223031012
/
DAMASK_EICMD
mirror of https://github.com/achalhp/DAMASK_EICMD.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

accesses to fourier space tensors now need to correspond to transposed structure

This commit is contained in:
Daniel Otto de Mentock 2022-07-13 14:10:13 +02:00
parent ec0c486a2c
commit dda157aa5a
1 changed files with 86 additions and 93 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

179
src/grid/spectral_utilities.f90
View File

@ -41,8 +41,8 @@ module spectral_utilities
real(C_DOUBLE), public, dimension(:,:,:,:), pointer :: vectorField_real !< vector field in real space
real(C_DOUBLE), public, dimension(:,:,:), pointer :: scalarField_real !< scalar field in real space
complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:,:), pointer :: tensorField_fourier !< tensor field in Fourier space
complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:), pointer :: vectorField_fourier !< tensor field in Fourier space
complex(C_DOUBLE_COMPLEX), dimension(:,:,:), pointer :: scalarField_fourier !< tensor field in Fourier space
complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field in Fourier space
complex(C_DOUBLE_COMPLEX), dimension(:,:,:), pointer :: scalarField_fourier !< scalar field in Fourier space
complex(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
complex(pReal), dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives
complex(pReal), dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives
@ -273,7 +273,10 @@ subroutine spectral_utilities_init()
call c_f_pointer(tensorField,tensorField_real, &
[3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
call c_f_pointer(tensorField,tensorField_fourier, &
[3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(2),cells3FFTW])
[3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
cells2=int(cells2FFTW)
cells2Offset=int(cells2_offset)
N = fftw_mpi_local_size_many_transposed(3,[cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T)], &
vectorSize,FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK,PETSC_COMM_WORLD, &
@ -283,7 +286,7 @@ subroutine spectral_utilities_init()
call c_f_pointer(vectorField,vectorField_real, &
[3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
call c_f_pointer(vectorField,vectorField_fourier, &
[3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(2),cells3FFTW])
[3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
N = fftw_mpi_local_size_3d_transposed(cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T), &
PETSC_COMM_WORLD,cells3FFTW,cells3_offset,cells2FFTW,cells2_offset)
@ -292,28 +295,24 @@ subroutine spectral_utilities_init()
call c_f_pointer(scalarField,scalarField_real, &
[int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
call c_f_pointer(scalarField,scalarField_fourier, &
[int(cells1Red, C_INTPTR_T),cellsFFTW(2),cells3FFTW])
![int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW]) ! ToDo
cells2Offset = 0 ! ToDo
cells2 = cells(2) ! ToDo
[int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
!--------------------------------------------------------------------------------------------------
! allocation
allocate (xi1st (3,cells1Red,cells2,cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, only half the size for first dimension
allocate (xi2nd (3,cells1Red,cells2,cells3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for second derivatives, only half the size for first dimension
allocate (xi1st (3,cells1Red,cells(3),cells2),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, only half the size for first dimension
allocate (xi2nd (3,cells1Red,cells(3),cells2),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for second derivatives, only half the size for first dimension
!--------------------------------------------------------------------------------------------------
! tensor MPI fftw plans
planTensorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),tensorSize, &
FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
tensorField_real,tensorField_fourier, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
if (.not. c_associated(planTensorForth)) error stop 'FFTW error r2c tensor'
planTensorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),tensorSize, &
FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
