365 lines
17 KiB
Fortran
365 lines
17 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Interpolation data used by the FEM solver
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!--------------------------------------------------------------------------------------------------
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module FEM_quadrature
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use prec
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implicit none
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private
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integer, parameter :: &
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maxOrder = 5 !< current max interpolation set at cubic (intended to be arbitrary)
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real(pReal), dimension(2,3), parameter :: &
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triangle = reshape([-1.0_pReal, -1.0_pReal, &
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1.0_pReal, -1.0_pReal, &
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-1.0_pReal, 1.0_pReal], shape=[2,3])
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real(pReal), dimension(3,4), parameter :: &
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tetrahedron = reshape([-1.0_pReal, -1.0_pReal, -1.0_pReal, &
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1.0_pReal, -1.0_pReal, -1.0_pReal, &
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-1.0_pReal, 1.0_pReal, -1.0_pReal, &
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-1.0_pReal, -1.0_pReal, 1.0_pReal], shape=[3,4])
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integer, dimension(2:3,maxOrder), public, protected :: &
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FEM_nQuadrature !< number of quadrature points for a given spatial dimension(2-3) and interpolation order(1-maxOrder)
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type(group_float), dimension(2:3,maxOrder), public, protected :: &
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FEM_quadrature_weights, & !< quadrature weights for each quadrature rule
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FEM_quadrature_points !< quadrature point coordinates (in simplical system) for each quadrature rule
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public :: &
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FEM_quadrature_init
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief initializes FEM interpolation data
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!--------------------------------------------------------------------------------------------------
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subroutine FEM_quadrature_init
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print'(/,a)', ' <<<+- FEM_quadrature init -+>>>'; flush(6)
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!--------------------------------------------------------------------------------------------------
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! 2D linear
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FEM_nQuadrature(2,1) = 1
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allocate(FEM_quadrature_weights(2,1)%p(1))
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FEM_quadrature_weights(2,1)%p(1) = 1.0_pReal
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allocate(FEM_quadrature_points (2,1)%p(2))
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FEM_quadrature_points (2,1)%p(1:2) = permutationStar3([1.0_pReal/3.0_pReal])
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!--------------------------------------------------------------------------------------------------
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! 2D quadratic
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FEM_nQuadrature(2,2) = 3
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allocate(FEM_quadrature_weights(2,2)%p(3))
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FEM_quadrature_weights(2,2)%p(1:3) = 1.0_pReal/3.0_pReal
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allocate(FEM_quadrature_points (2,2)%p(6))
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FEM_quadrature_points (2,2)%p(1:6) = permutationStar21([1.0_pReal/6.0_pReal])
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!--------------------------------------------------------------------------------------------------
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! 2D cubic
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FEM_nQuadrature(2,3) = 6
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allocate(FEM_quadrature_weights(2,3)%p(6))
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FEM_quadrature_weights(2,3)%p(1:3) = 0.22338158967801146570_pReal
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FEM_quadrature_weights(2,3)%p(4:6) = 0.10995174365532186764_pReal
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allocate(FEM_quadrature_points (2,3)%p(12))
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FEM_quadrature_points (2,3)%p(1:6) = permutationStar21([0.44594849091596488632_pReal])
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FEM_quadrature_points (2,3)%p(7:12)= permutationStar21([0.091576213509770743460_pReal])
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!--------------------------------------------------------------------------------------------------
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! 2D quartic
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FEM_nQuadrature(2,4) = 12
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allocate(FEM_quadrature_weights(2,4)%p(12))
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FEM_quadrature_weights(2,4)%p(1:3) = 0.11678627572638_pReal
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FEM_quadrature_weights(2,4)%p(4:6) = 0.05084490637021_pReal
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FEM_quadrature_weights(2,4)%p(7:12) = 0.08285107561837_pReal
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allocate(FEM_quadrature_points (2,4)%p(24))
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FEM_quadrature_points (2,4)%p(1:6) = permutationStar21([0.24928674517091_pReal])
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FEM_quadrature_points (2,4)%p(7:12) = permutationStar21([0.06308901449150_pReal])
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FEM_quadrature_points (2,4)%p(13:24)= permutationStar111([0.31035245103378_pReal, 0.63650249912140_pReal])
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!--------------------------------------------------------------------------------------------------
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! 2D quintic
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FEM_nQuadrature(2,5) = 16
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allocate(FEM_quadrature_weights(2,5)%p(16))
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FEM_quadrature_weights(2,5)%p(1 ) = 0.14431560767779_pReal
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FEM_quadrature_weights(2,5)%p(2:4) = 0.09509163426728_pReal
