace operator) 261* - `petsc` 262 - * BP1 (scalar mass operator) 263 * BP2 (vector mass operator) 264 * BP3 (scalar Laplace operator) 265 * BP4 (vector Laplace operator) 266 * BP5 (collocated scalar Laplace operator) 267 * BP6 (collocated vector Laplace operator) 268 * Navier-Stokes 269* - `nek5000` 270 - * BP1 (scalar mass operator) 271 * BP3 (scalar Laplace operator) 272::: 273 274(v0-4)= 275 276## v0.4 (Apr 1, 2019) 277 278libCEED v0.4 was made again publicly available in the second full CEED software 279distribution, release CEED 2.0. This release contained notable features, such as 280four new CPU backends, two new GPU backends, CPU backend optimizations, initial 281support for operator composition, performance benchmarking, and a Navier-Stokes demo. 282The new CPU backends in this release came in two families. The `/cpu/self/*/serial` 283backends process one element at a time and are intended for meshes with a smaller number 284of high order elements. The `/cpu/self/*/blocked` backends process blocked batches of 285eight interlaced elements and are intended for meshes with higher numbers of elements. 286The `/cpu/self/avx/*` backends rely upon AVX instructions to provide vectorized CPU 287performance. The `/cpu/self/xsmm/*` backends rely upon the 288[LIBXSMM](http://github.com/hfp/libxsmm) package to provide vectorized CPU 289performance. The `/gpu/cuda/*` backends provide GPU performance strictly using CUDA. 290The `/gpu/cuda/ref` backend is a reference CUDA backend, providing reasonable 291performance for most problem configurations. The `/gpu/cuda/reg` backend uses a simple 292parallelization approach, where each thread treats a finite element. Using just in time 293compilation, provided by nvrtc (NVidia Runtime Compiler), and runtime parameters, this 294backend unroll loops and map memory address to registers. The `/gpu/cuda/reg` backend 295achieve good peak performance for 1D, 2D, and low order 3D problems, but performance 296deteriorates very quickly when threads run out of registers. 297 298A new explicit time-stepping Navier-Stokes solver was added to the family of libCEED 299examples in the `examples/petsc` directory (see {ref}`example-petsc-navier-stokes`). 300This example solves the time-dependent Navier-Stokes equations of compressible gas 301dynamics in a static Eulerian three-dimensional frame, using structured high-order 302finite/spectral element spatial discretizations and explicit high-order time-stepping 303(available in PETSc). Moreover, the Navier-Stokes example was developed using PETSc, 304so that the pointwise physics (defined at quadrature points) is separated from the 305parallelization and meshing concerns. 306 307Backends available in this release: 308 309| CEED resource (`-ceed`) | Backend | 310|--------------------------|-----------------------------------------------------| 311| `/cpu/self/ref/serial` | Serial reference implementation | 312| `/cpu/self/ref/blocked` | Blocked reference implementation | 313| `/cpu/self/tmpl` | Backend template, defaults to `/cpu/self/blocked` | 314| `/cpu/self/avx/serial` | Serial AVX implementation | 315| `/cpu/self/avx/blocked` | Blocked AVX implementation | 316| `/cpu/self/xsmm/serial` | Serial LIBXSMM implementation | 317| `/cpu/self/xsmm/blocked` | Blocked LIBXSMM implementation | 318| `/cpu/occa` | Serial OCCA kernels | 319| `/gpu/occa` | CUDA OCCA kernels | 320| `/omp/occa` | OpenMP OCCA kernels | 321| `/ocl/occa` | OpenCL OCCA kernels | 322| `/gpu/cuda/ref` | Reference pure CUDA kernels | 323| `/gpu/cuda/reg` | Pure CUDA kernels using one thread per element | 324| `/gpu/magma` | CUDA MAGMA kernels | 325 326Examples available in this release: 327 328:::{list-table} 329:header-rows: 1 330:widths: auto 331* - User code 332 - Example 333* - `ceed` 334 - * ex1 (volume) 335* - `mfem` 336 - * BP1 (scalar mass operator) 337 * BP3 (scalar Laplace