tensorField_fourier,tensorField_real, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
if (.not. c_associated(planTensorBack)) error stop 'FFTW error c2r tensor'
!--------------------------------------------------------------------------------------------------
@ -321,51 +320,48 @@ subroutine spectral_utilities_init()
planVectorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),vectorSize, &
FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
vectorField_real,vectorField_fourier, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
if (.not. c_associated(planVectorForth)) error stop 'FFTW error r2c vector'
planVectorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),vectorSize, &
FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
vectorField_fourier,vectorField_real, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
if (.not. c_associated(planVectorBack)) error stop 'FFTW error c2r vector'
!--------------------------------------------------------------------------------------------------
! scalar MPI fftw plans
planScalarForth = fftw_mpi_plan_dft_r2c_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), &
scalarField_real,scalarField_fourier, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
if (.not. c_associated(planScalarForth)) error stop 'FFTW error r2c scalar'
planScalarBack = fftw_mpi_plan_dft_c2r_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), &
scalarField_fourier,scalarField_real, &
PETSC_COMM_WORLD,FFTW_planner_flag)
PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
if (.not. c_associated(planScalarBack)) error stop 'FFTW error c2r scalar'
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
do k = cells3Offset+1, cells3Offset+cells3
!do k = 1, cells(3) ToDo
do k = 1, cells(3)
k_s(3) = k - 1
if (k > cells(3)/2 + 1) k_s(3) = k_s(3) - cells(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do j = cells2Offset+1, cells2offset+cells2
do j = cells2Offset+1, cells2Offset+cells2
k_s(2) = j - 1
if (j > cells(2)/2 + 1) k_s(2) = k_s(2) - cells(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do i = 1, cells1Red
k_s(1) = i - 1 ! symmetry, junst running from 0,1,...,N/2,N/2+1
xi2nd(1:3,i,j,k-cells3Offset) = utilities_getFreqDerivative(k_s)
!xi2nd(1:3,i,j-cells2Offset,k) = utilities_getFreqDerivative(k_s) ToDo
xi2nd(1:3,i,k,j-cells2Offset) = utilities_getFreqDerivative(k_s)
where(mod(cells,2)==0 .and. [i,j,k] == cells/2+1 .and. &
spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) ! for even grids, set the Nyquist Freq component to 0.0
xi1st(1:3,i,j,k-cells3Offset) = cmplx(0.0_pReal,0.0_pReal,pReal)
xi1st(1:3,i,k,j-cells2Offset) = cmplx(0.0_pReal,0.0_pReal,pReal)
elsewhere
xi1st(1:3,i,j,k-cells3Offset) = xi2nd(1:3,i,j,k-cells3Offset)
xi1st(1:3,i,k,j-cells2Offset) = xi2nd(1:3,i,k,j-cells2Offset)
endwhere
end do; end do; end do
if (num%memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pReal,0.0_pReal,pReal))
else ! precalculation of gamma_hat field
allocate (gamma_hat(3,3,3,3,cells1Red,cells(2),cells3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
!allocate (gamma_hat(3,3,3,3,cells1Red,cells2,cells(3)), source = cmplx(0.0_pReal,0.0_pReal,pReal)) ToDo
allocate (gamma_hat(3,3,3,3,cells1Red,cells(3),cells2), source = cmplx(0.0_pReal,0.0_pReal,pReal))
end if
call selfTest()
@ -394,18 +390,18 @@ subroutine utilities_updateGamma(C)
if (.not. num%memory_efficient) then
gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal) ! for the singular point and any non invertible A
!$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err)
do k = cells3Offset+1, cells3Offset+cells3; do j = 1, cells(2); do i = 1, cells1Red
do k = 1, cells(3); do j = cells2Offset+1, cells2Offset+cells2; do i = 1, cells1Red
if (any([i,j,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
#ifndef __INTEL_COMPILER
do concurrent(l = 1:3, m = 1:3)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j-cells2Offset))*xi1st(m,i,k,j-cells2Offset)
end do
do concurrent(l = 1:3, m = 1:3)
temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx)
end do
#else
forall(l = 1:3, m = 1:3) &
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-cells3Offset))*xi1st(m,i,j,k-cells3Offset)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j-cells2Offset))*xi1st(m,i,k,j-cells2Offset)
