Electrostatic Application Conditions

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Some of the conditions are directly implemented in the Electrostatic Kratos Element files, electrosatic_2D.h/.cpp, like the surface sources, but there is other kind of conditions that needs separate files. In tis section we will see the point charge condition and the Neumann and infinit boundary conditions.

Contents

Point Charge Condition

pointcharge2D.h

//   
//   Project Name:        Kratos       
//   Last Modified by:    $Author: jmora $
//   Date:                $Date: 2009-09-24 16:46:49 $
//   Revision:            $Revision: 1.1 $
//
//


#if !defined(KRATOS_PointCharge2D_CONDITION_H_INCLUDED )
#define  KRATOS_PointCharge2D_CONDITION_H_INCLUDED



// System includes 


// External includes 
#include "boost/smart_ptr.hpp"


// Project includes
#include "includes/define.h"
#include "includes/condition.h"
#include "includes/ublas_interface.h"
#include "includes/variables.h"


namespace Kratos
{

  ///@name Kratos Globals
  ///@{ 
  
  ///@} 
  ///@name Type Definitions
  ///@{ 
  
  ///@} 
  ///@name  Enum's
  ///@{
      
  ///@}
  ///@name  Functions 
  ///@{
      
  ///@}
  ///@name Kratos Classes
  ///@{
  
  /// Short class definition.
  /** Detail class definition.
  */
  class PointCharge2D
	  : public Condition
    {
    public:
      ///@name Type Definitions
      ///@{
      
      /// Counted pointer of PointCharge2D
      KRATOS_CLASS_POINTER_DEFINITION(PointCharge2D);
 
      ///@}
      ///@name Life Cycle 
      ///@{ 
      
      /// Default constructor.
	  PointCharge2D(IndexType NewId, GeometryType::Pointer pGeometry);
      PointCharge2D(IndexType NewId, GeometryType::Pointer pGeometry,  
PropertiesType::Pointer pProperties);

      /// Destructor.
      virtual ~PointCharge2D();
      

      ///@}
      ///@name Operators 
      ///@{
      
      
      ///@}
      ///@name Operations
      ///@{

      Condition::Pointer Create(IndexType NewId, NodesArrayType const& 
ThisNodes,  PropertiesType::Pointer pProperties) const;

      void CalculateLocalSystem(MatrixType& rLeftHandSideMatrix, VectorType& 
rRightHandSideVector, ProcessInfo& rCurrentProcessInfo);
      
      void CalculateRightHandSide(VectorType& rRightHandSideVector, ProcessInfo& 
rCurrentProcessInfo);
      
      void EquationIdVector(EquationIdVectorType& rResult, ProcessInfo& 
rCurrentProcessInfo);

	  void GetDofList(DofsVectorType& ConditionalDofList,ProcessInfo& 
CurrentProcessInfo);

      ///@}
      ///@name Access
      ///@{ 
      
      
      ///@}
      ///@name Inquiry
      ///@{
      
      
      ///@}      
      ///@name Input and output
      ///@{

      /// Turn back information as a string.
//      virtual String Info() const;
      
      /// Print information about this object.
//      virtual void PrintInfo(std::ostream& rOStream) const;

      /// Print object's data.
//      virtual void PrintData(std::ostream& rOStream) const;
      
            
      ///@}      
      ///@name Friends
      ///@{

            
      ///@}
      
    protected:
      ///@name Protected static Member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Protected member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Protected Operators
      ///@{ 
        
        
      ///@} 
      ///@name Protected Operations
      ///@{ 
        
        
      ///@} 
      ///@name Protected  Access 
      ///@{ 
        
        
      ///@}      
      ///@name Protected Inquiry 
      ///@{ 
        
        
      ///@}    
      ///@name Protected LifeCycle 
      ///@{ 
      
            
      ///@}
      
    private:
      ///@name Static Member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Member Variables 
      ///@{ 
		
        
        
      ///@} 
      ///@name Private Operators
      ///@{ 

      ///@} 
      ///@name Private Operations
      ///@{ 
        
        
      ///@} 
      ///@name Private  Access 
      ///@{ 
        
        
      ///@}    
      ///@name Private Inquiry 
      ///@{ 
        
        
      ///@}    
      ///@name Un accessible methods 
      ///@{ 
      
      /// Assignment operator.
      //PointCharge2D& operator=(const PointCharge2D& rOther);

