getfem_derivatives.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2002-2020 Yves Renard, Julien Pommier
 
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/**@file getfem_derivatives.h
   @author Yves Renard <Yves.Renard@insa-lyon.fr>,
   @author Julien Pommier <Julien.Pommier@insa-toulouse.fr>
   @date June 17, 2002.
   @brief Compute the gradient of a field on a getfem::mesh_fem.
*/
#ifndef GETFEM_DERIVATIVES_H__
#define GETFEM_DERIVATIVES_H__
 
#include "getfem_mesh_fem.h"
#include "getfem_interpolation.h"
#include "gmm/gmm_dense_qr.h"
 
namespace getfem
{
  /** Compute the gradient of a field on a getfem::mesh_fem.
      @param mf the source mesh_fem.
      @param U the source field.
      @param mf_target should be a lagrange discontinous element
      @param V contains on output the gradient of U, evaluated on mf_target.
 
      mf_target may have the same Qdim than mf, or it may
      be a scalar mesh_fem, in which case the derivatives are stored in
      the order: DxUx,DyUx,DzUx,DxUy,DyUy,...
 
      in any case, the size of V should be
      N*(mf.qdim)*(mf_target.nbdof/mf_target.qdim)
      elements (this is not checked by the function!)
  */
  template<class VECT1, class VECT2>
  void compute_gradient(const mesh_fem &mf, const mesh_fem &mf_target,
                        const VECT1 &UU, VECT2 &VV) {
    typedef typename gmm::linalg_traits<VECT1>::value_type T;
 
    size_type N = mf.linked_mesh().dim();
    size_type qdim = mf.get_qdim();
    size_type target_qdim = mf_target.get_qdim();
    size_type qqdimt = qdim * N / target_qdim;
    std::vector<T> U(mf.nb_basic_dof());
    std::vector<T> V(mf_target.nb_basic_dof() * qqdimt);
 
    mf.extend_vector(UU, U);
 
    GMM_ASSERT1(&mf.linked_mesh() == &mf_target.linked_mesh(),
                "meshes are different.");
    GMM_ASSERT1(target_qdim == qdim*N || target_qdim == qdim
                || target_qdim == 1, "invalid Qdim for gradient mesh_fem");
    
    base_matrix G;
    std::vector<T> coeff;
 
    bgeot::pgeotrans_precomp pgp = NULL;
    pfem_precomp pfp = NULL;
    pfem pf, pf_target, pf_old = NULL, pf_targetold = NULL;
    bgeot::pgeometric_trans pgt;
 
    for (dal::bv_visitor cv(mf_target.convex_index()); !cv.finished(); ++cv) {
      pf = mf.fem_of_element(cv);
      pf_target = mf_target.fem_of_element(cv);
      if (!pf) continue;
      
      GMM_ASSERT1(!(pf_target->need_G()) && pf_target->is_lagrange(),
                  "finite element target not convenient");
      
      bgeot::vectors_to_base_matrix(G, mf.linked_mesh().points_of_convex(cv));
 
      pgt = mf.linked_mesh().trans_of_convex(cv);
      if (pf_targetold != pf_target) {
        pgp = bgeot::geotrans_precomp(pgt, pf_target->node_tab(cv), pf_target);
      }
      pf_targetold = pf_target;
 
      if (pf_old != pf) {
        pfp = fem_precomp(pf, pf_target->node_tab(cv), pf_target);
      }
      pf_old = pf;
 
      gmm::dense_matrix<T> grad(N,qdim), gradt(qdim,N);
      fem_interpolation_context ctx(pgp, pfp, 0, G, cv, short_type(-1));
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
      // gmm::resize(coeff, mf.nb_basic_dof_of_element(cv));
      // gmm::copy(gmm::sub_vector
      //          (U, gmm::sub_index(mf.ind_basic_dof_of_element(cv))), coeff);
      for (size_type j = 0; j < pf_target->nb_dof(cv); ++j) {
        size_type dof_t =
          mf_target.ind_basic_dof_of_element(cv)[j*target_qdim] * qqdimt;
        ctx.set_ii(j);
        pf->interpolation_grad(ctx, coeff, gradt, dim_type(qdim));
        gmm::copy(gmm::transposed(gradt),grad);
        std::copy(grad.begin(), grad.end(), V.begin() + dof_t);
      }
    }
 
    mf_target.reduce_vector(V, VV);
  }
 
  /** Compute the hessian of a field on a getfem::mesh_fem.
      @param mf the source mesh_fem.
      @param U the source field.
      @param mf_target should be a lagrange discontinous element
      does not work with vectorial elements. ... to be done ...
      @param V contains on output the gradient of U, evaluated on mf_target.
 
