fe_szabab.c

一个用来实现偏微分方程中网格的计算库

		case 0:
		case 1:
		case 2:
		case 3:
		  return 1;

		case 4:
		case 5:
		case 6:
		case 7:
		  return 3;
		  
		case 8:
		  return 9;
		  
		default:
		  libmesh_error();
		}
	    }


	  default:
	    libmesh_error();
	    
	  }
      }



      // The fifth-order Szabo-Babuska shape functions
    case FIFTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE2:
	  case EDGE3:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		  return 1;

		case 2:
		  return 4;
		  
		default:
		  libmesh_error();		  
		}
	    }

	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		  return 1;

		case 3:
		case 4:
		case 5:
		  return 4;

		default:
		  libmesh_error();
		}
	    }


	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD8:
	  case QUAD9:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		case 3:
		  return 1;

		case 4:
		case 5:
		case 6:
		case 7:
		  return 4;
		  
		case 8:
		  return 16;
		  
		default:
		  libmesh_error();
		}
	    }


	  default:
	    libmesh_error();
	    
	  }
      }



      // The sixth-order Szabo-Babuska shape functions
    case SIXTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE2:
	  case EDGE3:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		  return 1;

		case 2:
		  return 5;
		  
		default:
		  libmesh_error();		  
		}
	    }

	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		  return 1;

		case 3:
		case 4:
		case 5:
		  return 5;

		default:
		  libmesh_error();
		}
	    }


	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD8:
	  case QUAD9:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		case 3:
		  return 1;

		case 4:
		case 5:
		case 6:
		case 7:
		  return 5;
		  
		case 8:
		  return 25;
		  
		default:
		  libmesh_error();
		}
	    }


	  default:
	    libmesh_error();
	    
	  }
      }


      // The seventh-order Szabo-Babuska shape functions
    case SEVENTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE2:
	  case EDGE3:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		  return 1;

		case 2:
		  return 6;
		  
		default:
		  libmesh_error();		  
		}
	    }

	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		  return 1;

		case 3:
		case 4:
		case 5:
		  return 6;

		default:
		  libmesh_error();
		}
	    }


	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD8:
	  case QUAD9:
	    {
	      switch (n)
		{
		case 0:
		case 1:
		case 2:
		case 3:
		  return 1;

		case 4:
		case 5:
		case 6:
		case 7:
		  return 6;
		  
		case 8:
		  return 36;
		  
		default:
		  libmesh_error();
		}
	    }


	  default:
	    libmesh_error();
	    
	  }
      }

      
    default:
      {
	libmesh_error();
      }
    }
  
  libmesh_error();
  
  return 0;
}



template <unsigned int Dim, FEFamily T>
unsigned int FE<Dim,T>::n_dofs_per_elem(const ElemType t,
					const Order o)
{
  switch (o)
    {
      // The first-order Szabo-Babuska shape functions
    case FIRST:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 0;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 0;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD8:
	    return 0;
	    
	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	    
	  case QUAD9:
	    return 0;
	    
	    
	  default:
	    libmesh_error();
	    
	  }
      }



      // The second-order Szabo-Babuska shape functions
    case SECOND:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 1;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 0;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 0;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }



      // The third-order Szabo-Babuska shape functions
    case THIRD:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 2;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 1;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 4;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }



      // The fourth-order Szabo-Babuska shape functions
    case FOURTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 3;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 3;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 9;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }



      // The fifth-order Szabo-Babuska shape functions
    case FIFTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 4;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 6;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 16;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }


  // The sixth-order Szabo-Babuska shape functions
    case SIXTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 5;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 10;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 25;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }


  // The seventh-order Szabo-Babuska shape functions
    case SEVENTH:
      {
	switch (t)
	  {
	    // The 1D Szabo-Babuska defined on a two-noded edge
	  case EDGE2:
	    return 6;
	    
	    // The 1D Szabo-Babuska defined on a three-noded edge
	  case EDGE3:
	    return 0;
	    
	    // The 2D Szabo-Babuska defined on a 6-noded triangle
	  case TRI6:
	    return 15;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // eight-noded quadrilateral.
	  case QUAD8:
	    return 36;

	    // The 2D tensor-product Szabo-Babuska defined on a
	    // nine-noded quadrilateral.
	  case QUAD9:
	    return 0;

	    
	  default:
	    libmesh_error();
	    
	  }
      }

      
      // Otherwise no DOFS per element
    default:
      return 0;
    }
}



template <unsigned int Dim, FEFamily T>
FEContinuity FE<Dim,T>::get_continuity() const
{
  return C_ZERO;
}



template <unsigned int Dim, FEFamily T>
bool FE<Dim,T>::is_hierarchic() const
{
  return false;
}



template <unsigned int Dim, FEFamily T>
bool FE<Dim,T>::shapes_need_reinit() const
{
  // reinit is only necessary for
  // approximation orders >= 3
  // FIXME - but with p refinement it may be
  // needed with any base order
  // if(this->fe_type.order == FIRST ||
  //    this->fe_type.order == SECOND)
  //   return false;
  // else
    return true;
}



//--------------------------------------------------------------
// Explicit instantiation of member functions
INSTANTIATE_MBRF(1,SZABAB);
INSTANTIATE_MBRF(2,SZABAB);
INSTANTIATE_MBRF(3,SZABAB);

#endif //ENABLE_HIGHER_ORDER_SHAPES