added new set of accelerated spectral methods based on derivative approximations. use spectral_derivative to set the kind of derivative you like. valid options are:
‘continuous’: computed continuous derivatives (standard spectral method) ‘central_difference’: central difference approximation of derivatives ‘fwbw_difference’: forward difference for gradient and backward difference divergence
This commit is contained in:
Pratheek Shanthraj
parent
ce2400c8dc
commit
3a7f4bf43a
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@ -149,10 +149,10 @@ subroutine basicPETSc_init
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call DMDACreate3d(PETSC_COMM_WORLD, &
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DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, & ! cut off stencil at boundary
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DMDA_STENCIL_BOX, & ! Moore (26) neighborhood around central point
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grid(1),grid(2),grid(3), & ! global grid
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grid(1),grid(2),grid(3), & ! global grid
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1, 1, worldsize, &
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9, 0, & ! #dof (F tensor), ghost boundary width (domain overlap)
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grid (1),grid (2),localK, & ! local grid
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grid (1),grid (2),localK, & ! local grid
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da,ierr) ! handle, error
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CHKERRQ(ierr)
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call SNESSetDM(snes,da,ierr); CHKERRQ(ierr)
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@ -13,8 +13,6 @@ module DAMASK_spectral_utilities
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pInt
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use math, only: &
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math_I3
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use numerics, only: &
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spectral_filter
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implicit none
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private
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@ -50,9 +48,9 @@ module DAMASK_spectral_utilities
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field fourier representation for fftw
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real(C_DOUBLE), public, dimension(:,:,:), pointer :: scalarField_real !< scalar field real representation for fftw
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:), pointer :: scalarField_fourier !< scalar field fourier representation for fftw
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real(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
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real(pReal), private, dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives
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real(pReal), private, dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives
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complex(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
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complex(pReal), private, dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives
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complex(pReal), private, dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives
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real(pReal), private, dimension(3,3,3,3) :: C_ref !< mechanic reference stiffness
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real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence (Basic, Basic PETSc)
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@ -121,12 +119,12 @@ module DAMASK_spectral_utilities
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end type phaseFieldDataBin
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enum, bind(c)
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enumerator :: FILTER_NONE_ID, &
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FILTER_GRADIENT_ID, &
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FILTER_COSINE_ID
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enumerator :: DERIVATIVE_CONTINUOUS_ID, &
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DERIVATIVE_CENTRAL_DIFF_ID, &
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DERIVATIVE_FWBW_DIFF_ID
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end enum
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integer(kind(FILTER_NONE_ID)) :: &
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spectral_filter_ID
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integer(kind(DERIVATIVE_CONTINUOUS_ID)) :: &
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spectral_derivative_ID
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public :: &
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utilities_init, &
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@ -143,6 +141,8 @@ module DAMASK_spectral_utilities
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utilities_curlRMS, &
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utilities_fourierScalarGradient, &
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utilities_fourierVectorDivergence, &
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utilities_fourierVectorGradient, &
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utilities_fourierTensorDivergence, &
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utilities_maskedCompliance, &
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utilities_constitutiveResponse, &
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utilities_calculateRate, &
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@ -154,7 +154,7 @@ module DAMASK_spectral_utilities
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FIELD_THERMAL_ID, &
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FIELD_DAMAGE_ID