      mf_target may have the same Qdim than mf, or it may
      be a scalar mesh_fem, in which case the derivatives are stored in
      the order: DxxUx,DxyUx, DyxUx, DyyUx, ...
 
      in any case, the size of V should be
      N*N*(mf.qdim)*(mf_target.nbdof/mf_target.qdim)
      elements (this is not checked by the function!)
  */
  template<class VECT1, class VECT2>
  void compute_hessian(const mesh_fem &mf, const mesh_fem &mf_target,
                        const VECT1 &UU, VECT2 &VV) {
    typedef typename gmm::linalg_traits<VECT1>::value_type T;
 
    size_type N = mf.linked_mesh().dim();
    size_type qdim = mf.get_qdim();
    size_type target_qdim = mf_target.get_qdim();
    size_type qqdimt = qdim * N * N / target_qdim;
    std::vector<T> U(mf.nb_basic_dof());
    std::vector<T> V(mf_target.nb_basic_dof() * qqdimt);
 
    mf.extend_vector(UU, U);
 
    GMM_ASSERT1(&mf.linked_mesh() == &mf_target.linked_mesh(),
                "meshes are different.");
    GMM_ASSERT1(target_qdim == qdim || target_qdim == 1,
                "invalid Qdim for gradient mesh_fem");
    base_matrix G;
    std::vector<T> coeff;
 
    bgeot::pgeotrans_precomp pgp = NULL;
    pfem_precomp pfp = NULL;
    pfem pf, pf_target, pf_old = NULL, pf_targetold = NULL;
    bgeot::pgeometric_trans pgt;
 
    for (dal::bv_visitor cv(mf_target.convex_index()); !cv.finished(); ++cv) {
      pf = mf.fem_of_element(cv);
      pf_target = mf_target.fem_of_element(cv);
      GMM_ASSERT1(!(pf_target->need_G()) && pf_target->is_lagrange(),
                  "finite element target not convenient");
      
      bgeot::vectors_to_base_matrix(G, mf.linked_mesh().points_of_convex(cv));
 
      pgt = mf.linked_mesh().trans_of_convex(cv);
      if (pf_targetold != pf_target) {
        pgp = bgeot::geotrans_precomp(pgt, pf_target->node_tab(cv), pf_target);
      }
      pf_targetold = pf_target;
 
      if (pf_old != pf) {
        pfp = fem_precomp(pf, pf_target->node_tab(cv), pf_target);
      }
      pf_old = pf;
 
      gmm::dense_matrix<T> hess(N*N,qdim), hesst(qdim,N*N);
      fem_interpolation_context ctx(pgp, pfp, 0, G, cv, short_type(-1));
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);      
      // gmm::resize(coeff, mf.nb_basic_dof_of_element(cv));
      // gmm::copy(gmm::sub_vector
      //          (U, gmm::sub_index(mf.ind_basic_dof_of_element(cv))), coeff);
      for (size_type j = 0; j < pf_target->nb_dof(cv); ++j) {
        size_type dof_t
          = mf_target.ind_basic_dof_of_element(cv)[j*target_qdim] * qqdimt;
        ctx.set_ii(j);
        pf->interpolation_hess(ctx, coeff, hesst, dim_type(qdim));
        gmm::copy(gmm::transposed(hesst), hess);
        std::copy(hess.begin(), hess.end(), V.begin() + dof_t);
      }
    }
 
    mf_target.reduce_vector(V, VV);
  }
 
  /**Compute the Von-Mises stress of a field (only valid for
     linearized elasticity in 3D)
  */
  template <typename VEC1, typename VEC2>
  void interpolation_von_mises(const getfem::mesh_fem &mf_u, 
                               const getfem::mesh_fem &mf_vm, 
                               const VEC1 &U, VEC2 &VM,
                               scalar_type mu=1) {
    dal::bit_vector bv; bv.add(0, mf_vm.nb_dof());
    interpolation_von_mises(mf_u, mf_vm, U, VM, bv, mu);
  }
 
  template <typename VEC1, typename VEC2>
  void interpolation_von_mises(const getfem::mesh_fem &mf_u, 
                               const getfem::mesh_fem &mf_vm, 
                               const VEC1 &U, VEC2 &VM,
                               const dal::bit_vector &mf_vm_dofs,
                               scalar_type mu=1) {
 
    assert(mf_vm.get_qdim() == 1); 
    unsigned N = mf_u.linked_mesh().dim(); assert(N == mf_u.get_qdim());
    std::vector<scalar_type> DU(mf_vm.nb_dof() * N * N);
    
    getfem::compute_gradient(mf_u, mf_vm, U, DU);
    
