Type

  drive-* -help

for instructions on how to run any driver.

To run the examples, type

  mpirun -np 4 drive-*  [args]

1. drive-diffusion-2D implements the 2D heat equation on a regular grid. You must have hypre installed and these variables in examples/Makefile set correctly

      HYPRE_DIR = ../../linear_solvers/hypre
      HYPRE_FLAGS = -I$(HYPRE_DIR)/include
      HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
   

   This driver also support spatial coarsening and explicit time stepping. This allows you to use explicit time stepping on each Braid level, regardless of time step size.

2. drive-burgers-1D implements Burger's equation (and also linear advection) in 1D using forward or backward Euler in time and Lax-Friedrichs in space. Spatial coarsening is supported, allowing for stable time stepping on coarse time-grids.

   See also viz-burgers.py for visualizing the output.

3. drive-diffusion is a sophisticated test bed for finite element discretizations of the heat equation. It relies on the mfem package to create general finite element discretizations for the spatial problem. Other packages must be installed in this order.

   • Unpack and install Metis

   • Unpack and install hypre

   • Unpack mfem. Then make sure to set these variables correctly in the mfem Makefile:

       USE_METIS_5 = YES
       HYPRE_DIR   = where_ever_linear_solvers_is/hypre 
     

   • Make the parallel version of mfem first by typing

      make parallel
     

   • Make GLVIS. Set these variables in the glvis makefile

      MFEM_DIR   = mfem_location
      MFEM_LIB   = -L$(MFEM_DIR) -lmfem
     

   • Go to braid/examples and set these Makefile variables,

      METIS_DIR = ../../metis-5.1.0/lib
      MFEM_DIR = ../../mfem
      MFEM_FLAGS = -I$(MFEM_DIR)
      MFEM_LIB = -L$(MFEM_DIR) -lmfem -L$(METIS_DIR) -lmetis
     

     then type

      make drive-diffusion
     

   • To run drive-diffusion and glvis, open two windows. In one, start a glvis session

         ./glvis
     

     Then, in the other window, run drive-diffusion

         mpirun -np ... drive-diffusion [args]
     

     Glvis will listen on a port to which drive-diffusion will dump visualization information.

4. The other drive-.cpp files use MFEM to implement other PDEs

   • drive-adv-diff-DG: implements advection(-diffusion) with a discontinuous Galerkin discretization. This driver is under developement.

   • drive-diffusion-1D-moving-mesh: implements the 1D heat equation, but with a moving mesh that adapts to the forcing function so that the mesh equidistributes the arc-length of the solution.

   • drive-diffusion-1D-moving-mesh-serial: implements a serial time-stepping version of the above problem.

   • drive-pLaplacian: implements the 2D the \f$p\f$-Laplacian (nonlinear diffusion).

   • drive-diffusion-ben: implements the 2D/3D diffusion equation with time-dependent coefficients. This is essentially equivalent to drive-diffusion, and could be removed, but we're keeping it around because it implements linear diffusion in the same way that the p-Laplacian driver implemented nonlinear diffusion. This makes it suitable for head-to-head timings.

   • drive-lin-elasticity: implements time-dependent linearized elasticity and is under development.

   • drive-nonlin-elasticity: implements time-dependent nonlinear elasticity and is under development.

5. Directory drive-adv-diff-1D-Cython/ solves a simple 1D advection-diffussion equation using the Cython interface and numerous spatial and temporal discretizations

            drivers/drive-adv-diff-1D-Cython/drive_adv_diff_1D.pyx
   

   and

            drivers/drive-adv-diff-1D-Cython/drive_adv_diff_1D-setup.py
   

6. Directory drive-Lorenz-Delta/ implements the chaotic Lorenz system, with its trademark butterfly shaped attractor. The driver uses the Delta correction feature and Lyapunov estimation to solve for the backward Lyapunov vectors of the system and to accelerate XBraid convergence. Visualize the solution and the Lyapunov vectors with vis_lorenz_LRDelta.py Also see example 7 (examples/ex-07.c). This driver is in a broken state, and needs updating for compatibility with new Delta correction implementation.

7. Directory drive-KS-Delta/ solves the chaotic Kuramoto-Sivashinsky equation in 1D, using fourth order finite differencing in space and the Lobatto IIIC fully implicit RK method in time. The driver also uses Delta correction and Lyapunov estimation to accelerate convergence and to generate estimates to the unstable Lyapunov vectors for the system.