forall(l = 1:3, m = 1:3) &
temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx)
#endif
@ -416,11 +412,11 @@ subroutine utilities_updateGamma(C)
temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
#ifndef __INTEL_COMPILER
do concurrent(l=1:3, m=1:3, n=1:3, o=1:3)
gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
gamma_hat(l,m,n,o,i,k,j-cells2Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
end do
#else
forall(l=1:3, m=1:3, n=1:3, o=1:3) &
gamma_hat(l,m,n,o,i,j,k-cells3Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
gamma_hat(l,m,n,o,i,k,j-cells2Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m)
#endif
end if
end if
@ -527,18 +523,18 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
! do the actual spectral method calculation (mechanical equilibrium)
memoryEfficient: if (num%memory_efficient) then
!$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err,gamma_hat)
do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
if (any([i,j,k+cells3Offset] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
do k = 1, cells(3); do j = 1, cells2; do i = 1, cells1Red
if (any([i,j+cells2Offset,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
#ifndef __INTEL_COMPILER
do concurrent(l = 1:3, m = 1:3)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j))*xi1st(m,i,k,j)
end do
do concurrent(l = 1:3, m = 1:3)
temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx)
end do
#else
forall(l = 1:3, m = 1:3) &
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j))*xi1st(m,i,k,j)
forall(l = 1:3, m = 1:3) &
temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx)
#endif
@ -552,33 +548,33 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m)
end do
do concurrent(l = 1:3, m = 1:3)
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,k,j))
end do
#else
forall(l=1:3, m=1:3, n=1:3, o=1:3) &
gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m)
forall(l = 1:3, m = 1:3) &
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,k,j))
#endif
tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
tensorField_fourier(1:3,1:3,i,k,j) = temp33_cmplx
else
tensorField_fourier(1:3,1:3,i,j,k) = cmplx(0.0_pReal,0.0_pReal,pReal)
tensorField_fourier(1:3,1:3,i,k,j) = cmplx(0.0_pReal,0.0_pReal,pReal)
end if
end if
end do; end do; end do
!$OMP END PARALLEL DO
else memoryEfficient
!$OMP PARALLEL DO PRIVATE(l,m,temp33_cmplx)
do k = 1, cells3; do j = 1, cells(2); do i = 1,cells1Red
do k = 1, cells(3); do j = 1, cells2; do i = 1,cells1Red
#ifndef __INTEL_COMPILER
do concurrent(l = 1:3, m = 1:3)
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,k,j)*tensorField_fourier(1:3,1:3,i,k,j))
end do
#else
forall(l = 1:3, m = 1:3) &
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k)*tensorField_fourier(1:3,1:3,i,j,k))
temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,k,j)*tensorField_fourier(1:3,1:3,i,k,j))
#endif
tensorField_fourier(1:3,1:3,i,j,k) = temp33_cmplx
tensorField_fourier(1:3,1:3,i,k,j) = temp33_cmplx
end do; end do; end do
!$OMP END PARALLEL DO
end if memoryEfficient
@ -601,11 +597,11 @@ subroutine utilities_fourierGreenConvolution(D_ref, mu_ref, Delta_t)
!--------------------------------------------------------------------------------------------------
! do the actual spectral method calculation
!$OMP PARALLEL DO PRIVATE(GreenOp_hat)
do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
do k = 1, cells(3); do j = 1, cells2; do i = 1, cells1Red
GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal) &
/ (cmplx(mu_ref,0.0_pReal,pReal) + cmplx(Delta_t,0.0_pReal,pReal) &
* sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal,pReal),xi1st(1:3,i,j,k))))
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
* sum(conjg(xi1st(1:3,i,k,j))* matmul(cmplx(D_ref,0.0_pReal,pReal),xi1st(1:3,i,k,j))))
scalarField_fourier(i,k,j) = scalarField_fourier(i,k,j)*GreenOp_hat
end do; end do; end do
!$OMP END PARALLEL DO
@ -630,23 +626,23 @@ real(pReal) function utilities_divergenceRMS()
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
utilities_divergenceRMS = 0.0_pReal
do k = 1, cells3; do j = 1, cells(2)
do k = 1, cells(3); do j = 1, cells2
do i = 2, cells1Red -1 ! Has somewhere a conj. complex counterpart. Therefore count it twice.