operator) 338* - `petsc` 339 - * BP1 (scalar mass operator) 340 * BP3 (scalar Laplace operator) 341 * Navier-Stokes 342* - `nek5000` 343 - * BP1 (scalar mass operator) 344 * BP3 (scalar Laplace operator) 345::: 346 347(v0-3)= 348 349## v0.3 (Sep 30, 2018) 350 351Notable features in this release include active/passive field interface, support for 352non-tensor bases, backend optimization, and improved Fortran interface. This release 353also focused on providing improved continuous integration, and many new tests with code 354coverage reports of about 90%. This release also provided a significant change to the 355public interface: a {ref}`CeedQFunction` can take any number of named input and output 356arguments while {ref}`CeedOperator` connects them to the actual data, which may be 357supplied explicitly to `CeedOperatorApply()` (active) or separately via 358`CeedOperatorSetField()` (passive). This interface change enables reusable libraries 359of CeedQFunctions and composition of block solvers constructed using 360{ref}`CeedOperator`. A concept of blocked restriction was added to this release and 361used in an optimized CPU backend. Although this is typically not visible to the user, 362it enables effective use of arbitrary-length SIMD while maintaining cache locality. 363This CPU backend also implements an algebraic factorization of tensor product gradients 364to perform fewer operations than standard application of interpolation and 365differentiation from nodes to quadrature points. This algebraic formulation 366automatically supports non-polynomial and non-interpolatory bases, thus is more general 367than the more common derivation in terms of Lagrange polynomials on the quadrature points. 368 369Backends available in this release: 370 371| CEED resource (`-ceed`) | Backend | 372|-------------------------|-----------------------------------------------------| 373| `/cpu/self/blocked` | Blocked reference implementation | 374| `/cpu/self/ref` | Serial reference implementation | 375| `/cpu/self/tmpl` | Backend template, defaults to `/cpu/self/blocked` | 376| `/cpu/occa` | Serial OCCA kernels | 377| `/gpu/occa` | CUDA OCCA kernels | 378| `/omp/occa` | OpenMP OCCA kernels | 379| `/ocl/occa` | OpenCL OCCA kernels | 380| `/gpu/magma` | CUDA MAGMA kernels | 381 382Examples available in this release: 383 384:::{list-table} 385:header-rows: 1 386:widths: auto 387* - User code 388 - Example 389* - `ceed` 390 - * ex1 (volume) 391* - `mfem` 392 - * BP1 (scalar mass operator) 393 * BP3 (scalar Laplace operator) 394* - `petsc` 395 - * BP1 (scalar mass operator) 396 * BP3 (scalar Laplace operator) 397* - `nek5000` 398 - * BP1 (scalar mass operator) 399 * BP3 (scalar Laplace operator) 400::: 401 402(v0-21)= 403 404## v0.21 (Sep 30, 2018) 405 406A MAGMA backend (which relies upon the 407[MAGMA](https://bitbucket.org/icl/magma) package) was integrated in libCEED for this 408release. This initial integration set up the framework of using MAGMA and provided the 409libCEED functionality through MAGMA kernels as one of libCEED’s computational backends. 410As any other backend, the MAGMA backend provides extended basic data structures for 411{ref}`CeedVector`, {ref}`CeedElemRestriction`, and {ref}`CeedOperator`, and implements 412the fundamental CEED building blocks to work with the new data structures. 