DAMASK_EICMD/src/FEM_zoo.f90

!--------------------------------------------------------------------------------------------------
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @brief Interpolation data used by the FEM solver
!--------------------------------------------------------------------------------------------------
module FEM_Zoo     
 use prec, only: pReal, pInt, p_vec

 implicit none
 private
 integer(pInt), parameter, public:: &
   maxOrder = 5                                                                            !< current max interpolation set at cubic (intended to be arbitrary)
 real(pReal),   dimension(2,3),       private, protected :: &
   triangle    = reshape([-1.0_pReal, -1.0_pReal, &
                           1.0_pReal, -1.0_pReal, &
                          -1.0_pReal,  1.0_pReal], shape=[2,3])
 real(pReal),   dimension(3,4),       private, protected :: &
   tetrahedron = reshape([-1.0_pReal, -1.0_pReal, -1.0_pReal, &
                           1.0_pReal, -1.0_pReal, -1.0_pReal, &
                          -1.0_pReal,  1.0_pReal, -1.0_pReal, &
                          -1.0_pReal, -1.0_pReal,  1.0_pReal], shape=[3,4])
 integer(pInt), dimension(3,maxOrder), public, protected :: &
   FEM_Zoo_nQuadrature                                                                       !< number of quadrature points for a given spatial dimension(1-3) and interpolation order(1-maxOrder)
 type(p_vec),   dimension(3,maxOrder), public, protected :: &
   FEM_Zoo_QuadratureWeights, &                                                              !< quadrature weights for each quadrature rule 
   FEM_Zoo_QuadraturePoints                                                                  !< quadrature point coordinates (in simplical system) for each quadrature rule

 public :: &
   FEM_Zoo_init

contains


!--------------------------------------------------------------------------------------------------
!> @brief initializes FEM interpolation data
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_init
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
 use, intrinsic :: iso_fortran_env, only: &
   compiler_version, &
   compiler_options
#endif
 use IO, only: &
   IO_timeStamp
   
 implicit none
  
 write(6,'(/,a)')   ' <<<+-  FEM_Zoo init  -+>>>'
 write(6,'(a)')     ' $Id: FEM_Zoo.f90 4354 2015-08-04 15:04:53Z MPIE\p.shanthraj $'
 write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"

!--------------------------------------------------------------------------------------------------
! 2D linear
 FEM_Zoo_nQuadrature(2,1) = 1
 allocate(FEM_Zoo_QuadratureWeights(2,1)%p(1))
 allocate(FEM_Zoo_QuadraturePoints (2,1)%p(2))
 FEM_Zoo_QuadratureWeights(2,1)%p(1) = 1.0_pReal
 call FEM_Zoo_permutationStar3([1.0_pReal/3.0_pReal], &
                              FEM_Zoo_QuadraturePoints(2,1)%p(1:2))
 
!--------------------------------------------------------------------------------------------------
! 2D quadratic
 FEM_Zoo_nQuadrature(2,2) = 3
 allocate(FEM_Zoo_QuadratureWeights(2,2)%p(3))
 allocate(FEM_Zoo_QuadraturePoints (2,2)%p(6))
 FEM_Zoo_QuadratureWeights(2,2)%p(1:3) = 1.0_pReal/3.0_pReal
 call FEM_Zoo_permutationStar21([1.0_pReal/6.0_pReal], &
                               FEM_Zoo_QuadraturePoints(2,2)%p(1:6))
 
!--------------------------------------------------------------------------------------------------
! 2D cubic
 FEM_Zoo_nQuadrature(2,3) = 6
 allocate(FEM_Zoo_QuadratureWeights(2,3)%p(6 ))
 allocate(FEM_Zoo_QuadraturePoints (2,3)%p(12))
 FEM_Zoo_QuadratureWeights(2,3)%p(1:3) = 0.22338158967801146570_pReal
 call FEM_Zoo_permutationStar21([0.44594849091596488632_pReal], &
                               FEM_Zoo_QuadraturePoints(2,3)%p(1:6))
 FEM_Zoo_QuadratureWeights(2,3)%p(4:6) = 0.10995174365532186764_pReal
 call FEM_Zoo_permutationStar21([0.091576213509770743460_pReal], &
                               FEM_Zoo_QuadraturePoints(2,3)%p(7:12))

