mtop_integrators.hpp

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// Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.

#ifndef MTOPINTEGRATORS_HPP
#define MTOPINTEGRATORS_HPP

#include "mfem.hpp"
#include "paramnonlinearform.hpp"

#include <map>

namespace mfem
{

/// Base class for representing function at integration points.
class BaseQFunction
{
public:
   virtual ~BaseQFunction() {}

   /// Returns a user defined string identifying the function.
   virtual std::string GetType()=0;

   // Returns the energy at an integration point.
   virtual
   double QEnergy(ElementTransformation &T, const IntegrationPoint &ip,
                  mfem::Vector &dd, mfem::Vector &uu)
   {
      return 0.0;
   }

   // Returns the residual at an integration point.
   virtual
   void QResidual(ElementTransformation &T, const IntegrationPoint &ip,
                  mfem::Vector &dd, mfem::Vector &uu, mfem::Vector &rr)=0;

   /// Returns the gradient of the residual at a integration point.
   virtual
   void QGradResidual(ElementTransformation &T, const IntegrationPoint &ip,
                      mfem::Vector &dd, mfem::Vector &uu, mfem::DenseMatrix &hh)=0;

   /// Returns the gradient of the residual with respect to the design
   /// parameters, multiplied by the adjoint.
   virtual
   void AQResidual(ElementTransformation &T, const IntegrationPoint &ip,
                   mfem::Vector &dd, mfem::Vector &uu,
                   mfem::Vector &aa, mfem::Vector &rr)=0;

};

/* QLinearDiffusion implements methods for computing the energy, the residual,
 * gradient of the residual and the product of the adjoint fields with the
 * derivative of the residual with respect to the parameters. All computations
 * are performed at a integration point. Therefore the vectors (vv,uu,aa,rr ..)
 * hold the fields' values and the fields' derivatives at the integration
 * point. For example for a single scalar parametric field representing the
 * density in topology optimization the vector dd will have size one and the
 * element will be the density at the integration point. The map between state
 * and parameter is not fixed and depends on the implementation of the QFunction
 * class. */
class QLinearDiffusion:public BaseQFunction
{
public:
   QLinearDiffusion(mfem::Coefficient& diffco, mfem::Coefficient& hsrco,
                    double pp=1.0, double minrho=1e-7, double betac=4.0, double etac=0.5):
      diff(diffco),load(hsrco), powerc(pp), rhomin(minrho), beta(betac), eta(etac)
   {

   }

   virtual std::string GetType() override
   {
      return "QLinearDiffusion";
   }

   virtual
   double QEnergy(ElementTransformation &T, const IntegrationPoint &ip,
                  Vector &dd, Vector &uu) override
   {
      // dd[0] - density
      // uu[0] - grad_x
      // uu[1] - grad_y
      // uu[2] - grad_z
      // uu[3] - temperature/scalar field

      double di=diff.Eval(T,ip);
      double ll=load.Eval(T,ip);
      // Computes the physical density using projection.
      double rz=0.5+0.5*std::tanh(beta*(dd[0]-eta)); //projection
      // Computes the diffusion coefficient at the integration point.
      double fd=di*(std::pow(rz,powerc)+rhomin);
      // Computes the sum of the energy and the product of the temperature and
      // the external input at the integration point.
      double rez = 0.5*(uu[0]*uu[0]+uu[1]*uu[1]+uu[2]*uu[2])*fd-uu[3]*ll;
      return rez;
   }

   /// Returns the derivative of QEnergy with respect to the state vector uu.
   virtual
   void QResidual(ElementTransformation &T, const IntegrationPoint &ip,
                  Vector &dd, Vector &uu, Vector &rr) override
   {
      double di=diff.Eval(T,ip);
      double ll=load.Eval(T,ip);
      double rz=0.5+0.5*std::tanh(beta*(dd[0]-eta));
      double fd=di*(std::pow(rz,powerc)+rhomin);

      rr[0]=uu[0]*fd;
      rr[1]=uu[1]*fd;
      rr[2]=uu[2]*fd;
      rr[3]=-ll;
   }