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private :: &
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utilities_getFilter
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utilities_getFreqDerivative
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contains
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@ -174,6 +174,7 @@ subroutine utilities_init()
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IO_timeStamp, &
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IO_open_file
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use numerics, only: &
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spectral_derivative, &
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fftw_planner_flag, &
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fftw_timelimit, &
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memory_efficient, &
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@ -252,6 +253,17 @@ subroutine utilities_init()
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write(6,'(a,3(es12.5))') ' size x y z: ', geomSize
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endif
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select case (spectral_derivative)
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case ('continuous') ! default, no weighting
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spectral_derivative_ID = DERIVATIVE_CONTINUOUS_ID
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case ('central_difference') ! cosine curve with 1 for avg and zero for highest freq
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spectral_derivative_ID = DERIVATIVE_CENTRAL_DIFF_ID
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case ('fwbw_difference') ! gradient, might need grid scaling as for cosine filter
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spectral_derivative_ID = DERIVATIVE_FWBW_DIFF_ID
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case default
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call IO_error(892_pInt,ext_msg=trim(spectral_derivative))
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end select
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!--------------------------------------------------------------------------------------------------
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! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and
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! resolution-independent divergence
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@ -275,9 +287,9 @@ subroutine utilities_init()
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gridFFTW = int(grid,C_INTPTR_T)
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alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
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MPI_COMM_WORLD, local_K, local_K_offset)
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allocate (xi1st(3,grid1Red,grid(2),grid3),source = 0.0_pReal) ! frequencies, only half the size for first dimension
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allocate (xi2nd(3,grid1Red,grid(2),grid3),source = 0.0_pReal) ! frequencies, only half the size for first dimension
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allocate (xi1st (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies, only half the size for first dimension
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allocate (xi2nd (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies, only half the size for first dimension
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tensorField = fftw_alloc_complex(tensorSize*alloc_local)
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call c_f_pointer(tensorField, tensorField_real, [3_C_INTPTR_T,3_C_INTPTR_T, &
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2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T),gridFFTW(2),local_K]) ! place a pointer for a real tensor representation
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@ -353,31 +365,21 @@ subroutine utilities_init()
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if(j > grid(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - grid(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do i = 1_pInt, grid1Red
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k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
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xi2nd(1:3,i,j,k-grid3Offset) = real(k_s, pReal)/scaledGeomSize ! if divergence_correction is set, frequencies are calculated on unit length
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where(mod(grid,2)==0 .and. [i,j,k] == grid/2+1) ! for even grids, set the Nyquist Freq component to 0.0
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xi1st(1:3,i,j,k-grid3Offset) = 0.0_pReal
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xi2nd(1:3,i,j,k-grid3Offset) = utilities_getFreqDerivative(k_s) ! if divergence_correction is set, frequencies are calculated on unit length
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where(mod(grid,2)==0 .and. [i,j,k] == grid/2+1 .and. &
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spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) ! for even grids, set the Nyquist Freq component to 0.0
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xi1st(1:3,i,j,k-grid3Offset) = cmplx(0.0_pReal,0.0_pReal,pReal)
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elsewhere
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xi1st(1:3,i,j,k-grid3Offset) = xi2nd(1:3,i,j,k-grid3Offset)
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endwhere
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enddo; enddo; enddo
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if(memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(3,3,3,3,1,1,1), source = 0.0_pReal)
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allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pReal,0.0_pReal,pReal))
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = 0.0_pReal)
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allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