      /// Copy constructor.
      //PointCharge2D(const PointCharge2D& rOther);

        
      ///@}    
        
    }; // Class PointCharge2D 

  ///@} 
  
  ///@name Type Definitions       
  ///@{ 
  
  
  ///@} 
  ///@name Input and output 
  ///@{ 
        
 
  /// input stream function
/*  inline std::istream& operator >> (std::istream& rIStream, 
				    PointCharge2D& rThis);
*/
  /// output stream function
/*  inline std::ostream& operator << (std::ostream& rOStream, 
				    const PointCharge2D& rThis)
    {
      rThis.PrintInfo(rOStream);
      rOStream << std::endl;
      rThis.PrintData(rOStream);

      return rOStream;
    }*/
  ///@} 

}  // namespace Kratos.

#endif // KRATOS_PointCharge2D_CONDITION_H_INCLUDED  defined

pointcharge2D.cpp

/*
==============================================================================
KratosR1ElectrostaticApplication 
A library based on:
Kratos
A General Purpose Software for Multi-Physics Finite Element Analysis
Version 1.0 (Released on march 05, 2007).

Copyright 2007
Pooyan Dadvand, Riccardo Rossi, Javier Mora 
pooyan@cimne.upc.edu 
rrossi@cimne.upc.edu
mora@cimne.upc.edu
- CIMNE (International Center for Numerical Methods in Engineering),
Gran Capita' s/n, 08034 Barcelona, Spain


Permission is hereby granted, free  of charge, to any person obtaining
a  copy  of this  software  and  associated  documentation files  (the
"Software"), to  deal in  the Software without  restriction, including
without limitation  the rights to  use, copy, modify,  merge, publish,
distribute,  sublicense and/or  sell copies  of the  Software,  and to
permit persons to whom the Software  is furnished to do so, subject to
the following condition:

Distribution of this code for  any  commercial purpose  is permissible
ONLY BY DIRECT ARRANGEMENT WITH THE COPYRIGHT OWNERS.

The  above  copyright  notice  and  this permission  notice  shall  be
included in all copies or substantial portions of the Software.

THE  SOFTWARE IS  PROVIDED  "AS  IS", WITHOUT  WARRANTY  OF ANY  KIND,
EXPRESS OR  IMPLIED, INCLUDING  BUT NOT LIMITED  TO THE  WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT  SHALL THE AUTHORS OR COPYRIGHT HOLDERS  BE LIABLE FOR ANY
CLAIM, DAMAGES OR  OTHER LIABILITY, WHETHER IN AN  ACTION OF CONTRACT,
TORT  OR OTHERWISE, ARISING  FROM, OUT  OF OR  IN CONNECTION  WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

==============================================================================
*/
//   
//   Project Name:        Kratos       
//   Last modified by:    $Author: jmora $
//   Date:                $Date: 2009-09-24 16:46:55 $
//   Revision:            $Revision: 1.1 $
//
//


// System includes 


// External includes 


// Project includes 
#include "includes/define.h"

#include "custom_conditions/pointcharge2D.h"
#include "kElectrostatic.h"

#include "utilities/math_utils.h"

namespace Kratos
{
	//************************************************************************************
	//************************************************************************************
	PointCharge2D::PointCharge2D(IndexType NewId, GeometryType::Pointer 
pGeometry)
		: Condition(NewId, pGeometry)
	{		
		//DO NOT ADD DOFS HERE!!!
	}

	//************************************************************************************
	//************************************************************************************
	PointCharge2D::PointCharge2D(IndexType NewId, GeometryType::Pointer pGeometry,  PropertiesType::Pointer pProperties)
		: Condition(NewId, pGeometry, pProperties)
	{
	}

	Condition::Pointer PointCharge2D::Create(IndexType NewId, NodesArrayType 
const& ThisNodes,  PropertiesType::Pointer pProperties) const
	{
		return Condition::Pointer(new PointCharge2D(NewId, 
GetGeometry().Create(ThisNodes), pProperties));
	}

	PointCharge2D::~PointCharge2D()
	{
	}


	//************************************************************************************
	//************************************************************************************
	void PointCharge2D::CalculateRightHandSide(VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo)
	{
		KRATOS_TRY
		if(rRightHandSideVector.size() != 1)
			rRightHandSideVector.resize(1,false);

		double point_source = GetGeometry()[0].FastGetSolutionStepValue(ELECTROSTATIC_POINT_CHARGE);

		rRightHandSideVector[0] = point_source;

that is the following term of the right side vector of the sources:

\mathbf{f}^{(e)}=
    \int_{\Omega^{(e)}} \mathbf{N^T} \rho_v \partial \Omega^{(e)} = Q_p


		KRATOS_CATCH("")
	}

	//************************************************************************************
	//************************************************************************************
	void PointCharge2D::CalculateLocalSystem(MatrixType& rLeftHandSideMatrix, VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo)
	{
		KRATOS_TRY

		if(rLeftHandSideMatrix.size1() != 1)
			rLeftHandSideMatrix.resize(1,1,false);
		noalias(rLeftHandSideMatrix) = ZeroMatrix(1,1);

		if(rRightHandSideVector.size() != 1)
			rRightHandSideVector.resize(1,false);

		double point_source = GetGeometry()[0].FastGetSolutionStepValue(ELECTROSTATIC_POINT_CHARGE);
		rRightHandSideVector[0] = point_source;
		
		KRATOS_CATCH("")
	}


	//************************************************************************************
	//************************************************************************************
	void PointCharge2D::EquationIdVector(EquationIdVectorType& rResult, ProcessInfo& CurrentProcessInfo)
	{
		int number_of_nodes = GetGeometry().PointsNumber();
		unsigned int index;
		unsigned int dim = 1;
		rResult.resize(number_of_nodes*dim);
		for (int i=0;i<number_of_nodes;i++)
		{
			index = i*dim;
			rResult[index] = (GetGeometry()[i].GetDof(ELECTROSTATIC_POTENTIAL).EquationId());
			
		}
	}

	//************************************************************************************
	//************************************************************************************
	  void PointCharge2D::GetDofList(DofsVectorType& ConditionalDofList,ProcessInfo& CurrentProcessInfo)
	{
		unsigned int dim = 1;
		ConditionalDofList.resize(GetGeometry().size()*dim);
		unsigned int index;
		for (unsigned int i=0;i<GetGeometry().size();i++)
		{
			
			index = i*dim;
			ConditionalDofList[index] = (GetGeometry()[i].pGetDof(ELECTROSTATIC_POTENTIAL));
			
		}
	}
} // Namespace Kratos

Field Boundary Conditions

efield2D.h

/*
==============================================================================
KratosR1ElectrostaticApplication 
A library based on:
Kratos
A General Purpose Software for Multi-Physics Finite Element Analysis
Version 1.0 (Released on march 05, 2007).

Copyright 2007
Pooyan Dadvand, Riccardo Rossi, Javier Mora
pooyan@cimne.upc.edu 
rrossi@cimne.upc.edu
mora@cimne.upc.edu
- CIMNE (International Center for Numerical Methods in Engineering),
Gran Capita' s/n, 08034 Barcelona, Spain


Permission is hereby granted, free  of charge, to any person obtaining
a  copy  of this  software  and  associated  documentation files  (the
"Software"), to  deal in  the Software without  restriction, including
without limitation  the rights to  use, copy, modify,  merge, publish,
distribute,  sublicense and/or  sell copies  of the  Software,  and to
permit persons to whom the Software  is furnished to do so, subject to
the following condition:

Distribution of this code for  any  commercial purpose  is permissible
ONLY BY DIRECT ARRANGEMENT WITH THE COPYRIGHT OWNERS.

The  above  copyright  notice  and  this permission  notice  shall  be
included in all copies or substantial portions of the Software.

THE  SOFTWARE IS  PROVIDED  "AS  IS", WITHOUT  WARRANTY  OF ANY  KIND,
EXPRESS OR  IMPLIED, INCLUDING  BUT NOT LIMITED  TO THE  WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT  SHALL THE AUTHORS OR COPYRIGHT HOLDERS  BE LIABLE FOR ANY
CLAIM, DAMAGES OR  OTHER LIABILITY, WHETHER IN AN  ACTION OF CONTRACT,
TORT  OR OTHERWISE, ARISING  FROM, OUT  OF OR  IN CONNECTION  WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

==============================================================================
*/ 
//   
//   Project Name:        Kratos       
//   Last Modified by:    $Author: jmora $
//   Date:                $Date: 2009-09-06 10:30:32 $
//   Revision:            $Revision: 1.2 $
//
//

