
This tutorial demonstrates the solution of a nodal Poisson equation
to compute a potential flow field around nine obstacles. 

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To run it in serial, 

./main3d.ex inputs

To run it in parallel, for example on 4 ranks:

mpirun -n 4 ./main3d.ex inputs

The following parameters can be set at run-time -- these are currently set in the inputs
file but you can also set them on the command line.  

n_cell = 128                             # number of cells in x-direction; we double this in the y-direction
max_grid_size = 64                       # the maximum number of cells in any direction in a single grid

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The output from your run should look something like this:

********************************************************************
 Let's project the initial velocity to find
   the flow field around the obstacles ...
 The domain has 256 cells in the x-direction
 The maximum grid size is 64
********************************************************************

MLMG: # of AMR levels: 1
      # of MG levels on the coarsest AMR level: 3
MLMG: Initial rhs               = 126.3307824
MLMG: Initial residual (resid0) = 126.3307824
MLCGSolver_BiCGStab: Initial error (error0) =        0.0278389093
MLCGSolver_BiCGStab: Final: Iteration   77 rel. err. 6.543689448e-05
MLMG: Iteration   1 Fine resid/bnorm = 0.2499102826
MLCGSolver_BiCGStab: Initial error (error0) =        0.001461454468
MLCGSolver_BiCGStab: Final: Iteration   76 rel. err. 8.877403781e-05
MLMG: Iteration   2 Fine resid/bnorm = 0.02600341945
MLCGSolver_BiCGStab: Initial error (error0) =        0.0001077472471
MLCGSolver_BiCGStab: Final: Iteration   72 rel. err. 9.553802864e-05
MLMG: Iteration   3 Fine resid/bnorm = 0.00249434023
MLCGSolver_BiCGStab: Initial error (error0) =        1.011498575e-05
MLCGSolver_BiCGStab: Final: Iteration   79 rel. err. 8.516182967e-05
MLMG: Iteration   4 Fine resid/bnorm = 0.0002272675105
MLCGSolver_BiCGStab: Initial error (error0) =        9.876710493e-07
MLCGSolver_BiCGStab: Final: Iteration   77 rel. err. 7.625053604e-05
MLMG: Iteration   5 Fine resid/bnorm = 2.011881569e-05
MLCGSolver_BiCGStab: Initial error (error0) =        9.475250695e-08
MLCGSolver_BiCGStab: Final: Iteration   75 rel. err. 9.507528184e-05
MLMG: Iteration   6 Fine resid/bnorm = 1.760482725e-06
MLCGSolver_BiCGStab: Initial error (error0) =        9.039312908e-09
MLCGSolver_BiCGStab: Final: Iteration   76 rel. err. 8.428185988e-05
MLMG: Iteration   7 Fine resid/bnorm = 1.532406399e-07
MLCGSolver_BiCGStab: Initial error (error0) =        8.618104966e-10
MLCGSolver_BiCGStab: Final: Iteration   76 rel. err. 7.620489259e-05
MLMG: Iteration   8 Fine resid/bnorm = 1.317566921e-08
MLCGSolver_BiCGStab: Initial error (error0) =        8.18305383e-11
MLCGSolver_BiCGStab: Final: Iteration   77 rel. err. 6.119534384e-05
MLMG: Iteration   9 Fine resid/bnorm = 1.138344394e-09
MLMG: Final Iter. 9 resid, resid/bnorm = 1.43807938e-07, 1.138344394e-09
MLMG: Timers: Solve = 2.50906984 Iter = 1.970112343 Bottom = 0.559133407

********************************************************************
 Done solving the equation
 ... now subtracting off sigmna grad phi from vel
 ... now done with full projection operation
********************************************************************

Writing plt00000
Total run time 2.873842965