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endif
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select case (spectral_filter)
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case ('none') ! default, no weighting
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spectral_filter_ID = FILTER_NONE_ID
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case ('cosine') ! cosine curve with 1 for avg and zero for highest freq
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spectral_filter_ID = FILTER_COSINE_ID
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case ('gradient') ! gradient, might need grid scaling as for cosine filter
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spectral_filter_ID = FILTER_GRADIENT_ID
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case default
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call IO_error(892_pInt,ext_msg=trim(spectral_filter))
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end select
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end subroutine utilities_init
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@ -399,15 +401,18 @@ subroutine utilities_updateGamma(C,saveReference)
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grid3,&
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grid
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use math, only: &
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math_inv33
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math_det33, &
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math_invert
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implicit none
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real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness
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logical , intent(in) :: saveReference !< save reference stiffness to file for restart
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real(pReal), dimension(3,3) :: temp33_Real, xiDyad
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complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
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real(pReal), dimension(6,6) :: matA, matInvA
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integer(pInt) :: &
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i, j, k, &
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l, m, n, o
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logical :: ierr
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C_ref = C
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if (saveReference) then
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@ -424,12 +429,21 @@ subroutine utilities_updateGamma(C,saveReference)
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do k = grid3Offset+1_pInt, grid3Offset+grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
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if (any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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xiDyad(l,m) = xi1st(l, i,j,k-grid3Offset)*xi1st(m, i,j,k-grid3Offset)
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xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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temp33_Real(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad)
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temp33_Real = math_inv33(temp33_Real)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)&
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gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_Real(l,n)*xiDyad(m,o)
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temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
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matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
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matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
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if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
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call math_invert(6_pInt, matA, matInvA, ierr)
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temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_complex(l,n)* &
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conjg(-xi1st(o,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
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else
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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gamma_hat(l,m,n,o,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
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endif
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endif
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enddo; enddo; enddo
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endif
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@ -446,18 +460,11 @@ subroutine utilities_FFTtensorForward()
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grid
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implicit none
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integer(pInt) :: i, j, k
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!--------------------------------------------------------------------------------------------------
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! doing the tensor FFT
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call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
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!--------------------------------------------------------------------------------------------------
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! applying filter
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forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
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tensorField_fourier(1:3,1:3,i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
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tensorField_fourier(1:3,1:3,i,j,k)