utilities_divergenceRMS = utilities_divergenceRMS &
+ 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, i.e. do not take square root and square again
conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2) & ! --> 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))*rescaledGeom))**2))
+ 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,k,j), & ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2, i.e. do not take square root and square again
conjg(-xi1st(1:3,i,k,j))*rescaledGeom))**2) & ! --> sum squared L_2 norm of vector
+sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,k,j),&
conjg(-xi1st(1:3,i,k,j))*rescaledGeom))**2))
end do
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if cells(1) /= 1)
+ sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
+ sum( real(matmul(tensorField_fourier(1:3,1:3,cells1Red,j,k), &
conjg(-xi1st(1:3,cells1Red,j,k))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,cells1Red,j,k), &
conjg(-xi1st(1:3,cells1Red,j,k))*rescaledGeom))**2)
+ sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,k,j), &
conjg(-xi1st(1:3,1,k,j))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,k,j), &
conjg(-xi1st(1:3,1,k,j))*rescaledGeom))**2) &
+ sum( real(matmul(tensorField_fourier(1:3,1:3,cells1Red,k,j), &
conjg(-xi1st(1:3,cells1Red,k,j))*rescaledGeom))**2) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,cells1Red,k,j), &
conjg(-xi1st(1:3,cells1Red,k,j))*rescaledGeom))**2)
end do; end do
if (cells(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of cells(1) == 1
call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI)
@ -675,36 +671,36 @@ real(pReal) function utilities_curlRMS()
! calculating max curl criterion in Fourier space
utilities_curlRMS = 0.0_pReal
do k = 1, cells3; do j = 1, cells(2);
do k = 1, cells(3); do j = 1, cells2;
do i = 2, cells1Red - 1
do l = 1, 3
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2) &
-tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3))
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3) &
-tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1))
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1) &
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2))
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,k,j)*xi1st(2,i,k,j)*rescaledGeom(2) &
-tensorField_fourier(l,2,i,k,j)*xi1st(3,i,k,j)*rescaledGeom(3))
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,k,j)*xi1st(3,i,k,j)*rescaledGeom(3) &
-tensorField_fourier(l,3,i,k,j)*xi1st(1,i,k,j)*rescaledGeom(1))
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,k,j)*xi1st(1,i,k,j)*rescaledGeom(1) &
-tensorField_fourier(l,1,i,k,j)*xi1st(2,i,k,j)*rescaledGeom(2))
end do
utilities_curlRMS = utilities_curlRMS &
+2.0_pReal*sum(curl_fourier%re**2+curl_fourier%im**2) ! Has somewhere a conj. complex counterpart. Therefore count it twice.
end do
do l = 1, 3
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) &
-tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3))
curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3) &
-tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1))
curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1) &
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2))
curl_fourier = (+tensorField_fourier(l,3,1,k,j)*xi1st(2,1,k,j)*rescaledGeom(2) &
-tensorField_fourier(l,2,1,k,j)*xi1st(3,1,k,j)*rescaledGeom(3))
curl_fourier = (+tensorField_fourier(l,1,1,k,j)*xi1st(3,1,k,j)*rescaledGeom(3) &
-tensorField_fourier(l,3,1,k,j)*xi1st(1,1,k,j)*rescaledGeom(1))
curl_fourier = (+tensorField_fourier(l,2,1,k,j)*xi1st(1,1,k,j)*rescaledGeom(1) &
-tensorField_fourier(l,1,1,k,j)*xi1st(2,1,k,j)*rescaledGeom(2))
end do
utilities_curlRMS = utilities_curlRMS &
+ sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (DC) does not have a conjugate complex counterpart (if cells(1) /= 1)
do l = 1, 3
curl_fourier = (+tensorField_fourier(l,3,cells1Red,j,k)*xi1st(2,cells1Red,j,k)*rescaledGeom(2) &
-tensorField_fourier(l,2,cells1Red,j,k)*xi1st(3,cells1Red,j,k)*rescaledGeom(3))
curl_fourier = (+tensorField_fourier(l,1,cells1Red,j,k)*xi1st(3,cells1Red,j,k)*rescaledGeom(3) &
-tensorField_fourier(l,3,cells1Red,j,k)*xi1st(1,cells1Red,j,k)*rescaledGeom(1))
curl_fourier = (+tensorField_fourier(l,2,cells1Red,j,k)*xi1st(1,cells1Red,j,k)*rescaledGeom(1) &
-tensorField_fourier(l,1,cells1Red,j,k)*xi1st(2,cells1Red,j,k)*rescaledGeom(2))
curl_fourier = (+tensorField_fourier(l,3,cells1Red,k,j)*xi1st(2,cells1Red,k,j)*rescaledGeom(2) &
-tensorField_fourier(l,2,cells1Red,k,j)*xi1st(3,cells1Red,k,j)*rescaledGeom(3))
curl_fourier = (+tensorField_fourier(l,1,cells1Red,k,j)*xi1st(3,cells1Red,k,j)*rescaledGeom(3) &
-tensorField_fourier(l,3,cells1Red,k,j)*xi1st(1,cells1Red,k,j)*rescaledGeom(1))
curl_fourier = (+tensorField_fourier(l,2,cells1Red,k,j)*xi1st(1,cells1Red,k,j)*rescaledGeom(1) &
-tensorField_fourier(l,1,cells1Red,k,j)*xi1st(2,cells1Red,k,j)*rescaledGeom(2))
end do
utilities_curlRMS = utilities_curlRMS &
+ sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (Nyquist) does not have a conjugate complex counterpart (if cells(1) /= 1)
@ -796,8 +792,8 @@ subroutine utilities_fourierScalarGradient()
integer :: i, j, k
do k = 1, cells3; do j = 1, cells(2); do i = 1,cells1Red
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k) ! ToDo: no -conjg?