   // Returns the derivative, with respect to the density, of the product of
   // the adjoint field with the residual at the integration point ip.
   virtual
   void AQResidual(ElementTransformation &T, const IntegrationPoint &ip,
                   Vector &dd, Vector &uu, Vector &aa, Vector &rr) override
   {
      double di=diff.Eval(T,ip);
      double tt=std::tanh(beta*(dd[0]-eta));
      double rz=0.5+0.5*tt;
      double fd=di*powerc*std::pow(rz,powerc-1.0)*0.5*(1.0-tt*tt)*beta;

      rr[0] = -(aa[0]*uu[0]+aa[1]*uu[1]+aa[2]*uu[2])*fd;
   }

   // Returns the gradient of the residual with respect to the state vector at
   // the integration point ip.
   virtual
   void QGradResidual(ElementTransformation &T, const IntegrationPoint &ip,
                      Vector &dd, Vector &uu, DenseMatrix &hh) override
   {
      double di=diff.Eval(T,ip);
      double tt=std::tanh(beta*(dd[0]-eta));
      double rz=0.5+0.5*tt;
      double fd=di*(std::pow(rz,powerc)+rhomin);
      hh=0.0;

      hh(0,0)=fd;
      hh(1,1)=fd;
      hh(2,2)=fd;
      hh(3,3)=0.0;
   }

private:
   mfem::Coefficient& diff; //diffusion coefficient
   mfem::Coefficient& load; //load coefficient
   double powerc; //penalization coefficient
   double rhomin; //lower bound for the density
   double beta;   //controls the sharpness of the projection
   double eta;    //projection threshold for tanh
};

/// Provides implementation of an integrator for linear diffusion with
/// parametrization provided by a density field. The setup is standard for
/// topology optimization problems.
class ParametricLinearDiffusion: public ParametricBNLFormIntegrator
{
public:
   ParametricLinearDiffusion(BaseQFunction& qfunm): qfun(qfunm)
   {

   }

   /// Computes the local energy.
   virtual
   double GetElementEnergy(const Array<const FiniteElement *> &el,
                           const Array<const FiniteElement *> &pel,
                           ElementTransformation &Tr,
                           const Array<const Vector *> &elfun,
                           const Array<const Vector *> &pelfun) override;

   /// Computes the element's residual.
   virtual
   void AssembleElementVector(const Array<const FiniteElement *> &el,
                              const Array<const FiniteElement *> &pel,
                              ElementTransformation &Tr,
                              const Array<const Vector *> &elfun,
                              const Array<const Vector *> &pelfun,
                              const Array<Vector *> &elvec) override;

   /// Computes the stiffness/tangent matrix.
   virtual
   void AssembleElementGrad(const Array<const FiniteElement *> &el,
                            const Array<const FiniteElement *> &pel,
                            ElementTransformation &Tr,
                            const Array<const Vector *> &elfun,
                            const Array<const Vector *> &pelfun,
                            const Array2D<DenseMatrix *> &elmats) override;

   /// Computes the product of the adjoint solution and the derivative of the
   /// residual with respect to the parametric fields.
   virtual
   void AssemblePrmElementVector(const Array<const FiniteElement *> &el,
                                 const Array<const FiniteElement *> &pel,
                                 ElementTransformation &Tr,
                                 const Array<const Vector *> &elfun,
                                 const Array<const Vector *> &alfun,
                                 const Array<const Vector *> &pelfun,
                                 const Array<Vector *> &elvec) override;
private:
   BaseQFunction& qfun;
};


/// Computes an example of nonlinear objective
/// \f$\int \rm{field}*\rm{field}*\rm{weight})\rm{d}\Omega_e\f$.
class DiffusionObjIntegrator:public BlockNonlinearFormIntegrator
{
public:

   DiffusionObjIntegrator()
   {

   }

   /// Returns the objective contribution at element level.
   virtual
   double GetElementEnergy(const Array<const FiniteElement *> &el,
                           ElementTransformation &Tr,
                           const Array<const Vector *> &elfun) override;

   /// Returns the gradient of the objective contribution at element level.
   virtual
   void AssembleElementVector(const Array<const FiniteElement *> &el,
                              ElementTransformation &Tr,
                              const Array<const Vector *> &elfun,
                              const Array<Vector *> &elvec) override;
};

}

#endif