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end subroutine utilities_FFTtensorForward
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@ -483,18 +490,11 @@ subroutine utilities_FFTscalarForward()
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grid
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implicit none
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integer(pInt) :: i, j, k
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!--------------------------------------------------------------------------------------------------
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! doing the scalar FFT
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call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
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!--------------------------------------------------------------------------------------------------
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! applying filter
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forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
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scalarField_fourier(i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
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scalarField_fourier(i,j,k)
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end subroutine utilities_FFTscalarForward
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@ -521,18 +521,11 @@ subroutine utilities_FFTvectorForward()
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grid
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implicit none
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integer(pInt) :: i, j, k
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!--------------------------------------------------------------------------------------------------
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! doing the vector FFT
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call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
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!--------------------------------------------------------------------------------------------------
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! applying filter
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forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
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vectorField_fourier(1:3,i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
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vectorField_fourier(1:3,i,j,k)
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end subroutine utilities_FFTvectorForward
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@ -556,7 +549,8 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
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use numerics, only: &
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memory_efficient
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use math, only: &
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math_inv33
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math_det33, &
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math_invert
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use numerics, only: &
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worldrank
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use mesh, only: &
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@ -566,12 +560,14 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
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implicit none
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real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
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real(pReal), dimension(3,3) :: xiDyad, temp33_Real
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complex(pReal), dimension(3,3) :: temp33_complex
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complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
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real(pReal) :: matA(6,6), matInvA(6,6)
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integer(pInt) :: &
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i, j, k, &
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l, m, n, o
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logical :: ierr
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if (worldrank == 0_pInt) then
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write(6,'(/,a)') ' ... doing gamma convolution ...............................................'
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@ -581,18 +577,25 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
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!--------------------------------------------------------------------------------------------------
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! do the actual spectral method calculation (mechanical equilibrium)
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memoryEfficient: if(memory_efficient) then
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do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
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if(any([i,j,k+grid3Offset] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
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if (any([i,j,k+grid3Offset] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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xiDyad(l,m) = xi1st(l, i,j,k)*xi1st(m, i,j,k)
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xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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temp33_Real(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad)
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temp33_Real = math_inv33(temp33_Real)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)&
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gamma_hat(l,m,n,o, 1,1,1) = temp33_Real(l,n)*xiDyad(m,o)
