// @sect3{Include files}
// As usual, we start by including
- // some well-known files.
+ // some well-known files:
#include <base/quadrature_lib.h>
#include <base/logstream.h>
#include <base/function.h>
#include <numerics/data_out.h>
#include <numerics/error_estimator.h>
- // As in step-29, we include the libary for
- // the sparse direct solver UMFPACK.
+ // Then we need to include the header file
+ // for the sparse direct solver UMFPACK:
#include <lac/sparse_direct.h>
// This includes the libary for the
// incomplete LU factorization that will
- // be used as a preconditioner in 3D.
+ // be used as a preconditioner in 3D:
#include <lac/sparse_ilu.h>
// This is C++:
#include <fstream>
#include <sstream>
- // As in all programs, the namespace is set
- // to dealii.
+ // As in all programs, the namespace dealii
+ // in included:
using namespace dealii;
// @sect3{Defining the inner preconditioner type}