sll_m_poisson_2d_fem_sps_weak_form.F90

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module sll_m_poisson_2d_fem_sps_weak_form
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
   use sll_m_working_precision, only: f64
 
   use sll_m_ellipt_2d_fem_sps_weak_form, only: sll_c_ellipt_2d_fem_sps_weak_form
 
   implicit none
 
   public :: sll_t_poisson_2d_fem_sps_weak_form
 
   private
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
   ! Working precision
   integer, parameter :: wp = f64
 
   type, extends(sll_c_ellipt_2d_fem_sps_weak_form) :: sll_t_poisson_2d_fem_sps_weak_form
 
   contains
 
      procedure :: element_mat => s_poisson_2d_fem_sps_weak_form__element_mat
      procedure :: element_rhs => s_poisson_2d_fem_sps_weak_form__element_rhs
 
   end type sll_t_poisson_2d_fem_sps_weak_form
 
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
contains
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
   ! Compute elementary contribution to stiffness and mass matrices
   subroutine s_poisson_2d_fem_sps_weak_form__element_mat( &
      self, &
      test_values_and_derivs_eta1, &
      test_values_and_derivs_eta2, &
      trial_values_and_derivs_eta1, &
      trial_values_and_derivs_eta2, &
      int_volume, &
      inv_metric, &
      Aij, &
      Mij)
      class(sll_t_poisson_2d_fem_sps_weak_form), intent(in) :: self
      real(wp), intent(in) :: test_values_and_derivs_eta1(:, :)
      real(wp), intent(in) :: test_values_and_derivs_eta2(:, :)
      real(wp), intent(in) :: trial_values_and_derivs_eta1(:, :)
      real(wp), intent(in) :: trial_values_and_derivs_eta2(:, :)
      real(wp), intent(in) :: int_volume(:, :)
      real(wp), intent(in) :: inv_metric(:, :, :, :)
      real(wp), intent(out) :: Aij
      real(wp), intent(out) :: Mij
 
      integer :: q1, q2, Nq1, Nq2
 
      real(wp) :: v(2), w(2), t(2)
 
      ! Extract number of quadrature points
      nq1 = size(test_values_and_derivs_eta1, 1)
      nq2 = size(test_values_and_derivs_eta2, 1)
 
      aij = 0.0_wp
      mij = 0.0_wp
 
      ! Quadrature
      do q2 = 1, nq2
         do q1 = 1, nq1
 
            ! 2D gradient in logical test space
            v = [test_values_and_derivs_eta1(q1, 2)*test_values_and_derivs_eta2(q2, 1), &
                 test_values_and_derivs_eta1(q1, 1)*test_values_and_derivs_eta2(q2, 2)]
 
            ! 2D gradient in logical trial space
            w = [trial_values_and_derivs_eta1(q1, 2)*trial_values_and_derivs_eta2(q2, 1), &
                 trial_values_and_derivs_eta1(q1, 1)*trial_values_and_derivs_eta2(q2, 2)]
 
            t = matmul(inv_metric(q1, q2, :, :), w)
 
            ! Elementary contribution to stiffness matrix
            aij = aij + dot_product(v, t)*int_volume(q1, q2)
 
            ! Elementary contribution to mass matrix
            mij = mij + &
                  test_values_and_derivs_eta1(q1, 1)*test_values_and_derivs_eta2(q2, 1)* &
                  trial_values_and_derivs_eta1(q1, 1)*trial_values_and_derivs_eta2(q2, 1)* &
                  int_volume(q1, q2)
 
         end do
      end do
 
   end subroutine s_poisson_2d_fem_sps_weak_form__element_mat
 
   ! Compute elementary contribution to right hand side
   subroutine s_poisson_2d_fem_sps_weak_form__element_rhs( &
      self, &
      test_values_and_derivs_eta1, &
      test_values_and_derivs_eta2, &
      data_2d_rhs, &
      int_volume, &
      bi)
      class(sll_t_poisson_2d_fem_sps_weak_form), intent(in) :: self
      real(wp), intent(in) :: test_values_and_derivs_eta1(:, :)
      real(wp), intent(in) :: test_values_and_derivs_eta2(:, :)
      real(wp), intent(in) :: data_2d_rhs(:, :)
      real(wp), intent(in) :: int_volume(:, :)
      real(wp), intent(out) :: bi
 
      integer :: q1, q2, Nq1, Nq2
 
      ! Extract number of quadrature points
      nq1 = size(test_values_and_derivs_eta1, 1)
      nq2 = size(test_values_and_derivs_eta2, 1)
 
      bi = 0.0_wp
 
      ! Quadrature
      do q2 = 1, nq2
         do q1 = 1, nq1
 
            ! Elementary contribution to mass matrix
            bi = bi + &
                 test_values_and_derivs_eta1(q1, 1)*test_values_and_derivs_eta2(q2, 1)* &
                 data_2d_rhs(q1, q2)*int_volume(q1, q2)
 
         end do
      end do
 
   end subroutine s_poisson_2d_fem_sps_weak_form__element_rhs
 
end module sll_m_poisson_2d_fem_sps_weak_form