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temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
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matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
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matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
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if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
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call math_invert(6_pInt, matA, matInvA, ierr)
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temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*conjg(-xi1st(o,i,j,k))*xi1st(m,i,j,k)
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else
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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gamma_hat(l,m,n,o,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
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endif
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3, 1,1,1) * &
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tensorField_fourier(1:3,1:3,i,j,k))
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temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
|
||||
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
|
||||
endif
|
||||
enddo; enddo; enddo
|
||||
|
|
@ -600,13 +603,13 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
|
|||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
|
||||
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
||||
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k) * &
|
||||
tensorField_fourier(1:3,1:3,i,j,k))
|
||||
tensorField_fourier(1:3,1:3,i,j,k))
|
||||
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
|
||||
enddo; enddo; enddo
|
||||
endif memoryEfficient
|
||||
|
||||
if (grid3Offset == 0_pInt) &
|
||||
tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
||||
tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal)
|
||||
|
||||
end subroutine utilities_fourierGammaConvolution
|
||||
|
||||
|
|
@ -627,17 +630,15 @@ subroutine utilities_fourierGreenConvolution(D_ref, mobility_ref, deltaT)
|
|||
implicit none
|
||||
real(pReal), dimension(3,3), intent(in) :: D_ref !< desired average value of the field after convolution
|
||||
real(pReal), intent(in) :: mobility_ref, deltaT !< desired average value of the field after convolution
|
||||
real(pReal), dimension(3) :: k_s
|
||||
real(pReal) :: GreenOp_hat
|
||||
complex(pReal) :: GreenOp_hat
|
||||
integer(pInt) :: i, j, k
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! do the actual spectral method calculation
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
|
||||
k_s = xi2nd(1:3,i,j,k)*scaledGeomSize
|
||||
GreenOp_hat = 1.0_pReal/ &
|
||||
(mobility_ref + deltaT*sum((2.0_pReal*PI*k_s/geomSize)* &
|
||||
math_mul33x3(D_ref,(2.0_pReal*PI*k_s/geomSize)))) !< GreenOp_hat = iK^{T} * D_ref * iK, K is frequency
|
||||
GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ &
|
||||
(cmplx(mobility_ref,0.0_pReal,pReal) + &
|
||||
deltaT*sum(conjg(-xi1st(1:3,i,j,k))*matmul(D_ref,xi1st(1:3,i,j,k))))
|
||||
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
|
||||
enddo; enddo; enddo
|
||||
|
||||
|
|
@ -648,12 +649,10 @@ end subroutine utilities_fourierGreenConvolution
|
|||
!> @brief calculate root mean square of divergence of field_fourier
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
real(pReal) function utilities_divergenceRMS()
|
||||
use math, only: &
|
||||
TWOPIIMG, &
|
||||
math_mul33x3_complex
|
||||
use numerics, only: &
|
||||
worldrank
|
||||
use mesh, only: &
|
||||
geomSize, &
|
||||
grid, &
|
||||
grid3
|
||||
|
||||
|
|
@ -673,20 +672,20 @@ real(pReal) function utilities_divergenceRMS()
|
|||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2)
|
||||
do i = 2_pInt, grid1Red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
||||
utilities_divergenceRMS = utilities_divergenceRMS &
|
||||
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
|
||||
xi1st(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
||||
+sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,i,j,k),&
|
||||
xi1st(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
|
||||
+ 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
|
||||
conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
||||
+sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
|
||||
conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**2.0_pReal))
|
||||
enddo
|
||||
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1)
|
||||
+ sum( real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||||
xi1st(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) &
|
||||
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||||
xi1st(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) &
|
||||
+ sum( real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||||
xi1st(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal) &
|
||||
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||||
xi1st(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal)
|
||||
+ sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||||
conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
|
||||
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||||
conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
|
||||
+ sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||||
conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
|
||||
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||||
conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal)
|
||||
enddo; enddo
|
||||
if(grid(1) == 1_pInt) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
|
||||
call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||||
|
|
@ -700,10 +699,10 @@ end function utilities_divergenceRMS
|
|||
!> @brief calculate max of curl of field_fourier
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
real(pReal) function utilities_curlRMS()
|
||||
use math
|
||||
use numerics, only: &
|
||||
worldrank
|
||||
use mesh, only: &
|
||||
geomSize, &
|
||||
grid, &
|
||||
grid3
|
||||
|
||||
|
|
@ -724,33 +723,33 @@ real(pReal) function utilities_curlRMS()