 
#if !defined(KRATOS_EFIELD2D_CONDITION_H_INCLUDED )
#define  KRATOS_EFIELD2D_CONDITION_H_INCLUDED 



// System includes 


// External includes 
#include "boost/smart_ptr.hpp"


// Project includes
#include "includes/define.h"
#include "includes/condition.h"
#include "includes/ublas_interface.h"
#include "includes/variables.h"


namespace Kratos
{

  ///@name Kratos Globals
  ///@{ 
  
  ///@} 
  ///@name Type Definitions
  ///@{ 
  
  ///@} 
  ///@name  Enum's
  ///@{
      
  ///@}
  ///@name  Functions 
  ///@{
      
  ///@}
  ///@name Kratos Classes
  ///@{
  
  /// Short class definition.
  /** Detail class definition.
  */
  class Efield2D
	  : public Condition
    {
    public:
      ///@name Type Definitions
      ///@{
      
      /// Counted pointer of Efield2D
      KRATOS_CLASS_POINTER_DEFINITION(Efield2D);
 
      ///@}
      ///@name Life Cycle 
      ///@{ 
      
      /// Default constructor.
	  Efield2D(IndexType NewId, GeometryType::Pointer pGeometry);
      Efield2D(IndexType NewId, GeometryType::Pointer pGeometry,  PropertiesType::Pointer pProperties);

      /// Destructor.
      virtual ~Efield2D();
      

      ///@}
      ///@name Operators 
      ///@{
      
      
      ///@}
      ///@name Operations
      ///@{

      Condition::Pointer Create(IndexType NewId, NodesArrayType const& ThisNodes,  PropertiesType::Pointer pProperties) const;

      void CalculateLocalSystem(MatrixType& rLeftHandSideMatrix, VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo);
      
      void CalculateRightHandSide(VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo);
      //virtual void CalculateLeftHandSide(MatrixType& rLeftHandSideMatrix, ProcessInfo& rCurrentProcessInfo);
      
      void EquationIdVector(EquationIdVectorType& rResult, ProcessInfo& rCurrentProcessInfo);

	  void GetDofList(DofsVectorType& ConditionalDofList,ProcessInfo& CurrentProcessInfo);

      ///@}
      ///@name Access
      ///@{ 
      
      
      ///@}
      ///@name Inquiry
      ///@{
      
      
      ///@}      
      ///@name Input and output
      ///@{

      /// Turn back information as a string.
//      virtual String Info() const;
      
      /// Print information about this object.
//      virtual void PrintInfo(std::ostream& rOStream) const;

      /// Print object's data.
//      virtual void PrintData(std::ostream& rOStream) const;
      
            
      ///@}      
      ///@name Friends
      ///@{

            
      ///@}
      
    protected:
      ///@name Protected static Member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Protected member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Protected Operators
      ///@{ 
        
        
      ///@} 
      ///@name Protected Operations
      ///@{ 
        
        
      ///@} 
      ///@name Protected  Access 
      ///@{ 
        
        
      ///@}      
      ///@name Protected Inquiry 
      ///@{ 
        
        
      ///@}    
      ///@name Protected LifeCycle 
      ///@{ 
      
            
      ///@}
      
    private:
      ///@name Static Member Variables 
      ///@{ 
        
        
      ///@} 
      ///@name Member Variables 
      ///@{ 
		
        
        
      ///@} 
      ///@name Private Operators
      ///@{ 
		void CalculateAll(MatrixType& rLeftHandSideMatrix, VectorType& rRightHandSideVector, 
										ProcessInfo& rCurrentProcessInfo,
										bool CalculateStiffnessMatrixFlag,
										bool CalculateResidualVectorFlag);
        
      
      ///@} 
      ///@name Private Operations
      ///@{ 
        
        
      ///@} 
      ///@name Private  Access 
      ///@{ 
        
        
      ///@}    
      ///@name Private Inquiry 
      ///@{ 
        
        
      ///@}    
      ///@name Un accessible methods 
      ///@{ 
      
      /// Assignment operator.
      //Efield2D& operator=(const Efield2D& rOther);

      /// Copy constructor.
      //Efield2D(const Efield2D& rOther);

        
      ///@}    
        
    }; // Class Efield2D 

  ///@} 
  
  ///@name Type Definitions       
  ///@{ 
  
  
  ///@} 
  ///@name Input and output 
  ///@{ 
        
 
  /// input stream function
/*  inline std::istream& operator >> (std::istream& rIStream, 
				    Efield2D& rThis);
*/
  /// output stream function
/*  inline std::ostream& operator << (std::ostream& rOStream, 
				    const Efield2D& rThis)
    {
      rThis.PrintInfo(rOStream);
      rOStream << std::endl;
      rThis.PrintData(rOStream);

      return rOStream;
    }*/
  ///@} 

}  // namespace Kratos.

