reduced_basis_ex7.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2019 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
 
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
// rbOOmit: An implementation of the Certified Reduced Basis method.
// Copyright (C) 2009, 2010 David J. Knezevic
// This file is part of rbOOmit.
 
 
 
// <h1>Reduced Basis Example 7 - Acoustic Horn</h1>
// \author David Knezevic
// \date 2012
//
// In this example problem we use the Certified Reduced Basis method
// to solve a complex-valued Helmholtz problem for acoustics. There is only
// one parameter in this problem: the forcing frequency at the horn inlet.
// We impose a radiation boundary condition on the outer boundary.
//
// In the Online stage we write out the reflection coefficient as a function
// of frequency. The reflection coefficient gives the ratio of the reflected
// wave to the applied wave at the inlet.
 
// C++ include files that we need
#include <iostream>
#include <algorithm>
#include <cmath>
#include <set>
 
// Basic include file needed for the mesh functionality.
#include "libmesh/libmesh.h"
#include "libmesh/mesh.h"
#include "libmesh/mesh_generation.h"
#include "libmesh/exodusII_io.h"
#include "libmesh/equation_systems.h"
#include "libmesh/dof_map.h"
#include "libmesh/getpot.h"
#include "libmesh/elem.h"
#include "libmesh/rb_data_serialization.h"
#include "libmesh/rb_data_deserialization.h"
#include "libmesh/enum_solver_package.h"
 
// local includes
#include "rb_classes.h"
#include "assembly.h"
 
// Bring in everything from the libMesh namespace
using namespace libMesh;
 
// The main program.
int main (int argc, char** argv)
{
  // Initialize libMesh.
  LibMeshInit init (argc, argv);
 
#ifndef LIBMESH_USE_COMPLEX_NUMBERS
  libmesh_example_requires(false, "--enable-complex");
#else
 
#if !defined(LIBMESH_HAVE_XDR)
  // We need XDR support to write out reduced bases
  libmesh_example_requires(false, "--enable-xdr");
#elif defined(LIBMESH_DEFAULT_SINGLE_PRECISION)
  // XDR binary support requires double precision
  libmesh_example_requires(false, "--disable-singleprecision");
#elif defined(LIBMESH_DEFAULT_TRIPLE_PRECISION)
  // long double doesn't work on the previous examples, don't try it
  // here
  libmesh_example_requires(false, "double precision");
#endif
  // FIXME: This example currently segfaults with Trilinos?
  libmesh_example_requires(libMesh::default_solver_package() == PETSC_SOLVERS, "--enable-petsc");
 
#if LIBMESH_HAVE_PETSC
  // lets parse the input to check which set of arguments was provided.
  // Skip the runs with wrong arguments:
  GetPot input(argc, argv);
 
  // skip if the specification of the solver-package is given in wrong syntax:
#if PETSC_VERSION_LESS_THAN(3,9,0)
  if (input.search("-pc_factor_mat_solver_type"))
   {
      libMesh::out << "LibMesh was configured with PETSc < 3.9, but command-line options "
                   << "use syntax understood by later versions only. Skipping this example."
                   << std::endl;
      return 77;
   }
#else
  if (input.search("-pc_factor_mat_solver_package"))
    {
      libMesh::out << "LibMesh was configured with PETSc >= 3.9, but command-line options "
                   << "use deprecated syntax. Skipping now."
                   << std::endl;
      return 77;
    }
#endif
 
  // check that we have the required solver:
  std::string solver;
  solver = input.next(solver);
  if (solver == "mumps")
  {
#ifndef LIBMESH_PETSC_HAVE_MUMPS
    libmesh_example_requires(false, "PETSc compiled with MUMPS support");
#endif
  }
  else if (solver == "superlu")
  {
#ifndef LIBMESH_PETSC_HAVE_SUPERLU_DIST
    libmesh_example_requires(false, "PETSc compiled with SuperLU support");
#endif
  }
  else
  {
     libMesh::err << "Error: Solver " << solver << " is unknown."
                  << std::endl;
     return 1;
  }
 
#endif //LIBMESH_HAVE_PETSC
 
  // Skip this 2D example if libMesh was compiled as 1D-only.
  libmesh_example_requires(2 <= LIBMESH_DIM, "2D support");
 
  // Parse the input file (reduced_basis_ex7.in) using GetPot
  std::string parameters_filename = "reduced_basis_ex7.in";
  GetPot infile(parameters_filename);
 
  const unsigned int dim = 2;                      // The number of spatial dimensions
 
  bool store_basis_functions = infile("store_basis_functions", true); // Do we write the RB basis functions to disk?
 
