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DAMASK_EICMD
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DAMASK_EICMD/src/FEM_zoo.f90

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!--------------------------------------------------------------------------------------------------
!> @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, group_float
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(group_float), 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
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