|
|||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2);
|
||||
do i = 2_pInt, grid1Red - 1_pInt
|
||||
do l = 1_pInt, 3_pInt
|
||||
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)&
|
||||
-tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k))*TWOPIIMG
|
||||
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)&
|
||||
-tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k))*TWOPIIMG
|
||||
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)&
|
||||
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k))*TWOPIIMG
|
||||
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*geomSize(2)/scaledGeomSize(2) &
|
||||
-tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*geomSize(3)/scaledGeomSize(3))
|
||||
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)*geomSize(3)/scaledGeomSize(3) &
|
||||
-tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k)*geomSize(1)/scaledGeomSize(1))
|
||||
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)*geomSize(1)/scaledGeomSize(1) &
|
||||
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*geomSize(2)/scaledGeomSize(2))
|
||||
enddo
|
||||
utilities_curlRMS = utilities_curlRMS + &
|
||||
2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
||||
enddo
|
||||
do l = 1_pInt, 3_pInt
|
||||
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)&
|
||||
-tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)&
|
||||
-tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)&
|
||||
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*geomSize(2)/scaledGeomSize(2) &
|
||||
-tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k)*geomSize(3)/scaledGeomSize(3))
|
||||
curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)*geomSize(3)/scaledGeomSize(3) &
|
||||
-tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k)*geomSize(1)/scaledGeomSize(1))
|
||||
curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)*geomSize(1)/scaledGeomSize(1) &
|
||||
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*geomSize(2)/scaledGeomSize(2))
|
||||
enddo
|
||||
utilities_curlRMS = utilities_curlRMS + &
|
||||
sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
|
||||
do l = 1_pInt, 3_pInt
|
||||
curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)&
|
||||
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)&
|
||||
-tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)&
|
||||
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k))*TWOPIIMG
|
||||
curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*geomSize(2)/scaledGeomSize(2) &
|
||||
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*geomSize(3)/scaledGeomSize(3))
|
||||
curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*geomSize(3)/scaledGeomSize(3) &
|
||||
-tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*geomSize(1)/scaledGeomSize(1))
|
||||
curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*geomSize(1)/scaledGeomSize(1) &
|
||||
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*geomSize(2)/scaledGeomSize(2))
|
||||
enddo
|
||||
utilities_curlRMS = utilities_curlRMS + &
|
||||
sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
|
||||
|
|
@ -882,9 +881,7 @@ subroutine utilities_fourierScalarGradient()
|
|||
|
||||
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
|
||||
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)* &
|
||||
cmplx(0.0_pReal,2.0_pReal*PI*xi1st(1:3,i,j,k)* &
|
||||
scaledGeomSize/geomSize,pReal)
|
||||
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)
|
||||
enddo; enddo; enddo
|
||||
end subroutine utilities_fourierScalarGradient
|
||||
|
||||
|
|
@ -908,13 +905,56 @@ subroutine utilities_fourierVectorDivergence()
|
|||
do m = 1_pInt, 3_pInt
|
||||
scalarField_fourier(i,j,k) = &
|
||||
scalarField_fourier(i,j,k) + &
|
||||
vectorField_fourier(m,i,j,k)* &
|
||||
cmplx(0.0_pReal,2.0_pReal*PI*xi1st(m,i,j,k)*scaledGeomSize(m)/geomSize(m),pReal)
|
||||
vectorField_fourier(m,i,j,k)*conjg(-xi1st(m,i,j,k))
|
||||
enddo
|
||||
enddo; enddo; enddo
|
||||
end subroutine utilities_fourierVectorDivergence
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculate vector gradient in fourier field
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine utilities_fourierVectorGradient()
|
||||
use mesh, only: &
|
||||
grid3, &
|
||||
grid, &
|
||||
geomSize
|
||||
|
||||
implicit none
|
||||
integer(pInt) :: i, j, k, m, n
|
||||
|
||||
tensorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
|
||||
do m = 1_pInt, 3_pInt; do n = 1_pInt, 3_pInt
|
||||
tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
|
||||
enddo; enddo
|
||||
enddo; enddo; enddo
|
||||
end subroutine utilities_fourierVectorGradient
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculate tensor divergence in fourier field
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine utilities_fourierTensorDivergence()
|
||||
use mesh, only: &
|
||||
grid3, &
|
||||
grid, &
|
||||
geomSize
|
||||
|
||||
implicit none
|
||||
integer(pInt) :: i, j, k, m, n
|
||||
|
||||
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
|
||||
do m = 1_pInt, 3_pInt; do n = 1_pInt, 3_pInt
|
||||
vectorField_fourier(m,i,j,k) = &
|
||||
vectorField_fourier(m,i,j,k) + &
|
||||
tensorField_fourier(m,n,i,j,k)*conjg(-xi1st(n,i,j,k))
|
||||
enddo; enddo
|
||||
enddo; enddo; enddo
|
||||
end subroutine utilities_fourierTensorDivergence
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculates constitutive response
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -1122,29 +1162,54 @@ end function utilities_forwardField
|
|||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function utilities_getFilter(k)
|
||||
pure function utilities_getFreqDerivative(k_s)
|
||||
use math, only: &
|
||||
PI
|
||||
use mesh, only: &
|
||||
geomSize, &
|
||||
grid
|
||||
|
||||
implicit none
|
||||
real(pReal), intent(in), dimension(3) :: k !< indices of frequency
|
||||
complex(pReal) :: utilities_getFilter
|
||||
integer(pInt), intent(in), dimension(3) :: k_s !< indices of frequency
|
||||
complex(pReal), dimension(3) :: utilities_getFreqDerivative
|
||||
|
||||
select case (spectral_derivative_ID)
