ex4.c

一个用来实现偏微分方程中网格的计算库

/* $Id: ex4.C 2837 2008-05-08 17:23:37Z roystgnr $ */

/* The Next Great Finite Element Library. */
/* Copyright (C) 2003  Benjamin S. Kirk */

/* 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 */



 // <h1>Example 4 - Solving a 1D, 2D or 3D Poisson Problem in Parallel</h1>
 //
 // This is the fourth example program.  It builds on
 // the third example program by showing how to formulate
 // the code in a dimension-independent way.  Very minor
 // changes to the example will allow the problem to be
 // solved in one, two or three dimensions.
 //
 // This example will also introduce the PerfLog class
 // as a way to monitor your code's performance.  We will
 // use it to instrument the matrix assembly code and look
 // for bottlenecks where we should focus optimization efforts.
 //
 // This example also shows how to extend example 3 to run in
 // parallel.  Notice how litte has changed!  The significant
 // differences are marked with "PARALLEL CHANGE".


// C++ include files that we need
#include <iostream>
#include <algorithm>
#include <math.h>

// Basic include file needed for the mesh functionality.
#include "libmesh.h"
#include "mesh.h"
#include "mesh_generation.h"
#include "gmv_io.h"
#include "gnuplot_io.h"
#include "linear_implicit_system.h"
#include "equation_systems.h"

// Define the Finite Element object.
#include "fe.h"

// Define Gauss quadrature rules.
#include "quadrature_gauss.h"

// Define the DofMap, which handles degree of freedom
// indexing.
#include "dof_map.h"

// Define useful datatypes for finite element
// matrix and vector components.
#include "sparse_matrix.h"
#include "numeric_vector.h"
#include "dense_matrix.h"
#include "dense_vector.h"

// Define the PerfLog, a performance logging utility.
// It is useful for timing events in a code and giving
// you an idea where bottlenecks lie.
#include "perf_log.h"

// The definition of a geometric element
#include "elem.h"

#include "string_to_enum.h"
#include "getpot.h"



// Function prototype.  This is the function that will assemble
// the linear system for our Poisson problem.  Note that the
// function will take the \p EquationSystems object and the
// name of the system we are assembling as input.  From the
// \p EquationSystems object we have acess to the \p Mesh and
// other objects we might need.
void assemble_poisson(EquationSystems& es,
                      const std::string& system_name);

// Exact solution function prototype.
Real exact_solution (const Real x,
                     const Real y = 0.,
                     const Real z = 0.);

// Begin the main program.
int main (int argc, char** argv)
{
  // Initialize libMesh and any dependent libaries, like in example 2.
  LibMeshInit init (argc, argv);

  // Declare a performance log for the main program
  // PerfLog perf_main("Main Program");
  
  // Create a GetPot object to parse the command line
  GetPot command_line (argc, argv);
  
  // Check for proper calling arguments.
  if (argc < 3)
    {
      if (libMesh::processor_id() == 0)
        std::cerr << "Usage:\n"
                  <<"\t " << argv[0] << " -d 2(3)" << " -n 15"
                  << std::endl;

      // This handy function will print the file name, line number,
      // and then abort.  Currrently the library does not use C++
      // exception handling.
      libmesh_error();
    }
  
  // Brief message to the user regarding the program name
  // and command line arguments.
  else 
    {
      std::cout << "Running " << argv[0];
      
      for (int i=1; i<argc; i++)
        std::cout << " " << argv[i];
      
      std::cout << std::endl << std::endl;
    }
  

  // Read problem dimension from command line.  Use int
  // instead of unsigned since the GetPot overload is ambiguous
  // otherwise.
  int dim = 2;
  if ( command_line.search(1, "-d") )
    dim = command_line.next(dim);
  
  // Read number of elements from command line
  int ps = 15;
  if ( command_line.search(1, "-n") )
    ps = command_line.next(ps);
  
  // Read FE order from command line
  std::string order = "SECOND"; 
  if ( command_line.search(2, "-Order", "-o") )
    order = command_line.next(order);