!--------------------------------------------------------------------------------------------------
! 2D quartic
 FEM_Zoo_nQuadrature(2,4) = 12
 allocate(FEM_Zoo_QuadratureWeights(2,4)%p(12))
 allocate(FEM_Zoo_QuadraturePoints (2,4)%p(24))
 FEM_Zoo_QuadratureWeights(2,4)%p(1:3) = 0.11678627572638_pReal
 call FEM_Zoo_permutationStar21([0.24928674517091_pReal], &
                               FEM_Zoo_QuadraturePoints(2,4)%p(1:6))
 FEM_Zoo_QuadratureWeights(2,4)%p(4:6) = 0.05084490637021_pReal
 call FEM_Zoo_permutationStar21([0.06308901449150_pReal], &
                               FEM_Zoo_QuadraturePoints(2,4)%p(7:12))
 FEM_Zoo_QuadratureWeights(2,4)%p(7:12) = 0.08285107561837_pReal
 call FEM_Zoo_permutationStar111([0.31035245103378_pReal, 0.63650249912140_pReal], &
                                FEM_Zoo_QuadraturePoints(2,4)%p(13:24))

!--------------------------------------------------------------------------------------------------
! 2D order 5
 FEM_Zoo_nQuadrature(2,5) = 16
 allocate(FEM_Zoo_QuadratureWeights(2,5)%p(16))
 allocate(FEM_Zoo_QuadraturePoints (2,5)%p(32))
 FEM_Zoo_QuadratureWeights(2,5)%p(1  ) = 0.14431560767779_pReal
 call FEM_Zoo_permutationStar3([0.33333333333333_pReal], &
                              FEM_Zoo_QuadraturePoints(2,5)%p(1:2))
 FEM_Zoo_QuadratureWeights(2,5)%p(2:4) = 0.09509163426728_pReal
 call FEM_Zoo_permutationStar21([0.45929258829272_pReal], &
                               FEM_Zoo_QuadraturePoints(2,5)%p(3:8))
 FEM_Zoo_QuadratureWeights(2,5)%p(5:7) = 0.10321737053472_pReal
 call FEM_Zoo_permutationStar21([0.17056930775176_pReal], &
                               FEM_Zoo_QuadraturePoints(2,5)%p(9:14))
 FEM_Zoo_QuadratureWeights(2,5)%p(8:10) = 0.03245849762320_pReal
 call FEM_Zoo_permutationStar21([0.05054722831703_pReal], &
                               FEM_Zoo_QuadraturePoints(2,5)%p(15:20))
 FEM_Zoo_QuadratureWeights(2,5)%p(11:16) = 0.02723031417443_pReal
 call FEM_Zoo_permutationStar111([0.26311282963464_pReal, 0.72849239295540_pReal], &
                                FEM_Zoo_QuadraturePoints(2,5)%p(21:32))

!--------------------------------------------------------------------------------------------------
! 3D linear
 FEM_Zoo_nQuadrature(3,1) = 1
 allocate(FEM_Zoo_QuadratureWeights(3,1)%p(1))
 allocate(FEM_Zoo_QuadraturePoints (3,1)%p(3))
 FEM_Zoo_QuadratureWeights(3,1)%p(1) = 1.0_pReal
 call FEM_Zoo_permutationStar4([0.25_pReal], &
                              FEM_Zoo_QuadraturePoints(3,1)%p(1:3))
 
!--------------------------------------------------------------------------------------------------
! 3D quadratic
 FEM_Zoo_nQuadrature(3,2) = 4
 allocate(FEM_Zoo_QuadratureWeights(3,2)%p(4 ))
 allocate(FEM_Zoo_QuadraturePoints (3,2)%p(12))
 FEM_Zoo_QuadratureWeights(3,2)%p(1:4) = 0.25_pReal
 call FEM_Zoo_permutationStar31([0.13819660112501051518_pReal], &
                               FEM_Zoo_QuadraturePoints(3,2)%p(1:12))
 