|
||||
case (DERIVATIVE_CONTINUOUS_ID)
|
||||
utilities_getFreqDerivative = cmplx(0.0_pReal, 2.0_pReal*PI*real(k_s,pReal)/geomSize,pReal)
|
||||
|
||||
case (DERIVATIVE_CENTRAL_DIFF_ID)
|
||||
utilities_getFreqDerivative = cmplx(0.0_pReal, sin(2.0_pReal*PI*real(k_s,pReal)/real(grid,pReal)), pReal)/ &
|
||||
cmplx(2.0_pReal*geomSize/real(grid,pReal), 0.0_pReal, pReal)
|
||||
|
||||
case (DERIVATIVE_FWBW_DIFF_ID)
|
||||
utilities_getFreqDerivative(1) = &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) - 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||||
cmplx(4.0_pReal*geomSize(1)/real(grid(1),pReal), 0.0_pReal, pReal)
|
||||
utilities_getFreqDerivative(2) = &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) - 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||||
cmplx(4.0_pReal*geomSize(2)/real(grid(2),pReal), 0.0_pReal, pReal)
|
||||
utilities_getFreqDerivative(3) = &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) - 1.0_pReal, &
|
||||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||||
cmplx(4.0_pReal*geomSize(3)/real(grid(3),pReal), 0.0_pReal, pReal)
|
||||
|
||||
select case (spectral_filter_ID)
|
||||
case (FILTER_NONE_ID) ! default, no weighting
|
||||
utilities_getFilter = (1.0_pReal,0.0_pReal)
|
||||
case (FILTER_COSINE_ID) ! cosine curve with 1 for avg and zero for highest freq
|
||||
utilities_getFilter = cmplx(product(1.0_pReal + cos(PI*k*scaledGeomSize/grid))/8.0_pReal,&
|
||||
0.0_pReal)
|
||||
case (FILTER_GRADIENT_ID) ! gradient, might need grid scaling as for cosine filter
|
||||
utilities_getFilter = cmplx(1.0_pReal/(1.0_pReal + sum(k**2)),0.0_pReal)
|
||||
case default
|
||||
utilities_getFilter = (0.0_pReal,0.0_pReal)
|
||||
end select
|
||||
|
||||
end function
|
||||
end function utilities_getFreqDerivative
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -1154,7 +1219,6 @@ end function
|
|||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine utilities_updateIPcoords(F)
|
||||
use math, only: &
|
||||
PI, &
|
||||
math_mul33x3
|
||||
use mesh, only: &
|
||||
grid, &
|
||||
|
|
@ -1166,41 +1230,34 @@ subroutine utilities_updateIPcoords(F)
|
|||
|
||||
real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F
|
||||
integer(pInt) :: i, j, k, m
|
||||
real(pReal), dimension(3) :: step, offset_coords, integrator
|
||||
real(pReal), dimension(3) :: step, offset_coords
|
||||
real(pReal), dimension(3,3) :: Favg
|
||||
PetscErrorCode :: ierr
|
||||
external &
|
||||
MPI_Bcast
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! integration in Fourier space
|
||||
tensorField_real = 0.0_pReal
|
||||
tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F
|
||||
call utilities_FFTtensorForward()
|
||||
call utilities_fourierTensorDivergence()
|
||||
|
||||
integrator = geomSize * 0.5_pReal / PI
|
||||
step = geomSize/real(grid, pReal)
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
|
||||
if (any(abs(xi1st(1:3,i,j,k)) > tiny(0.0_pReal))) &
|
||||
vectorField_fourier(1:3,i,j,k) = vectorField_fourier(1:3,i,j,k)/ &
|
||||
sum(conjg(-xi1st(1:3,i,j,k))*xi1st(1:3,i,j,k))
|
||||
enddo; enddo; enddo
|
||||
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! average F
|
||||
if (grid3Offset == 0_pInt) Favg = real(tensorField_fourier(1:3,1:3,1,1,1),pReal)*wgt
|
||||
call MPI_Bcast(Favg,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! integration in Fourier space
|
||||
vectorField_fourier = cmplx(0.0_pReal, 0.0_pReal, pReal)
|
||||
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
|
||||
do m = 1_pInt,3_pInt
|
||||
vectorField_fourier(m,i,j,k) = sum(tensorField_fourier(m,1:3,i,j,k)*&
|
||||
cmplx(0.0_pReal,xi2nd(1:3,i,j,k)*scaledGeomSize*integrator,pReal))
|
||||
enddo
|
||||
if (any(abs(xi2nd(1:3,i,j,k)) > tiny(0.0_pReal))) &
|
||||
vectorField_fourier(1:3,i,j,k) = &
|
||||
vectorField_fourier(1:3,i,j,k)/cmplx(-sum(xi2nd(1:3,i,j,k)*scaledGeomSize*xi2nd(1:3,i,j,k)* &
|
||||
scaledGeomSize),0.0_pReal,pReal)
|
||||
enddo; enddo; enddo
|
||||
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! add average to fluctuation and put (0,0,0) on (0,0,0)
|
||||
step = geomSize/real(grid, pReal)
|
||||
if (grid3Offset == 0_pInt) offset_coords = vectorField_real(1:3,1,1,1)
|
||||
call MPI_Bcast(offset_coords,3,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
|
||||
offset_coords = math_mul33x3(Favg,step/2.0_pReal) - offset_coords
|
||||
|
|
|
|||
|
|
@ -113,7 +113,7 @@ module numerics
|
|||
fftw_plan_mode = 'FFTW_PATIENT' !< reads the planing-rigor flag, see manual on www.fftw.org, Default FFTW_PATIENT: use patient planner flag
|
||||
character(len=64), protected, public :: &
|
||||
spectral_solver = 'basicpetsc' , & !< spectral solution method
|
||||
spectral_filter = 'none' !< spectral filtering method
|
||||
spectral_derivative = 'continuous' !< spectral filtering method
|
||||
character(len=1024), protected, public :: &
|
||||
petsc_defaultOptions = '-mech_snes_type ngmres &
|
||||
&-damage_snes_type ngmres &
|
||||
|
|
@ -432,8 +432,8 @@ subroutine numerics_init
|
|||
fftw_timelimit = IO_floatValue(line,chunkPos,2_pInt)
|
||||
case ('fftw_plan_mode')
|
||||
fftw_plan_mode = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
|
||||
case ('spectralfilter','myfilter')
|
||||
spectral_filter = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
|
||||
case ('spectralderivative')
|
||||
spectral_derivative = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
|
||||
case ('divergence_correction')
|
||||
divergence_correction = IO_intValue(line,chunkPos,2_pInt)
|
||||
case ('update_gamma')
|
||||
|
|
@ -609,7 +609,7 @@ subroutine numerics_init
|
|||
write(6,'(a24,1x,i8)') ' continueCalculation: ',continueCalculation
|
||||
write(6,'(a24,1x,L8)') ' memory_efficient: ',memory_efficient
|
||||
write(6,'(a24,1x,i8)') ' divergence_correction: ',divergence_correction
|
||||
write(6,'(a24,1x,a)') ' spectral filter: ',trim(spectral_filter)
|
||||
write(6,'(a24,1x,a)') ' spectral derivative: ',trim(spectral_derivative)
|
||||
if(fftw_timelimit<0.0_pReal) then
|
||||
write(6,'(a24,1x,L8)') ' fftw_timelimit: ',.false.
|
||||
else
|
||||
|
|
|
|||
Loading…
Reference in New Issue