1# libCEED: Examples 2 3This page provides a brief description of the examples for the libCEED 4library. 5 6## Basic libCEED Examples 7 8Two examples that rely only upon libCEED without any external libraries are provided in the [ceed/](./ceed) folder. For more details, please see the dedicated [documentation section](https://libceed.readthedocs.io/en/latest/examples/ceed/index.html). 9 10## Bakeoff Problems 11 12% bps-inclusion-marker 13 14The Center for Efficient Exascale Discretizations (CEED) uses Bakeoff Problems (BPs) 15to test and compare the performance of high-order finite element implementations. The 16definitions of the problems are given on the ceed 17[website](https://ceed.exascaleproject.org/bps/). Each of the following bakeoff 18problems that use external discretization libraries (such as MFEM, PETSc, and Nek5000) 19are located in the subdirectories `mfem/`, `petsc/`, and 20`nek5000/`, respectively. 21 22Here we provide a short summary: 23 24:::{list-table} 25:header-rows: 1 26:widths: auto 27* - User code 28 - Supported BPs 29* - `mfem` 30 - * BP1 (scalar mass operator) with $Q=P+1$ 31 * BP3 (scalar Laplace operator) with $Q=P+1$ 32* - `petsc` 33 - * BP1 (scalar mass operator) with $Q=P+1$ 34 * BP2 (vector mass operator) with $Q=P+1$ 35 * BP3 (scalar Laplace operator) with $Q=P+1$ 36 * BP4 (vector Laplace operator) with $Q=P+1$ 37 * BP5 (collocated scalar Laplace operator) with $Q=P$ 38 * BP6 (collocated vector Laplace operator) with $Q=P$ 39* - `nek5000` 40 - * BP1 (scalar mass operator) with $Q=P+1$ 41 * BP3 (scalar Laplace operator) with $Q=P+1$ 42::: 43 44These are all **T-vector**-to-**T-vector** and include parallel scatter, element 45scatter, element evaluation kernel, element gather, and parallel gather (with the 46parallel gathers/scatters done externally to libCEED). 47 48BP1 and BP2 are $L^2$ projections, and thus have no boundary condition. 49The rest of the BPs have homogeneous Dirichlet boundary conditions. 50 51The BPs are parametrized by the number $P$ of Gauss-Legendre-Lobatto nodal points 52(with $P=p+1$, and $p$ the degree of the basis polynomial) for the Lagrange 53polynomials, as well as the number of quadrature points, $Q$. 54A $Q$-point Gauss-Legendre quadrature is used for all BPs except BP5 and BP6, 55which choose $Q = P$ and Gauss-Legendre-Lobatto quadrature to collocate with the 56interpolation nodes. This latter choice is popular in applications that use spectral 57element methods because it produces a diagonal mass matrix (enabling easy explicit 58time integration) and significantly reduces the number of floating point operations 59to apply the operator. 60 61% bps-exclusion-marker 62 63For a more detailed description of the operators employed in the BPs, please see the dedicated [BPs documentation section](https://libceed.readthedocs.io/en/latest/examples/bps.html). 64 65## PETSc+libCEED Navier-Stokes Solver 66 67The Navier-Stokes problem solves the compressible Navier-Stokes 68equations using an explicit or implicit time integration. A more detailed 69description of the problem formulation can be found in the 70[fluids/](./fluids) folder and the corresponding [fluids documentation page](https://libceed.readthedocs.io/en/latest/examples/fluids/index.html). 71 72## PETSc+libCEED Solid mechanics elasticity mini-app 73 74This example solves the steady-state static momentum balance equations using unstructured high-order finite/spectral element spatial discretizations. A more detailed 75description of the problem formulation can be found in the 76[solids/](./solids) folder and the corresponding [solids documentation page](https://libceed.readthedocs.io/en/latest/examples/solids/index.html). 77 78## PETSc+libCEED Surface Area Examples 79 80These examples, located in the [petsc/](./petsc) folder, use the mass operator to compute the surface area of a 81cube or a discrete cubed-sphere, using PETSc. For a detailed description, please see the corresponding [area documentation page](https://libceed.readthedocs.io/en/latest/examples/petsc/index.html#area). 82 83## PETSc+libCEED Bakeoff Problems on the Cubed-Sphere 84 85These examples, located in the [petsc/](./petsc) folder, reproduce the Bakeoff Problems 1-6 on a discrete 86cubed-sphere, using PETSc. For a detailed description, please see the corresponding [problems on the cubed-sphere documentation page](https://libceed.readthedocs.io/en/latest/examples/petsc/index.html#bakeoff-problems-on-the-cubed-sphere). 87 88## Running Examples 89 90To build the examples, set the `MFEM_DIR`, `PETSC_DIR`, and 91`NEK5K_DIR` variables and, from the `examples/` directory, run 92 93```{include} ../README.md 94:start-after: running-examples-inclusion-marker 95:end-before: benchmarks-marker 96``` 97