1# libCEED: Examples 2 3This page provides a brief description of the examples for the libCEED library. 4 5## Basic libCEED Examples 6 7Two examples are provided that rely only upon libCEED without any external 8libraries. 9 10### Example 1: ex1-volume 11 12This example uses the mass matrix to compute the length, area, or volume of a 13region, depending upon runtime parameters. 14 15### Example 2: ex2-surface 16 17This example uses the diffusion matrix to compute the surface area of a region, 18depending upon runtime parameters. 19 20## Bakeoff Problems 21 22This section provides a brief description of the bakeoff problems, used as examples 23for the libCEED library. These bakeoff problems are high-order benchmarks designed 24to test and compare the performance of high-order finite element codes. 25 26For further documentation, readers may wish to consult the 27[CEED documentation](http://ceed.exascaleproject.org/bps/) of the bakeoff problems. 28 29### Bakeoff Problem 1 30 31Bakeoff problem 1 is the *L<sup>2</sup>* projection problem into the finite element space. 32 33The supplied examples solve *_B_ u = f*, where *_B_* is the mass matrix. 34 35The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre. There is one more quadrature point in each dimension than nodal point, *q = p + 1*. 36 37### Bakeoff Problem 2 38 39Bakeoff problem 2 is the *L<sup>2</sup>* projection problem into the finite element space on a vector system. 40 41The supplied examples solve *_B_ _u_ = f*, where *_B_* is the mass matrix. 42 43The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre. There is one more quadrature point in each dimension than nodal point, *q = p + 1*. 44 45### Bakeoff Problem 3 46 47Bakeoff problem 3 is the Poisson problem. 48 49The supplied examples solve *_A_ u = f*, where *_A_* is the Poisson operator. 50 51The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre. There is one more quadrature point in each dimension than nodal point, *q = p + 1*. 52 53### Bakeoff Problem 4 54 55Bakeoff problem 4 is the Poisson problem on a vector system. 56 57The supplied examples solve *_A_ _u_ = f*, where *_A_* is the Laplace operator for the Poisson equation. 58 59The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre. There is one more quadrature point in each dimension than nodal point, *q = p + 1*. 60 61### Bakeoff Problem 5 62 63Bakeoff problem 5 is the Poisson problem. 64 65The supplied examples solve *_A_ u = f*, where *_A_* is the Poisson operator. 66 67The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre-Lobatto. The nodal points and quadrature points are collocated. 68 69### Bakeoff Problem 6 70 71Bakeoff problem 6 is the Poisson problem on a vector system. 72 73The supplied examples solve *_A_ _u_ = f*, where *_A_* is the Laplace operator for the Poisson equation. 74 75The nodal points, *p*, are Gauss-Legendre-Lobatto, and the quadrature points, *q* are Gauss-Legendre-Lobatto. The nodal points and quadrature points are collocated. 76 77## PETSc+libCEED Navier-Stokes Solver 78 79The Navier-Stokes problem solves the compressible Navier-Stokes equations using an explicit time integration. A more detailed description of the problem formulation 80can be found in the [`navier-stokes`](./navierstokes) folder. 81 82## PETSc+libCEED Surface Area Examples 83 84These examples use the mass operator to compute the surface area of a cube or a discrete cubed-sphere, using PETSc. 85 86These examples show in particular the constructions of geometric factors to handle problems in which the elements topological dimension is different from the 87geometrical dimension and for which the coordinate transformation Jacobian from the 2D reference space to a manifold embedded in 3D physical space is a non-square matrix. 88 89## Running Examples 90 91To build the examples, set the `MFEM_DIR`, `PETSC_DIR` and `NEK5K_DIR` variables 92and run: 93 94```console 95# libCEED examples on CPU and GPU 96cd ceed 97make 98./ex1-volume -ceed /cpu/self 99./ex1-volume -ceed /gpu/occa 100./ex2-surface -ceed /cpu/self 101./ex2-surface -ceed /gpu/occa 102cd .. 103 104# MFEM+libCEED examples on CPU and GPU 105cd mfem 106make 107./bp1 -ceed /cpu/self -no-vis 108./bp3 -ceed /gpu/occa -no-vis 109cd .. 110 111# Nek5000+libCEED examples on CPU and GPU 112cd nek 113make 114./nek-examples.sh -e bp1 -ceed /cpu/self -b 3 115./nek-examples.sh -e bp3 -ceed /gpu/occa -b 3 116cd .. 117 118# PETSc+libCEED examples on CPU and GPU 119cd petsc 120make 121./bpsraw -problem bp1 -ceed /cpu/self 122./bpsraw -problem bp2 -ceed /gpu/occa 123./bpsraw -problem bp3 -ceed /cpu/self 124./bpsraw -problem bp4 -ceed /gpu/occa 125./bpsraw -problem bp5 -ceed /cpu/self 126./bpsraw -problem bp6 -ceed /gpu/occa 127cd .. 128 129cd petsc 130make 131./area -problem cube -ceed /cpu/self -petscspace_degree 3 132./area -problem cube -ceed /gpu/occa -petscspace_degree 3 133./area -problem sphere -ceed /cpu/self -petscspace_degree 3 -dm_refine 2 134./area -problem sphere -ceed /gpu/occa -petscspace_degree 3 -dm_refine 2 135 136cd navier-stokes 137make 138./navierstokes -ceed /cpu/self 139./navierstokes -ceed /gpu/occa 140cd .. 141``` 142 143The above code assumes a GPU-capable machine with the OCCA backend 144enabled. Depending on the available backends, other CEED resource specifiers can 145be provided with the `-ceed` option. Other command line arguments can be found in the 146[`petsc`](./petsc/README.md) folder. 147