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FEM_quadrature_weights(2,5)%p(5:7) = 0.10321737053472_pReal
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FEM_quadrature_weights(2,5)%p(8:10) = 0.03245849762320_pReal
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FEM_quadrature_weights(2,5)%p(11:16)= 0.02723031417443_pReal
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allocate(FEM_quadrature_points (2,5)%p(32))
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FEM_quadrature_points (2,5)%p(1:2) = permutationStar3([0.33333333333333_pReal])
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FEM_quadrature_points (2,5)%p(3:8) = permutationStar21([0.45929258829272_pReal])
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FEM_quadrature_points (2,5)%p(9:14) = permutationStar21([0.17056930775176_pReal])
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FEM_quadrature_points (2,5)%p(15:20)= permutationStar21([0.05054722831703_pReal])
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FEM_quadrature_points (2,5)%p(21:32)= permutationStar111([0.26311282963464_pReal, 0.72849239295540_pReal])
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!--------------------------------------------------------------------------------------------------
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! 3D linear
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FEM_nQuadrature(3,1) = 1
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allocate(FEM_quadrature_weights(3,1)%p(1))
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FEM_quadrature_weights(3,1)%p(1) = 1.0_pReal
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allocate(FEM_quadrature_points (3,1)%p(3))
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FEM_quadrature_points (3,1)%p(1:3)= permutationStar4([0.25_pReal])
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!--------------------------------------------------------------------------------------------------
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! 3D quadratic
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FEM_nQuadrature(3,2) = 4
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allocate(FEM_quadrature_weights(3,2)%p(4))
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FEM_quadrature_weights(3,2)%p(1:4) = 0.25_pReal
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allocate(FEM_quadrature_points (3,2)%p(12))
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FEM_quadrature_points (3,2)%p(1:12)= permutationStar31([0.13819660112501051518_pReal])
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!--------------------------------------------------------------------------------------------------
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! 3D cubic
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FEM_nQuadrature(3,3) = 14
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allocate(FEM_quadrature_weights(3,3)%p(14))
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FEM_quadrature_weights(3,3)%p(5:8) = 0.11268792571801585080_pReal
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FEM_quadrature_weights(3,3)%p(1:4) = 0.073493043116361949544_pReal
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FEM_quadrature_weights(3,3)%p(9:14) = 0.042546020777081466438_pReal
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allocate(FEM_quadrature_points (3,3)%p(42))
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FEM_quadrature_points (3,3)%p(1:12) = permutationStar31([0.092735250310891226402_pReal])
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FEM_quadrature_points (3,3)%p(13:24)= permutationStar31([0.31088591926330060980_pReal])
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FEM_quadrature_points (3,3)%p(25:42)= permutationStar22([0.045503704125649649492_pReal])
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!--------------------------------------------------------------------------------------------------
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! 3D quartic
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FEM_nQuadrature(3,4) = 35
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allocate(FEM_quadrature_weights(3,4)%p(35))
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FEM_quadrature_weights(3,4)%p(1:4) = 0.0021900463965388_pReal
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FEM_quadrature_weights(3,4)%p(5:16) = 0.0143395670177665_pReal
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FEM_quadrature_weights(3,4)%p(17:22) = 0.0250305395686746_pReal
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FEM_quadrature_weights(3,4)%p(23:34) = 0.0479839333057554_pReal
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FEM_quadrature_weights(3,4)%p(35) = 0.0931745731195340_pReal
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allocate(FEM_quadrature_points (3,4)%p(105))
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FEM_quadrature_points (3,4)%p(1:12) = permutationStar31([0.0267367755543735_pReal])
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FEM_quadrature_points (3,4)%p(13:48) = permutationStar211([0.0391022406356488_pReal, 0.7477598884818090_pReal])
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FEM_quadrature_points (3,4)%p(49:66) = permutationStar22([0.4547545999844830_pReal])
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FEM_quadrature_points (3,4)%p(67:102) = permutationStar211([0.2232010379623150_pReal, 0.0504792790607720_pReal])
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FEM_quadrature_points (3,4)%p(103:105)= permutationStar4([0.25_pReal])
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!--------------------------------------------------------------------------------------------------
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! 3D quintic
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FEM_nQuadrature(3,5) = 56
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allocate(FEM_quadrature_weights(3,5)%p(56))
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FEM_quadrature_weights(3,5)%p(1:4) = 0.0010373112336140_pReal
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FEM_quadrature_weights(3,5)%p(5:16) = 0.0096016645399480_pReal
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FEM_quadrature_weights(3,5)%p(17:28) = 0.0164493976798232_pReal
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FEM_quadrature_weights(3,5)%p(29:40) = 0.0153747766513310_pReal
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FEM_quadrature_weights(3,5)%p(41:52) = 0.0293520118375230_pReal
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FEM_quadrature_weights(3,5)%p(53:56) = 0.0366291366405108_pReal
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allocate(FEM_quadrature_points (3,5)%p(168))
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FEM_quadrature_points (3,5)%p(1:12) = permutationStar31([0.0149520651530592_pReal])
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FEM_quadrature_points (3,5)%p(13:48) = permutationStar211([0.0340960211962615_pReal, 0.1518319491659370_pReal])
