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