libCEED: Examples

This page provides a brief description of the examples for the libCEED library.

Basic libCEED Examples

Two examples that rely only upon libCEED without any external libraries are provided in the ceed/ folder. For more details, please see the dedicated documenttaion section.

Bakeoff Problems

The Center for Efficient Exascale Discretizations (CEED) uses Bakeoff Problems (BPs) to test and compare the performance of high-order finite element implementations. The definitions of the problems are given on the ceed website. Each of the following bakeoff problems that use external discretization libraries (such as MFEM, PETSc, and Nek5000) are located in the subdirectories mfem/, petsc/, and nek5000/, respectively.

Here we provide a short summary:

User code	BPs
mfem	BP1 (scalar mass operator), with Q=P+1 BP3 (scalar Laplace operator), with Q=P+1
petsc	BP1 (scalar mass operator), with Q=P+1 BP2 (vector mass operator), with Q=P+1 BP3 (scalar Laplace operator), with Q=P+1 BP4 (vector Laplace operator), with Q=P+1 BP5 (collocated scalar Laplace operator), with Q=P BP6 (collocated vector Laplace operator), with Q=P
nek5000	BP1 (scalar mass operator), with Q=P+1 BP3 (scalar Laplace operator), with Q=P+1

These are all T-vector-to-T-vector and include parallel scatter, element scatter, element evaluation kernel, element gather, and parallel gather (with the parallel gathers/scatters done externally to libCEED).

BP1 and BP2 are L^2 projections, and thus have no boundary condition. The rest of the BPs have homogeneous Dirichlet boundary conditions.

The BPs are parametrized by the number P of Gauss-Legendre-Lobatto nodal points (with P=p+1, and p the degree of the basis polynomial) for the Lagrange polynomials, as well as the number of quadrature points, Q. A Q-point Gauss-Legendre quadrature is used for all BPs except BP5 and BP6, which choose Q = P and Gauss-Legendre-Lobatto quadrature to collocate with the interpolation nodes. This latter choice is popular in applications that use spectral element methods because it produces a diagonal mass matrix (enabling easy explicit time integration) and significantly reduces the number of floating point operations to apply the operator.

For a more detailed description of the operators employed in the BPs, please see the dedicated BPs documentation section.

PETSc+libCEED Navier-Stokes Solver

The Navier-Stokes problem solves the compressible Navier-Stokes equations using an explicit or implicit time integration. A more detailed description of the problem formulation can be found in the fluids/ folder and the corresponding fluids documentation page.

PETSc+libCEED Solid mechanics elasticity mini-app

This example solves the steady-state static momentum balance equations using unstructured high-order finite/spectral element spatial discretizations. A more detailed description of the problem formulation can be found in the solids/ folder and the corresponding solids documentation page.

PETSc+libCEED Surface Area Examples

These examples, located in the petsc/ folder, use the mass operator to compute the surface area of a cube or a discrete cubed-sphere, using PETSc. For a detailed description, please see the corresponding area documentation page.

PETSc+libCEED Bakeoff Problems on the Cubed-Sphere

These examples, located in the petsc/ folder, reproduce the Bakeoff Problems 1-6 on a discrete cubed-sphere, using PETSc. For a detailed description, please see the corresponding problems on the cubed-sphere documentation page.

Running Examples

To build the examples, set the MFEM_DIR, PETSC_DIR, and NEK5K_DIR variables and, from the examples/ directory, run