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FEM_quadrature_points (3,5)%p(49:84) = permutationStar211([0.0462051504150017_pReal, 0.3549340560639790_pReal])
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FEM_quadrature_points (3,5)%p(85:120) = permutationStar211([0.2281904610687610_pReal, 0.0055147549744775_pReal])
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FEM_quadrature_points (3,5)%p(121:156)= permutationStar211([0.3523052600879940_pReal, 0.0992057202494530_pReal])
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FEM_quadrature_points (3,5)%p(157:168)= permutationStar31([0.1344783347929940_pReal])
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end subroutine FEM_quadrature_init
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!--------------------------------------------------------------------------------------------------
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!> @brief star 3 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar3(point) result(qPt)
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real(pReal), dimension(2) :: qPt
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real(pReal), dimension(1), intent(in) :: point
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real(pReal), dimension(3,1) :: temp
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temp(:,1) = [point(1), point(1), point(1)]
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qPt = reshape(matmul(triangle, temp),[2])
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end function permutationStar3
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!--------------------------------------------------------------------------------------------------
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!> @brief star 21 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar21(point) result(qPt)
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real(pReal), dimension(6) :: qPt
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real(pReal), dimension(1), intent(in) :: point
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real(pReal), dimension(3,3) :: temp
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temp(:,1) = [point(1), point(1), 1.0_pReal - 2.0_pReal*point(1)]
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temp(:,2) = [point(1), 1.0_pReal - 2.0_pReal*point(1), point(1)]
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temp(:,3) = [1.0_pReal - 2.0_pReal*point(1), point(1), point(1)]
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qPt = reshape(matmul(triangle, temp),[6])
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end function permutationStar21
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!--------------------------------------------------------------------------------------------------
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!> @brief star 111 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar111(point) result(qPt)
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real(pReal), dimension(12) :: qPt
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real(pReal), dimension(2), intent(in) :: point
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real(pReal), dimension(3,6) :: temp
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temp(:,1) = [point(1), point(2), 1.0_pReal - point(1) - point(2)]
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temp(:,2) = [point(1), 1.0_pReal - point(1) - point(2), point(2)]
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temp(:,4) = [point(2), 1.0_pReal - point(1) - point(2), point(1)]
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temp(:,5) = [1.0_pReal - point(1) - point(2), point(2), point(1)]
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temp(:,6) = [1.0_pReal - point(1) - point(2), point(1), point(2)]
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qPt = reshape(matmul(triangle, temp),[12])
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end function permutationStar111
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!--------------------------------------------------------------------------------------------------
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!> @brief star 4 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar4(point) result(qPt)
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real(pReal), dimension(3) :: qPt
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real(pReal), dimension(1), intent(in) :: point
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real(pReal), dimension(4,1) :: temp
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temp(:,1) = [point(1), point(1), point(1), point(1)]
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qPt = reshape(matmul(tetrahedron, temp),[3])
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end function permutationStar4
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!--------------------------------------------------------------------------------------------------
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!> @brief star 31 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar31(point) result(qPt)
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real(pReal), dimension(12) :: qPt
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real(pReal), dimension(1), intent(in) :: point
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real(pReal), dimension(4,4) :: temp
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temp(:,1) = [point(1), point(1), point(1), 1.0_pReal - 3.0_pReal*point(1)]
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temp(:,2) = [point(1), point(1), 1.0_pReal - 3.0_pReal*point(1), point(1)]
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temp(:,3) = [point(1), 1.0_pReal - 3.0_pReal*point(1), point(1), point(1)]
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temp(:,4) = [1.0_pReal - 3.0_pReal*point(1), point(1), point(1), point(1)]
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qPt = reshape(matmul(tetrahedron, temp),[12])
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end function permutationStar31
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!--------------------------------------------------------------------------------------------------
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!> @brief star 22 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar22(point) result(qPt)
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real(pReal), dimension(18) :: qPt
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real(pReal), dimension(1), intent(in) :: point
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real(pReal), dimension(4,6) :: temp
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temp(:,1) = [point(1), point(1), 0.5_pReal - point(1), 0.5_pReal - point(1)]
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temp(:,2) = [point(1), 0.5_pReal - point(1), point(1), 0.5_pReal - point(1)]
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temp(:,3) = [0.5_pReal - point(1), point(1), point(1), 0.5_pReal - point(1)]