#endif // KRATOS_EFIELD2D_CONDITION_H_INCLUDED   defined 





efield2D.cpp

/*
==============================================================================
KratosR1ElectrostaticApplication 
A library based on:
Kratos
A General Purpose Software for Multi-Physics Finite Element Analysis
Version 1.0 (Released on march 05, 2007).

Copyright 2007
Pooyan Dadvand, Riccardo Rossi,Javier Mora
pooyan@cimne.upc.edu 
rrossi@cimne.upc.edu
mora@cimne.upc.edu
- CIMNE (International Center for Numerical Methods in Engineering),
Gran Capita' s/n, 08034 Barcelona, Spain


Permission is hereby granted, free  of charge, to any person obtaining
a  copy  of this  software  and  associated  documentation files  (the
"Software"), to  deal in  the Software without  restriction, including
without limitation  the rights to  use, copy, modify,  merge, publish,
distribute,  sublicense and/or  sell copies  of the  Software,  and to
permit persons to whom the Software  is furnished to do so, subject to
the following condition:

Distribution of this code for  any  commercial purpose  is permissible
ONLY BY DIRECT ARRANGEMENT WITH THE COPYRIGHT OWNERS.

The  above  copyright  notice  and  this permission  notice  shall  be
included in all copies or substantial portions of the Software.

THE  SOFTWARE IS  PROVIDED  "AS  IS", WITHOUT  WARRANTY  OF ANY  KIND,
EXPRESS OR  IMPLIED, INCLUDING  BUT NOT LIMITED  TO THE  WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT  SHALL THE AUTHORS OR COPYRIGHT HOLDERS  BE LIABLE FOR ANY
CLAIM, DAMAGES OR  OTHER LIABILITY, WHETHER IN AN  ACTION OF CONTRACT,
TORT  OR OTHERWISE, ARISING  FROM, OUT  OF OR  IN CONNECTION  WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

==============================================================================
*/ 
//   
//   Project Name:        Kratos       
//   Last modified by:    $Author: jmora $
//   Date:                $Date: 2009-09-06 10:30:32 $
//   Revision:            $Revision: 1.4 $
//
// 


// System includes 


// External includes 


// Project includes 
#include "includes/define.h"
#include "custom_conditions/efield2D.h"
#include "utilities/math_utils.h"
#include "kElectrostatic.h"


namespace Kratos
{
	//************************************************************************************
	//************************************************************************************
	Efield2D::Efield2D(IndexType NewId, GeometryType::Pointer pGeometry)
		: Condition(NewId, pGeometry)
	{		
		//DO NOT ADD DOFS HERE!!!
	}

	//************************************************************************************
	//************************************************************************************
	Efield2D::Efield2D(IndexType NewId, GeometryType::Pointer pGeometry,  PropertiesType::Pointer pProperties)
		: Condition(NewId, pGeometry, pProperties)
	{
	}

	Condition::Pointer Efield2D::Create(IndexType NewId, NodesArrayType const& ThisNodes,  PropertiesType::Pointer pProperties) const
	{
		return Condition::Pointer(new Efield2D(NewId, GetGeometry().Create(ThisNodes), pProperties));
	}

	Efield2D::~Efield2D()
	{
	}


	//************************************************************************************
	//************************************************************************************
	void Efield2D::CalculateRightHandSide(VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo)
	{
		//calculation flags
		bool CalculateStiffnessMatrixFlag = false;
		bool CalculateResidualVectorFlag = true;
		MatrixType temp = Matrix();

		CalculateAll(temp, rRightHandSideVector, rCurrentProcessInfo, CalculateStiffnessMatrixFlag, CalculateResidualVectorFlag);
	}

	//************************************************************************************
	//************************************************************************************
	void Efield2D::CalculateLocalSystem(MatrixType& rLeftHandSideMatrix, VectorType& rRightHandSideVector, ProcessInfo& rCurrentProcessInfo)
	{
		//calculation flags
		bool CalculateStiffnessMatrixFlag = true;
		bool CalculateResidualVectorFlag = true;
		