!--------------------------------------------------------------------------------------------------
! 3D cubic
 FEM_Zoo_nQuadrature(3,3) = 14
 allocate(FEM_Zoo_QuadratureWeights(3,3)%p(14))
 allocate(FEM_Zoo_QuadraturePoints (3,3)%p(42))
 FEM_Zoo_QuadratureWeights(3,3)%p(1:4) = 0.073493043116361949544_pReal
 call FEM_Zoo_permutationStar31([0.092735250310891226402_pReal], &
                               FEM_Zoo_QuadraturePoints(3,3)%p(1:12))
 FEM_Zoo_QuadratureWeights(3,3)%p(5:8) = 0.11268792571801585080_pReal
 call FEM_Zoo_permutationStar31([0.31088591926330060980_pReal], &
                               FEM_Zoo_QuadraturePoints(3,3)%p(13:24))
 FEM_Zoo_QuadratureWeights(3,3)%p(9:14) = 0.042546020777081466438_pReal
 call FEM_Zoo_permutationStar22([0.045503704125649649492_pReal], &
                               FEM_Zoo_QuadraturePoints(3,3)%p(25:42))

!--------------------------------------------------------------------------------------------------
! 3D quartic
 FEM_Zoo_nQuadrature(3,4) = 35
 allocate(FEM_Zoo_QuadratureWeights(3,4)%p(35))
 allocate(FEM_Zoo_QuadraturePoints (3,4)%p(105))
 FEM_Zoo_QuadratureWeights(3,4)%p(1:4) = 0.0021900463965388_pReal
 call FEM_Zoo_permutationStar31([0.0267367755543735_pReal], &
                               FEM_Zoo_QuadraturePoints(3,4)%p(1:12))
 FEM_Zoo_QuadratureWeights(3,4)%p(5:16) = 0.0143395670177665_pReal
 call FEM_Zoo_permutationStar211([0.0391022406356488_pReal, 0.7477598884818090_pReal], &
                                FEM_Zoo_QuadraturePoints(3,4)%p(13:48))
 FEM_Zoo_QuadratureWeights(3,4)%p(17:22) = 0.0250305395686746_pReal
 call FEM_Zoo_permutationStar22([0.4547545999844830_pReal], &
                               FEM_Zoo_QuadraturePoints(3,4)%p(49:66))
 FEM_Zoo_QuadratureWeights(3,4)%p(23:34) = 0.0479839333057554_pReal
 call FEM_Zoo_permutationStar211([0.2232010379623150_pReal, 0.0504792790607720_pReal], &
                                FEM_Zoo_QuadraturePoints(3,4)%p(67:102))
 FEM_Zoo_QuadratureWeights(3,4)%p(35) = 0.0931745731195340_pReal
 call FEM_Zoo_permutationStar4([0.25_pReal], &
                              FEM_Zoo_QuadraturePoints(3,4)%p(103:105))
!--------------------------------------------------------------------------------------------------
! 3D quintic
 FEM_Zoo_nQuadrature(3,5) = 56
 allocate(FEM_Zoo_QuadratureWeights(3,5)%p(56))
 allocate(FEM_Zoo_QuadraturePoints (3,5)%p(168))
 FEM_Zoo_QuadratureWeights(3,5)%p(1:4) = 0.0010373112336140_pReal
 call FEM_Zoo_permutationStar31([0.0149520651530592_pReal], &
                               FEM_Zoo_QuadraturePoints(3,5)%p(1:12))
 FEM_Zoo_QuadratureWeights(3,5)%p(5:16) = 0.0096016645399480_pReal
 call FEM_Zoo_permutationStar211([0.0340960211962615_pReal, 0.1518319491659370_pReal], &
                                FEM_Zoo_QuadraturePoints(3,5)%p(13:48))
 FEM_Zoo_QuadratureWeights(3,5)%p(17:28) = 0.0164493976798232_pReal
 call FEM_Zoo_permutationStar211([0.0462051504150017_pReal, 0.3549340560639790_pReal], &
                                FEM_Zoo_QuadraturePoints(3,5)%p(49:84))
 FEM_Zoo_QuadratureWeights(3,5)%p(29:40) = 0.0153747766513310_pReal
 call FEM_Zoo_permutationStar211([0.2281904610687610_pReal, 0.0055147549744775_pReal], &
                                FEM_Zoo_QuadraturePoints(3,5)%p(85:120))
 FEM_Zoo_QuadratureWeights(3,5)%p(41:52) = 0.0293520118375230_pReal
 call FEM_Zoo_permutationStar211([0.3523052600879940_pReal, 0.0992057202494530_pReal], &
                                FEM_Zoo_QuadraturePoints(3,5)%p(121:156))
 FEM_Zoo_QuadratureWeights(3,5)%p(53:56) = 0.0366291366405108_pReal
 call FEM_Zoo_permutationStar31([0.1344783347929940_pReal], &
                               FEM_Zoo_QuadraturePoints(3,5)%p(157:168))

