DAMASK_EICMD/code/DAMASK_spectral.f90

1124 lines
72 KiB
Fortran

! Copyright 2012 Max-Planck-Institut fuer Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Duesseldorf Advanced Material Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##################################################################################################
!* $Id$
!##################################################################################################
! Material subroutine for BVP solution using spectral method
!
! Run 'DAMASK_spectral.exe --help' to get usage hints
!
! written by P. Eisenlohr,
! F. Roters,
! L. Hantcherli,
! W.A. Counts,
! D.D. Tjahjanto,
! C. Kords,
! M. Diehl,
! R. Lebensohn
!
! MPI fuer Eisenforschung, Duesseldorf
!##################################################################################################
! used modules
!##################################################################################################
program DAMASK_spectral
use DAMASK_interface
use prec, only: pInt, pReal, DAMASK_NaN
use IO
use debug, only: debug_spectral, &
debug_spectralGeneral, &
debug_spectralDivergence, &
debug_spectralRestart, &
debug_spectralFFTW
use math
use kdtree2_module
use CPFEM, only: CPFEM_general, CPFEM_initAll
use FEsolving, only: restartWrite, restartReadInc
use numerics, only: err_div_tol, err_stress_tolrel, rotation_tol, itmax, &
memory_efficient, update_gamma, &
simplified_algorithm, divergence_correction, &
cut_off_value, &
DAMASK_NumThreadsInt, &
fftw_planner_flag, fftw_timelimit
use homogenization, only: materialpoint_sizeResults, materialpoint_results
!$ use OMP_LIB ! the openMP function library
!##################################################################################################
! variable declaration
!##################################################################################################
implicit none
!--------------------------------------------------------------------------------------------------
! variables to read from load case and geom file
real(pReal), dimension(9) :: temp_valueVector ! stores information temporarily from loadcase file
logical, dimension(9) :: temp_maskVector
integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
(1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
1_pInt, & ! dropguessing
maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
myUnit = 234_pInt
integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
integer(pInt) :: headerLength,&
N_l = 0_pInt,&
N_t = 0_pInt,&
N_n = 0_pInt,&
N_Fdot = 0_pInt
character(len=1024) :: path, line, keyword
logical :: gotResolution = .false.,&
gotDimension = .false.,&
gotHomogenization = .false.
type bc_type
real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
stress = 0.0_pReal, & ! stress BC (if applicable)
rotation = math_I3 ! rotation of BC (if applicable)
real(pReal) :: time = 0.0_pReal, & ! length of increment
temperature = 300_pReal ! isothermal starting conditions
integer(pInt) :: incs = 0_pInt, & ! number of increments
outputfrequency = 1_pInt, & ! frequency of result writes
restartfrequency = 0_pInt, & ! frequency of restart writes
logscale = 0_pInt ! linear/logaritmic time inc flag
logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
velGradApplied = .false. ! decide wether velocity gradient or fdot is given
logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
maskStress = .false. ! mask of stress boundary conditions
logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
end type
type(bc_type), allocatable, dimension(:) :: bc
character(len=6) :: loadcase_string
!--------------------------------------------------------------------------------------------------
! variables storing information from geom file
real(pReal) :: wgt
real(pReal), dimension(3) :: geomdim = 0.0_pReal ! physical dimension of volume element per direction
integer(pInt) :: Npoints,& ! number of Fourier points
homog ! homogenization scheme used
integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
integer(pInt) :: res1_red ! to store res(1)/2 +1
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
real(pReal), dimension(3,3) :: pstress, pstress_av, &
defgradAim = math_I3, defgradAimOld = math_I3,&
mask_stress, mask_defgrad, fDot, &
pstress_av_lab, defgradAim_lab, defgrad_av_lab ! quantities rotated to other coordinate system
real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current = 0.0_pReal, s_prev, c_prev ! stiffness and compliance
real(pReal), dimension(6) :: cstress ! cauchy stress
real(pReal), dimension(6,6) :: dsde ! small strain stiffness
real(pReal), dimension(9,9) :: s_prev99, c_prev99 ! compliance and stiffness in matrix notation
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
integer(pInt) :: size_reduced = 0.0_pReal ! number of stress BCs
!--------------------------------------------------------------------------------------------------
! pointwise data
type(C_PTR) :: tensorField, tau ! fields in real an fourier space
real(pReal), dimension(:,:,:,:,:), pointer :: tensorField_real ! fields in real space (pointer)
real(pReal), dimension(:,:,:,:,:), pointer :: tau_real
complex(pReal), dimension(:,:,:,:,:), pointer :: tensorField_complex ! fields in fourier space (pointer)
complex(pReal), dimension(:,:,:,:,:), pointer :: tau_complex
real(pReal), dimension(:,:,:,:,:), allocatable :: defgrad, defgradold
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
