static char help[] = "2d Bratu problem in shared memory parallel with SNES.\n\
We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
domain, uses SHARED MEMORY to evaluate the user function.\n\
The command line options include:\n\
-par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\
-mx <xg>, where <xg> = number of grid points in the x-direction\n\
-my <yg>, where <yg> = number of grid points in the y-direction\n\
-use_fortran_function: use Fortran coded function, rather than C\n";
/*
This code compiles ONLY on SGI systems
========================================
*/
/*T
Concepts: SNES^parallel Bratu example
Concepts: shared memory
Processors: n
T*/
/*
Programming model: Combination of
1) MPI message passing for PETSc routines
2) automatic loop parallism (using shared memory) for user
provided function.
While the user function is being evaluated all MPI processes except process
0 blocks. Process zero spawns nt threads to evaluate the user function. Once
the user function is complete, the worker threads are suspended and all the MPI processes
static const char help[] = "p-Bratu nonlinear PDE in 2d.\n\
We solve the p-Laplacian (nonlinear diffusion) combined with\n\
the Bratu (solid fuel ignition) nonlinearity in a 2D rectangular\n\
domain, using distributed arrays (DAs) to partition the parallel grid.\n\
The command line options include:\n\
-p <2>: `p' in p-Laplacian term\n\
-epsilon <1e-05>: Strain-regularization in p-Laplacian\n\
-lambda <6>: Bratu parameter\n\
\n";
/*F
The $p$-Bratu problem is a combination of the $p$-Laplacian (nonlinear diffusion) and the Brutu solid fuel ignition problem.
This problem is modeled by the partial differential equation
\begin{equation*}
-\nabla\cdot (\eta \nabla u) - \lambda \exp(u) = 0
\end{equation*}
on $\Omega = (-1,1)^2$ with closure
\begin{align*}
\eta(\gamma) &= (\epsilon^2 + \gamma)^{(p-2)/2} & \gamma &= \frac 1 2 |\nabla u|^2
\end{align*}
and boundary conditions $u = 0$ for $(x,y) \in \partial \Omega$
A 9-point finite difference stencil is used to discretize
the boundary value problem to obtain a nonlinear system of equations.
This would be a 5-point stencil if not for the $p$-Laplacian's nonlinearity.
F*/