    GMM_ASSERT1(!mf_vm.is_reduced(), "Sorry, to be done");
 
    scalar_type vm_min = 0., vm_max = 0.;
    for (dal::bv_visitor i(mf_vm_dofs); !i.finished(); ++i) {
      VM[i] = 0;
      scalar_type sdiag = 0.;
      for (unsigned j=0; j < N; ++j) {
        sdiag += DU[i*N*N + j*N + j];
        for (unsigned k=0; k < N; ++k) {
          scalar_type e = .5*(DU[i*N*N + j*N + k] + DU[i*N*N + k*N + j]);
          VM[i] += e*e; 
        }
      }
      VM[i] -= 1./N * sdiag * sdiag;
      vm_min = (i == 0 ? VM[0] : std::min(vm_min, VM[i]));
      vm_max = (i == 0 ? VM[0] : std::max(vm_max, VM[i]));
    }
    cout << "Von Mises : min=" << 4*mu*mu*vm_min << ", max="
         << 4*mu*mu*vm_max << "\n";
    gmm::scale(VM, 4*mu*mu);
  }
  
 
  /** Compute the Von-Mises stress of a field (valid for
      linearized elasticity in 2D and 3D)
  */
  template <typename VEC1, typename VEC2, typename VEC3>
  void interpolation_von_mises_or_tresca(const getfem::mesh_fem &mf_u, 
                                         const getfem::mesh_fem &mf_vm, 
                                         const VEC1 &U, VEC2 &VM,
                                         const getfem::mesh_fem &mf_lambda,
                                         const VEC3 &lambda, 
                                         const getfem::mesh_fem &mf_mu,
                                         const VEC3 &mu,
                                         bool tresca) {
    assert(mf_vm.get_qdim() == 1);
    typedef typename gmm::linalg_traits<VEC1>::value_type T;
    size_type N = mf_u.get_qdim();
    std::vector<T> GRAD(mf_vm.nb_dof()*N*N), 
      LAMBDA(mf_vm.nb_dof()), MU(mf_vm.nb_dof());
    base_matrix sigma(N,N);
    base_vector eig(N);
    if (tresca) interpolation(mf_lambda, mf_vm, lambda, LAMBDA);
    interpolation(mf_mu, mf_vm, mu, MU);
    compute_gradient(mf_u, mf_vm, U, GRAD);
 
    GMM_ASSERT1(!mf_vm.is_reduced(), "Sorry, to be done");
    GMM_ASSERT1(N>=2 && N<=3, "Only for 2D and 3D");
    
    for (size_type i = 0; i < mf_vm.nb_dof(); ++i) {
      scalar_type trE = 0, diag = 0;
      for (unsigned j = 0; j < N; ++j)
        trE += GRAD[i*N*N + j*N + j];
      if (tresca)
        diag = LAMBDA[i]*trE; // calculation of sigma
      else
        diag = (-2./3.)*MU[i]*trE;  // for the calculation of deviator(sigma)
      for (unsigned j = 0; j < N; ++j) {
        for (unsigned k = 0; k < N; ++k) {
          scalar_type eps = /* 0.5* */ (GRAD[i*N*N + j*N + k] + 
                                        GRAD[i*N*N + k*N + j]);
          sigma(j,k) = /* 2* */ MU[i]*eps;
        }
        sigma(j,j) += diag;
      }
      if (!tresca) {
        /* von mises: norm(deviator(sigma)) */
        //gmm::add(gmm::scaled(Id, -gmm::mat_trace(sigma) / N), sigma); 
        if (N==3)
          VM[i] = sqrt((3./2.)*gmm::mat_euclidean_norm_sqr(sigma));
        else // for plane strains ( s_33 = -diag )
          VM[i] = sqrt((3./2.)*(gmm::mat_euclidean_norm_sqr(sigma) + diag*diag));
      } else {
        /* else compute the tresca criterion */
        gmm::symmetric_qr_algorithm(sigma, eig);
        std::sort(eig.begin(), eig.end());
        VM[i] = eig.back() - eig.front();
      }
    }
  }
}
 
#endif