end subroutine FEM_Zoo_init

!--------------------------------------------------------------------------------------------------
!> @brief star 3 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar3(point,qPt)

 implicit none
 real(pReal)                  :: point(1), qPt(2,1), temp(3,1)
 
 temp(:,1) = [point(1), point(1), point(1)]
 qPt = matmul(triangle, temp)
  
end subroutine FEM_Zoo_permutationStar3

!--------------------------------------------------------------------------------------------------
!> @brief star 21 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar21(point,qPt)

 implicit none
 real(pReal)                  :: point(1), qPt(2,3), temp(3,3)
 
 temp(:,1) = [point(1), point(1), 1.0_pReal - 2.0_pReal*point(1)]
 temp(:,2) = [point(1), 1.0_pReal - 2.0_pReal*point(1), point(1)]
 temp(:,3) = [1.0_pReal - 2.0_pReal*point(1), point(1), point(1)]
 qPt = matmul(triangle, temp)
  
end subroutine FEM_Zoo_permutationStar21

!--------------------------------------------------------------------------------------------------
!> @brief star 111 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar111(point,qPt)

 implicit none
 real(pReal)                  :: point(2), qPt(2,6), temp(3,6)
 
 temp(:,1) = [point(1), point(2), 1.0_pReal - point(1) - point(2)]
 temp(:,2) = [point(1), 1.0_pReal - point(1) - point(2), point(2)]
 temp(:,4) = [point(2), 1.0_pReal - point(1) - point(2), point(1)]
 temp(:,5) = [1.0_pReal - point(1) - point(2), point(2), point(1)]
 temp(:,6) = [1.0_pReal - point(1) - point(2), point(1), point(2)]
 qPt = matmul(triangle, temp)
  
end subroutine FEM_Zoo_permutationStar111

!--------------------------------------------------------------------------------------------------
!> @brief star 4 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar4(point,qPt)

 implicit none
 real(pReal)                  :: point(1), qPt(3,1), temp(4,1)
 
 temp(:,1) = [point(1), point(1), point(1), point(1)]
 qPt = matmul(tetrahedron, temp)
  
end subroutine FEM_Zoo_permutationStar4

!--------------------------------------------------------------------------------------------------
!> @brief star 31 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar31(point,qPt)

 implicit none
 real(pReal)                  :: point(1), qPt(3,4), temp(4,4)
 
 temp(:,1) = [point(1), point(1), point(1), 1.0_pReal - 3.0_pReal*point(1)]
 temp(:,2) = [point(1), point(1), 1.0_pReal - 3.0_pReal*point(1), point(1)]
 temp(:,3) = [point(1), 1.0_pReal - 3.0_pReal*point(1), point(1), point(1)]
 temp(:,4) = [1.0_pReal - 3.0_pReal*point(1), point(1), point(1), point(1)]
 qPt = matmul(tetrahedron, temp)
  
end subroutine FEM_Zoo_permutationStar31

!--------------------------------------------------------------------------------------------------
!> @brief star 22 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar22(point,qPt)

 implicit none
 real(pReal)                  :: point(1), qPt(3,6), temp(4,6)
 
 temp(:,1) = [point(1), point(1), 0.5_pReal - point(1), 0.5_pReal - point(1)]
 temp(:,2) = [point(1), 0.5_pReal - point(1), point(1), 0.5_pReal - point(1)]
 temp(:,3) = [0.5_pReal - point(1), point(1), point(1), 0.5_pReal - point(1)]
 temp(:,4) = [0.5_pReal - point(1), point(1), 0.5_pReal - point(1), point(1)]
 temp(:,5) = [0.5_pReal - point(1), 0.5_pReal - point(1), point(1), point(1)]
 temp(:,6) = [point(1), 0.5_pReal - point(1), 0.5_pReal - point(1), point(1)]
 qPt = matmul(tetrahedron, temp)
  