		CalculateAll(rLeftHandSideMatrix, rRightHandSideVector, rCurrentProcessInfo, CalculateStiffnessMatrixFlag, CalculateResidualVectorFlag);
	}

	//************************************************************************************
	//************************************************************************************
	void Efield2D::CalculateAll(MatrixType& rLeftHandSideMatrix, VectorType& rRightHandSideVector, 
										ProcessInfo& rCurrentProcessInfo,
										bool CalculateStiffnessMatrixFlag,
										bool CalculateResidualVectorFlag)
	{
		KRATOS_TRY

		unsigned int number_of_nodes = GetGeometry().size();

		//resizing as needed the LHS
		unsigned int MatSize=number_of_nodes;

		//calculate lenght
		double x21 = GetGeometry()[1].X() - GetGeometry()[0].X();
		double y21 = GetGeometry()[1].Y() - GetGeometry()[0].Y();
		double length = x21*x21 + y21*y21;
		length = sqrt(length);

		double infinit_coefficient = (this)->GetValue(INFINIT_COEFFICIENT);
		double convection_coefficient = pow(length,infinit_coefficient);
		convection_coefficient = infinit_coefficient/convection_coefficient;

		const double& V0 = GetGeometry()[0].FastGetSolutionStepValue(ELECTROSTATIC_POTENTIAL);
		const double& V1 = GetGeometry()[1].FastGetSolutionStepValue(ELECTROSTATIC_POTENTIAL);

		array_1d<double,3>& ConditionalField = GetValue(ELECTRIC_DISPLACEMENT_FIELD);

		const double& c0 = ConditionalField[0];
		const double& c1 = ConditionalField[1];
		const double& c2 = ConditionalField[2];



		if (CalculateStiffnessMatrixFlag == true) //calculation of the matrix is required
		{
			if(rLeftHandSideMatrix.size1() != MatSize )
				rLeftHandSideMatrix.resize(MatSize,MatSize,false);
			noalias(rLeftHandSideMatrix) = ZeroMatrix(MatSize,MatSize);	
			
			rLeftHandSideMatrix(0,0) = convection_coefficient * 0.5 * length;
			rLeftHandSideMatrix(1,1) = convection_coefficient * 0.5 * length; 
		}


		//resizing as needed the RHS
		if (CalculateResidualVectorFlag == true) //calculation of the matrix is required
		{
			if(rRightHandSideVector.size() != MatSize )
				rRightHandSideVector.resize(MatSize,false);
			
			rRightHandSideVector[0] =  c0  -  convection_coefficient *  V0 ;
			rRightHandSideVector[1] =  c1  -  convection_coefficient *  V1 ;

			rRightHandSideVector *= 0.5*length;

That is:

\mathbf{K}^{(e)}=
    \oint_{\Gamma_{\infty}^{(e)}} \mathbf{N^T} \alpha \mathbf{N} \Gamma_{\infty}^{(e)}
\mathbf{f}^{(e)}=
    \oint_{\Gamma_q^{(e)}} \mathbf{N^T} \bar D_n \partial \Gamma_q^{(e)}



		}

		KRATOS_CATCH("")
	}



	//************************************************************************************
	//************************************************************************************
	void Efield2D::EquationIdVector(EquationIdVectorType& rResult, ProcessInfo& CurrentProcessInfo)
	{
		unsigned int number_of_nodes = GetGeometry().PointsNumber();
		if(rResult.size() != number_of_nodes)
			rResult.resize(number_of_nodes,false);
		for (unsigned int i=0;i<number_of_nodes;i++)
		{
			rResult[i] = (GetGeometry()[i].GetDof(ELECTROSTATIC_POTENTIAL)).EquationId();
		}
	}

	//************************************************************************************
	//************************************************************************************
	  void Efield2D::GetDofList(DofsVectorType& ConditionalDofList,ProcessInfo& CurrentProcessInfo)
	{
		ConditionalDofList.resize(GetGeometry().size());
		for (unsigned int i=0;i<GetGeometry().size();i++)
		{
			ConditionalDofList[i] = (GetGeometry()[i].pGetDof(ELECTROSTATIC_POTENTIAL));
		}
	}
	  
} // Namespace Kratos
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