  // Read FE Family from command line
  std::string family = "LAGRANGE"; 
  if ( command_line.search(2, "-FEFamily", "-f") )
    family = command_line.next(family);
  
  // Cannot use dicontinuous basis.
  if ((family == "MONOMIAL") || (family == "XYZ"))
    {
      std::cout << "ex4 currently requires a C^0 (or higher) FE basis." << std::endl;
      libmesh_error();
    }
    
  // Create a mesh with user-defined dimension.
  Mesh mesh (dim);
  

  // Use the MeshTools::Generation mesh generator to create a uniform
  // grid on the square [-1,1]^D.  We instruct the mesh generator
  // to build a mesh of 8x8 \p Quad9 elements in 2D, or \p Hex27
  // elements in 3D.  Building these higher-order elements allows
  // us to use higher-order approximation, as in example 3.
  if ((family == "LAGRANGE") && (order == "FIRST"))
    {
      // No reason to use high-order geometric elements if we are
      // solving with low-order finite elements.
      MeshTools::Generation::build_cube (mesh,
                                         ps, ps, ps,
                                         -1., 1.,
                                         -1., 1.,
                                         -1., 1.,
                                         (dim==1)    ? EDGE2 : 
                                         ((dim == 2) ? QUAD4 : HEX8));
    }
  
  else
    {
      MeshTools::Generation::build_cube (mesh,
                                         ps, ps, ps,
                                         -1., 1.,
                                         -1., 1.,
                                         -1., 1.,
                                         (dim==1)    ? EDGE3 : 
                                         ((dim == 2) ? QUAD9 : HEX27));
    }

  
  // Print information about the mesh to the screen.
  mesh.print_info();
  
  
  // Create an equation systems object.
  EquationSystems equation_systems (mesh);
  
  // Declare the system and its variables.
  // Create a system named "Poisson"
  LinearImplicitSystem& system =
    equation_systems.add_system<LinearImplicitSystem> ("Poisson");

  
  // Add the variable "u" to "Poisson".  "u"
  // will be approximated using second-order approximation.
  system.add_variable("u",
                      Utility::string_to_enum<Order>   (order),
                      Utility::string_to_enum<FEFamily>(family));

  // Give the system a pointer to the matrix assembly
  // function.
  system.attach_assemble_function (assemble_poisson);
  
  // Initialize the data structures for the equation system.
  equation_systems.init();

  // Print information about the system to the screen.
  equation_systems.print_info();
  mesh.print_info();

  // Solve the system "Poisson", just like example 2.
  equation_systems.get_system("Poisson").solve();

  // After solving the system write the solution
  // to a GMV-formatted plot file.
  if(dim == 1)
  {        
    GnuPlotIO plot(mesh,"Example 4, 1D",GnuPlotIO::GRID_ON);
    plot.write_equation_systems("out_1",equation_systems);
  }
  else
  {
    GMVIO (mesh).write_equation_systems ((dim == 3) ? 
      "out_3.gmv" : "out_2.gmv",equation_systems);
  }
  
  // All done.  
  return 0;
}




//
//
//
// We now define the matrix assembly function for the
// Poisson system.  We need to first compute element
// matrices and right-hand sides, and then take into
// account the boundary conditions, which will be handled
// via a penalty method.
void assemble_poisson(EquationSystems& es,
                      const std::string& system_name)
{
  // It is a good idea to make sure we are assembling
  // the proper system.
  libmesh_assert (system_name == "Poisson");


  // Declare a performance log.  Give it a descriptive
  // string to identify what part of the code we are
  // logging, since there may be many PerfLogs in an
  // application.
  PerfLog perf_log ("Matrix Assembly");
  
    // Get a constant reference to the mesh object.
  const MeshBase& mesh = es.get_mesh();

  // The dimension that we are running
  const unsigned int dim = mesh.mesh_dimension();

  // Get a reference to the LinearImplicitSystem we are solving
  LinearImplicitSystem& system = es.get_system<LinearImplicitSystem>("Poisson");
  
  // A reference to the \p DofMap object for this system.  The \p DofMap
  // object handles the index translation from node and element numbers
  // to degree of freedom numbers.  We will talk more about the \p DofMap