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temp(:,4) = [0.5_pReal - point(1), point(1), 0.5_pReal - point(1), point(1)]
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temp(:,5) = [0.5_pReal - point(1), 0.5_pReal - point(1), point(1), point(1)]
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temp(:,6) = [point(1), 0.5_pReal - point(1), 0.5_pReal - point(1), point(1)]
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qPt = reshape(matmul(tetrahedron, temp),[18])
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end function permutationStar22
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!--------------------------------------------------------------------------------------------------
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!> @brief star 211 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar211(point) result(qPt)
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real(pReal), dimension(36) :: qPt
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real(pReal), dimension(2), intent(in) :: point
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real(pReal), dimension(4,12) :: temp
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temp(:,1 ) = [point(1), point(1), point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
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temp(:,2 ) = [point(1), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(2)]
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temp(:,3 ) = [point(1), point(2), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
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temp(:,4 ) = [point(1), point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1)]
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temp(:,5 ) = [point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(2)]
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temp(:,6 ) = [point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(2), point(1)]
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temp(:,7 ) = [point(2), point(1), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2)]
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temp(:,8 ) = [point(2), point(1), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1)]
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temp(:,9 ) = [point(2), 1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(1)]
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temp(:,10) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(1), point(2)]
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temp(:,11) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(1), point(2), point(1)]
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temp(:,12) = [1.0_pReal - 2.0_pReal*point(1) - point(2), point(2), point(1), point(1)]
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qPt = reshape(matmul(tetrahedron, temp),[36])
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end function permutationStar211
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!--------------------------------------------------------------------------------------------------
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!> @brief star 1111 permutation of input
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!--------------------------------------------------------------------------------------------------
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pure function permutationStar1111(point) result(qPt)
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real(pReal), dimension(72) :: qPt
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real(pReal), dimension(3), intent(in) :: point
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real(pReal), dimension(4,24) :: temp
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temp(:,1 ) = [point(1), point(2), point(3), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,2 ) = [point(1), point(2), 1.0_pReal - point(1) - point(2)- point(3), point(3)]
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temp(:,3 ) = [point(1), point(3), point(2), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,4 ) = [point(1), point(3), 1.0_pReal - point(1) - point(2)- point(3), point(2)]
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temp(:,5 ) = [point(1), 1.0_pReal - point(1) - point(2)- point(3), point(2), point(3)]
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temp(:,6 ) = [point(1), 1.0_pReal - point(1) - point(2)- point(3), point(3), point(2)]
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temp(:,7 ) = [point(2), point(1), point(3), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,8 ) = [point(2), point(1), 1.0_pReal - point(1) - point(2)- point(3), point(3)]
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temp(:,9 ) = [point(2), point(3), point(1), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,10) = [point(2), point(3), 1.0_pReal - point(1) - point(2)- point(3), point(1)]
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temp(:,11) = [point(2), 1.0_pReal - point(1) - point(2)- point(3), point(1), point(3)]
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temp(:,12) = [point(2), 1.0_pReal - point(1) - point(2)- point(3), point(3), point(1)]
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temp(:,13) = [point(3), point(1), point(2), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,14) = [point(3), point(1), 1.0_pReal - point(1) - point(2)- point(3), point(2)]
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temp(:,15) = [point(3), point(2), point(1), 1.0_pReal - point(1) - point(2)- point(3)]
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temp(:,16) = [point(3), point(2), 1.0_pReal - point(1) - point(2)- point(3), point(1)]
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temp(:,17) = [point(3), 1.0_pReal - point(1) - point(2)- point(3), point(1), point(2)]
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temp(:,18) = [point(3), 1.0_pReal - point(1) - point(2)- point(3), point(2), point(1)]
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temp(:,19) = [1.0_pReal - point(1) - point(2)- point(3), point(1), point(2), point(3)]
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temp(:,20) = [1.0_pReal - point(1) - point(2)- point(3), point(1), point(3), point(2)]
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temp(:,21) = [1.0_pReal - point(1) - point(2)- point(3), point(2), point(1), point(3)]
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temp(:,22) = [1.0_pReal - point(1) - point(2)- point(3), point(2), point(3), point(1)]
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temp(:,23) = [1.0_pReal - point(1) - point(2)- point(3), point(3), point(1), point(2)]
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temp(:,24) = [1.0_pReal - point(1) - point(2)- point(3), point(3), point(2), point(1)]
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qPt = reshape(matmul(tetrahedron, temp),[72])
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end function permutationStar1111
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end module FEM_quadrature
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