do k = 1, cells(3); do j = 1, cells2; do i = 1,cells1Red
vectorField_fourier(1:3,i,k,j) = scalarField_fourier(i,k,j)*xi1st(1:3,i,k,j) ! ToDo: no -conjg?
end do; end do; end do
end subroutine utilities_fourierScalarGradient
@ -808,8 +804,7 @@ end subroutine utilities_fourierScalarGradient
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierVectorDivergence()
scalarField_fourier(1:cells1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:cells1Red,1:cells(2),1:cells3) &
scalarField_fourier(1:cells1Red,1:cells(2),1:cells3) = sum(vectorField_fourier(1:3,1:cells1Red,1:cells(3),1:cells2) &
*conjg(-xi1st),1)
end subroutine utilities_fourierVectorDivergence
@ -822,10 +817,9 @@ subroutine utilities_fourierVectorGradient()
integer :: i, j, k, m, n
do k = 1, cells3; do j = 1, cells(2); do i = 1,cells1Red
do k = 1, cells(3); do j = 1, cells2; do i = 1,cells1Red
do m = 1, 3; do n = 1, 3
tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
tensorField_fourier(m,n,i,k,j) = vectorField_fourier(m,i,k,j)*xi1st(n,i,k,j)
end do; end do
end do; end do; end do
@ -839,9 +833,8 @@ subroutine utilities_fourierTensorDivergence()
integer :: i, j, k
do k = 1, cells3; do j = 1, cells(2); do i = 1,cells1Red
vectorField_fourier(:,i,j,k) = matmul(tensorField_fourier(:,:,i,j,k),conjg(-xi1st(:,i,j,k)))
do k = 1, cells(3); do j = 1, cells2; do i = 1,cells1Red
vectorField_fourier(:,i,k,j) = matmul(tensorField_fourier(:,:,i,k,j),conjg(-xi1st(:,i,k,j)))
end do; end do; end do
end subroutine utilities_fourierTensorDivergence
@ -1082,12 +1075,12 @@ subroutine utilities_updateCoords(F)
call utilities_FFTtensorForward()
!$OMP PARALLEL DO
do k = 1, cells3; do j = 1, cells(2); do i = 1, cells1Red
if (any([i,j,k+cells3Offset] /= 1)) then
vectorField_fourier(1:3,i,j,k) = matmul(tensorField_fourier(1:3,1:3,i,j,k),xi2nd(1:3,i,j,k)) &
/ sum(conjg(-xi2nd(1:3,i,j,k))*xi2nd(1:3,i,j,k)) * cmplx(wgt,0.0,pReal)
do k = 1, cells(3); do j = 1, cells2; do i = 1, cells1Red
if (any([i,j+cells2Offset,k] /= 1)) then
vectorField_fourier(1:3,i,k,j) = matmul(tensorField_fourier(1:3,1:3,i,k,j),xi2nd(1:3,i,k,j)) &
/ sum(conjg(-xi2nd(1:3,i,k,j))*xi2nd(1:3,i,k,j)) * cmplx(wgt,0.0,pReal)
else
vectorField_fourier(1:3,i,j,k) = cmplx(0.0,0.0,pReal)
vectorField_fourier(1:3,i,k,j) = cmplx(0.0,0.0,pReal)
end if
end do; end do; end do
!$OMP END PARALLEL DO