413In general, the MAGMA-specific data structures keep the libCEED pointers to CPU data 414but also add corresponding device (e.g., GPU) pointers to the data. Coherency is handled 415internally, and thus seamlessly to the user, through the functions/methods that are 416provided to support them. 417 418Backends available in this release: 419 420| CEED resource (`-ceed`) | Backend | 421|-------------------------|---------------------------------| 422| `/cpu/self` | Serial reference implementation | 423| `/cpu/occa` | Serial OCCA kernels | 424| `/gpu/occa` | CUDA OCCA kernels | 425| `/omp/occa` | OpenMP OCCA kernels | 426| `/ocl/occa` | OpenCL OCCA kernels | 427| `/gpu/magma` | CUDA MAGMA kernels | 428 429Examples available in this release: 430 431:::{list-table} 432:header-rows: 1 433:widths: auto 434* - User code 435 - Example 436* - `ceed` 437 - * ex1 (volume) 438* - `mfem` 439 - * BP1 (scalar mass operator) 440 * BP3 (scalar Laplace operator) 441* - `petsc` 442 - * BP1 (scalar mass operator) 443* - `nek5000` 444 - * BP1 (scalar mass operator) 445::: 446 447(v0-2)= 448 449## v0.2 (Mar 30, 2018) 450 451libCEED was made publicly available the first full CEED software distribution, release 452CEED 1.0. The distribution was made available using the Spack package manager to provide 453a common, easy-to-use build environment, where the user can build the CEED distribution 454with all dependencies. This release included a new Fortran interface for the library. 455This release also contained major improvements in the OCCA backend (including a new 456`/ocl/occa` backend) and new examples. The standalone libCEED example was modified to 457compute the volume volume of a given mesh (in 1D, 2D, or 3D) and placed in an 458`examples/ceed` subfolder. A new `mfem` example to perform BP3 (with the application 459of the Laplace operator) was also added to this release. 460 461Backends available in this release: 462 463| CEED resource (`-ceed`) | Backend | 464|-------------------------|---------------------------------| 465| `/cpu/self` | Serial reference implementation | 466| `/cpu/occa` | Serial OCCA kernels | 467| `/gpu/occa` | CUDA OCCA kernels | 468| `/omp/occa` | OpenMP OCCA kernels | 469| `/ocl/occa` | OpenCL OCCA kernels | 470 471Examples available in this release: 472 473:::{list-table} 474:header-rows: 1 475:widths: auto 476* - User code 477 - Example 478* - `ceed` 479 - * ex1 (volume) 480* - `mfem` 481 - * BP1 (scalar mass operator) 482 * BP3 (scalar Laplace operator) 483* - `petsc` 484 - * BP1 (scalar mass operator) 485* - `nek5000` 486 - * BP1 (scalar mass operator) 487::: 488 489(v0-1)= 490 491## v0.1 (Jan 3, 2018) 492 493Initial low-level API of the CEED project. The low-level API provides a set of Finite 494Elements kernels and components for writing new low-level kernels. Examples include: 495vector and sparse linear algebra, element matrix assembly over a batch of elements, 496partial assembly and action for efficient high-order operators like mass, diffusion, 497advection, etc. The main goal of the low-level API is to establish the basis for the 498high-level API. Also, identifying such low-level kernels and providing a reference 499implementation for them serves as the basis for specialized backend implementations. 500This release contained several backends: `/cpu/self`, and backends which rely upon the 501[OCCA](http://github.com/libocca/occa) package, such as `/cpu/occa`, 502`/gpu/occa`, and `/omp/occa`. 503It also included several examples, in the `examples` folder: 504A standalone code that shows the usage of libCEED (with no external 505dependencies) to apply the Laplace operator, `ex1`; an `mfem` example to perform BP1 506(with the application of the mass operator); and a `petsc` example to perform BP1 507(with the application of the mass operator). 508 509Backends available in this release: 510 511| CEED resource (`-ceed`) | Backend | 512|-------------------------|---------------------------------| 513| `/cpu/self` | Serial reference implementation | 514| `/cpu/occa` | Serial OCCA kernels | 515| `/gpu/occa` | CUDA OCCA kernels | 516| `/omp/occa` | OpenMP OCCA kernels | 517 518Examples available in this release: 519 520| User code | Example | 521|-----------------------|-----------------------------------| 522| `ceed` | ex1 (scalar Laplace operator) | 523| `mfem` | BP1 (scalar mass operator) | 524| `petsc` | BP1 (scalar mass operator) | 525``` 526