BVPHarmonic.cpp File Reference

#include <BVP_bundle.h>
#include "../Utils_Fill.h"

Go to the source code of this file.

Classes
class	CppNoddy::Example::Harmonic_equation< _Type, _Xtype >
	Define the harmonic equation by inheriting the Equation base class. More...
class	CppNoddy::Example::Harmonic_left_BC< _Type >
class	CppNoddy::Example::Harmonic_right_BC< _Type >

Namespaces
namespace	CppNoddy
	A collection of OO numerical routines aimed at simple (typical) applied problems in continuum mechanics.
namespace	CppNoddy::Example

Enumerations
enum	{ f , fd }

Functions
int	main ()

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
f
fd

Definition at line 17 of file BVPHarmonic.cpp.

{f, fd };

Function Documentation

main()

int main

(

)

Definition at line 77 of file BVPHarmonic.cpp.

{
  cout << "\n";
  cout << "=== BVP: finite-difference solution of Harmonic eqn =\n";
  cout << "\n";
 
  Example::Harmonic_equation<double, double> real_problem;
  Example::Harmonic_left_BC <double> real_BC_left;
  Example::Harmonic_right_BC<double> real_BC_right;
  Example::Harmonic_equation<D_complex, D_complex> complex_problem;
  Example::Harmonic_left_BC <D_complex> complex_BC_left;
  Example::Harmonic_right_BC<D_complex> complex_BC_right;
 
  double left =  0.0;
  double right = 1.0;
  // number of nodal points
  unsigned N = 21;
  // a real mesh -- along real axis
  DenseVector<double> real_nodes( Utility::uniform_node_vector( left, right, N ) );
  // a complex mesh -- along imaginary axis
  D_complex eye( 0.0, 1.0 );
  DenseVector<D_complex> complex_nodes( real_nodes );
  complex_nodes *= eye;
  // Example tolerance
  const double tol = 1.e-4;
 
  // a real ODE BVP
  ODE_BVP<double> real_ode( &real_problem, real_nodes, &real_BC_left, &real_BC_right );
  // a complex ODE BVP solved on a line in the complex plane
  ODE_BVP<D_complex, D_complex> complex_ode( &complex_problem, complex_nodes, &complex_BC_left, &complex_BC_right );
  complex_ode.set_monitor_det( false );
 
  // our initial guess
  for ( unsigned i = 0; i < N; ++i )
  {
    double y = real_ode.solution().coord( i );
    // set f(y)
    real_ode.solution()( i, f ) = y;
    complex_ode.solution()( i, f ) = y;
    // set f'(y)
    real_ode.solution()( i, fd ) = 1;
    complex_ode.solution()( i, fd ) = 1;
  }
 
  // solve the problem using 2nd order finite-difference
  try
  {
    real_ode.solve2();
    complex_ode.solve2();
  }
  catch ( const std::runtime_error &error )
  {
    cout << " \033[1;31;48m  * FAILED THROUGH EXCEPTION BEING RAISED \033[0m\n";
    return 1;
  }
 
  // find the maximum deviation from the analytical solutions of sin(x)/sin(1) and sinh(z)/sinh(1)
  double real_diff = 0;
  double complex_diff = 0;
  for ( unsigned i = 0; i < N; ++i )
  {
    real_diff = std::max( std::abs( real_ode.solution()( i, f ) - sin( real_ode.solution().coord( i ) ) / sin( 1 ) ), real_diff );
    complex_diff = std::max( std::abs( complex_ode.solution()( i, f ) - sin( complex_ode.solution().coord( i ) ) / sin( eye ) ), complex_diff );
  }
 
  // validation test
  if ( real_diff > tol || complex_diff > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << "Real problem error " << real_diff << "\n";
    cout << "Complex problem error " << complex_diff << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
}

References f, fd, CppNoddy::ODE_BVP< _Type, _Xtype >::set_monitor_det(), CppNoddy::ODE_BVP< _Type, _Xtype >::solution(), CppNoddy::ODE_BVP< _Type, _Xtype >::solve2(), and CppNoddy::Utility::uniform_node_vector().