  // Read the "online_mode" flag from the command line
  GetPot command_line (argc, argv);
  int online_mode = 0;
  if (command_line.search(1, "-online_mode"))
    online_mode = command_line.next(online_mode);
 
  // Create a mesh on the default MPI communicator.
  Mesh mesh(init.comm(), dim);
  mesh.read("horn.msh");
 
  // Create an equation systems object.
  EquationSystems equation_systems (mesh);
 
  // We override RBConstruction with SimpleRBConstruction in order to
  // specialize a few functions for this particular problem.
  SimpleRBConstruction & rb_con =
    equation_systems.add_system<SimpleRBConstruction> ("Acoustics");
 
  // Initialize the data structures for the equation system.
  equation_systems.init ();
 
  // Print out some information about the "truth" discretization
  equation_systems.print_info();
  mesh.print_info();
 
  // Build a new RBEvaluation object which will be used to perform
  // Reduced Basis calculations. This is required in both the
  // "Offline" and "Online" stages.
  SimpleRBEvaluation rb_eval(mesh.comm());
 
  // We need to give the RBConstruction object a pointer to
  // our RBEvaluation object
  rb_con.set_rb_evaluation(rb_eval);
 
  if (!online_mode) // Perform the Offline stage of the RB method
    {
      // Read in the data that defines this problem from the specified text file
      rb_con.process_parameters_file(parameters_filename);
 
      // Print out info that describes the current setup of rb_con
      rb_con.print_info();
 
      // Prepare rb_con for the Construction stage of the RB method.
      // This sets up the necessary data structures and performs
      // initial assembly of the "truth" affine expansion of the PDE.
      rb_con.initialize_rb_construction();
 
      // Compute the reduced basis space by computing "snapshots", i.e.
      // "truth" solves, at well-chosen parameter values and employing
      // these snapshots as basis functions.
      libmesh_try
        {
          rb_con.train_reduced_basis();
        }
      libmesh_catch (LogicError & e)
        {
          libMesh::err << "\n\n"
                       << "********************************************************************************\n"
                       << "Training reduced basis failed, this example requires a direct solver.\n"
                       << "Try running with -ksp_type preonly -pc_type lu instead.\n"
                       << "********************************************************************************"
                       << std::endl;
          return 77;
        }
 
      // Write out the data that will subsequently be required for the Evaluation stage
#if defined(LIBMESH_HAVE_CAPNPROTO)
      RBDataSerialization::RBEvaluationSerialization rb_eval_writer(rb_con.get_rb_evaluation());
      rb_eval_writer.write_to_file("rb_eval.bin");
#else
      rb_con.get_rb_evaluation().legacy_write_offline_data_to_files();
#endif
 
      // If requested, write out the RB basis functions for visualization purposes
      if (store_basis_functions)
        {
          // Write out the basis functions
          rb_con.get_rb_evaluation().write_out_basis_functions(rb_con);
        }
 
      // Basis functions should be orthonormal, so
      // print out the inner products to check this
      rb_con.print_basis_function_orthogonality();
    }
  else // Perform the Online stage of the RB method
    {
      // Read in the reduced basis data
#if defined(LIBMESH_HAVE_CAPNPROTO)
      RBDataDeserialization::RBEvaluationDeserialization rb_eval_reader(rb_eval);
      rb_eval_reader.read_from_file("rb_eval.bin", /*read_error_bound_data*/ true);
#else
      rb_eval.legacy_read_offline_data_from_files();
#endif
 
      // Read in online_N and initialize online parameters
      Real online_frequency = infile("online_frequency", 0.);
      RBParameters online_mu;
      online_mu.set_value("frequency", online_frequency);
      rb_eval.set_parameters(online_mu);
      rb_eval.print_parameters();
 
      // Now do the Online solve using the precomputed reduced basis
      rb_eval.rb_solve(rb_eval.get_n_basis_functions());
 
      if (store_basis_functions)
        {
          // Read in the basis functions
          rb_eval.read_in_basis_functions(rb_con);
 
          // Plot the solution
          rb_con.load_rb_solution();
 
          //Output the variable in ExodusII format (single precision)
          ExodusII_IO(mesh, /*single_precision=*/true).write_equation_systems ("RB_sol_float.exo", equation_systems);
        }
 
      // Now do a sweep over frequencies and write out the reflection coefficient for each frequency
      std::ofstream reflection_coeffs_out("reflection_coefficients.dat");
 
      Real n_frequencies = infile("n_frequencies", 0.);
      Real delta_f = (rb_eval.get_parameter_max("frequency") - rb_eval.get_parameter_min("frequency")) / (n_frequencies-1);
      for (unsigned int freq_i=0; freq_i<n_frequencies; freq_i++)
        {
          Real frequency = rb_eval.get_parameter_min("frequency") + freq_i * delta_f;
          online_mu.set_value("frequency", frequency);
          rb_eval.set_parameters(online_mu);
          rb_eval.rb_solve(rb_eval.get_n_basis_functions());
 
          Number complex_one(1., 0.);
          reflection_coeffs_out << frequency << " " << std::abs(rb_eval.RB_outputs[0] - complex_one) << std::endl;
        }
      reflection_coeffs_out.close();
 
    }
 
#endif
 
  return 0;
}