end subroutine FEM_Zoo_permutationStar22

!--------------------------------------------------------------------------------------------------
!> @brief star 211 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar211(point,qPt)

 implicit none
 real(pReal)                  :: point(2), qPt(3,12), temp(4,12)
 
 temp(:,1 ) = [point(1), point(1), point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
 temp(:,2 ) = [point(1), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(2)]
 temp(:,3 ) = [point(1), point(2), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
 temp(:,4 ) = [point(1), point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1)]
 temp(:,5 ) = [point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(2)]
 temp(:,6 ) = [point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(2), point(1)]
 temp(:,7 ) = [point(2), point(1), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
 temp(:,8 ) = [point(2), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1)]
 temp(:,9 ) = [point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(1)]
 temp(:,10) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(1), point(2)]
 temp(:,11) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(2), point(1)]
 temp(:,12) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(2), point(1), point(1)]
 qPt = matmul(tetrahedron, temp)
  
end subroutine FEM_Zoo_permutationStar211

!--------------------------------------------------------------------------------------------------
!> @brief star 1111 permutation of input 
!--------------------------------------------------------------------------------------------------
subroutine FEM_Zoo_permutationStar1111(point,qPt)

 implicit none
 real(pReal)                  :: point(3), qPt(3,24), temp(4,24)
 
 temp(:,1 ) = [point(1), point(2), point(3), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,2 ) = [point(1), point(2), 1.0_pReal - point(1) - point(2)- point(3), point(3)]
 temp(:,3 ) = [point(1), point(3), point(2), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,4 ) = [point(1), point(3), 1.0_pReal - point(1) - point(2)- point(3), point(2)]
 temp(:,5 ) = [point(1), 1.0_pReal - point(1) - point(2)- point(3), point(2), point(3)]
 temp(:,6 ) = [point(1), 1.0_pReal - point(1) - point(2)- point(3), point(3), point(2)]
 temp(:,7 ) = [point(2), point(1), point(3), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,8 ) = [point(2), point(1), 1.0_pReal - point(1) - point(2)- point(3), point(3)]
 temp(:,9 ) = [point(2), point(3), point(1), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,10) = [point(2), point(3), 1.0_pReal - point(1) - point(2)- point(3), point(1)]
 temp(:,11) = [point(2), 1.0_pReal - point(1) - point(2)- point(3), point(1), point(3)]
 temp(:,12) = [point(2), 1.0_pReal - point(1) - point(2)- point(3), point(3), point(1)]
 temp(:,13) = [point(3), point(1), point(2), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,14) = [point(3), point(1), 1.0_pReal - point(1) - point(2)- point(3), point(2)]
 temp(:,15) = [point(3), point(2), point(1), 1.0_pReal - point(1) - point(2)- point(3)]
 temp(:,16) = [point(3), point(2), 1.0_pReal - point(1) - point(2)- point(3), point(1)]
 temp(:,17) = [point(3), 1.0_pReal - point(1) - point(2)- point(3), point(1), point(2)]
 temp(:,18) = [point(3), 1.0_pReal - point(1) - point(2)- point(3), point(2), point(1)]
 temp(:,19) = [1.0_pReal - point(1) - point(2)- point(3), point(1), point(2), point(3)]
 temp(:,20) = [1.0_pReal - point(1) - point(2)- point(3), point(1), point(3), point(2)]
 temp(:,21) = [1.0_pReal - point(1) - point(2)- point(3), point(2), point(1), point(3)]
 temp(:,22) = [1.0_pReal - point(1) - point(2)- point(3), point(2), point(3), point(1)]
 temp(:,23) = [1.0_pReal - point(1) - point(2)- point(3), point(3), point(1), point(2)]
 temp(:,24) = [1.0_pReal - point(1) - point(2)- point(3), point(3), point(2), point(1)]
 qPt = matmul(tetrahedron, temp)
  
end subroutine FEM_Zoo_permutationStar1111


end module FEM_Zoo