real(pReal), dimension(:,:,:), allocatable :: temperature
!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
type(C_PTR) :: plan_stress, plan_correction, plan_tau ! plans for fftw
real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
integer(pInt), dimension(3) :: k_s, cutting_freq
!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc ! elapsed time, begin of interval, time interval
real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
complex(pReal), dimension(3) :: temp3_Complex
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(3,3) :: temp33_Real
integer(pInt) :: i, j, k, l, m, n, p, errorID
integer(pInt) :: N_Loadcases, loadcase, inc, iter, ielem, CPFEM_mode, &
ierr, notConvergedCounter = 0_pInt, totalIncsCounter = 0_pInt,&
writtenRestart = 0_pInt
logical :: errmatinv
real(pReal) :: defgradDet, correctionFactor
!--------------------------------------------------------------------------------------------------
!variables controlling debugging
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
!--------------------------------------------------------------------------------------------------
!variables for additional output due to general debugging
real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
!--------------------------------------------------------------------------------------------------
! variables for additional output of divergence calculations
type(C_PTR) :: divergence, plan_divergence
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
complex(pReal), dimension(:,:,:,:), pointer :: divergence_complex
real(pReal), dimension(:,:,:,:), allocatable :: divergence_postProc
real(pReal) :: p_hat_avg, p_real_avg,&
err_div_RMS, err_real_div_RMS,&
err_div_max, err_real_div_max,&
max_div_error
!--------------------------------------------------------------------------------------------------
! variables for debugging fft using a scalar field
type(C_PTR) :: scalarField_realPointer, scalarField_complexPointer,&
plan_scalarField_forth, plan_scalarField_back
real(pReal), dimension(:,:,:), pointer :: scalarField_real
complex(pReal), dimension(:,:,:), pointer :: scalarField_complex
integer(pInt) :: row, column
!##################################################################################################
! reading of information from load case file and geometry file
!##################################################################################################
!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
call DAMASK_interface_init()
print '(a)', ''
print '(a)', ' <<<+- DAMASK_spectral init -+>>>'
print '(a)', ' $Id$'
#include "compilation_info.f90"
print '(a,a)', ' Working Directory: ',trim(getSolverWorkingDirectoryName())
print '(a,a)', ' Solver Job Name: ',trim(getSolverJobName())
print '(a)', ''
!--------------------------------------------------------------------------------------------------
! reading the load case file and allocate data structure containing load cases
path = getLoadcaseName()
if (.not. IO_open_file(myUnit,path)) call IO_error(error_ID = 30_pInt,ext_msg = trim(path))
rewind(myUnit)
do
read(myUnit,'(a1024)',END = 100) line
if (IO_isBlank(line)) cycle ! skip empty lines
positions = IO_stringPos(line,maxNchunksLoadcase)
do i = 1_pInt, maxNchunksLoadcase, 1_pInt ! reading compulsory parameters for loadcase
select case (IO_lc(IO_stringValue(line,positions,i)))
case('l','velocitygrad','velgrad','velocitygradient')
N_l = N_l + 1_pInt
case('fdot')
N_Fdot = N_Fdot + 1_pInt
case('t','time','delta')
N_t = N_t + 1_pInt
case('n','incs','increments','steps','logincs','logsteps')
N_n = N_n + 1_pInt
end select
enddo ! count all identifiers to allocate memory and do sanity check
enddo
100 N_Loadcases = N_n
if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
call IO_error(error_ID=37_pInt,ext_msg = trim(path)) ! error message for incomplete loadcase
allocate (bc(N_Loadcases))
!--------------------------------------------------------------------------------------------------
! reading the load case and assign values to the allocated data structure
rewind(myUnit)
loadcase = 0_pInt
do
read(myUnit,'(a1024)',END = 101) line
if (IO_isBlank(line)) cycle ! skip empty lines
loadcase = loadcase + 1_pInt
positions = IO_stringPos(line,maxNchunksLoadcase)
do j = 1_pInt,maxNchunksLoadcase
select case (IO_lc(IO_stringValue(line,positions,j)))
case('fdot','l','velocitygrad','velgrad','velocitygradient') ! assign values for the deformation BC matrix
bc(loadcase)%velGradApplied = &
(IO_lc(IO_stringValue(line,positions,j)) == 'l'.or. & ! in case of given L, set flag to true
IO_lc(IO_stringValue(line,positions,j)) == 'velocitygrad'.or.&
IO_lc(IO_stringValue(line,positions,j)) == 'velgrad'.or.&
IO_lc(IO_stringValue(line,positions,j)) == 'velocitygradient')
temp_valueVector = 0.0_pReal
temp_maskVector = .false.
forall (k = 1_pInt:9_pInt) temp_maskVector(k) = IO_stringValue(line,positions,j+k) /= '*'
do k = 1_pInt,9_pInt
if (temp_maskVector(k)) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
enddo
bc(loadcase)%maskDeformation = transpose(reshape(temp_maskVector,(/3,3/)))
bc(loadcase)%deformation = math_plain9to33(temp_valueVector)
case('p','pk1','piolakirchhoff','stress')
temp_valueVector = 0.0_pReal
forall (k = 1_pInt:9_pInt) bc(loadcase)%maskStressVector(k) =&
IO_stringValue(line,positions,j+k) /= '*'
do k = 1_pInt,9_pInt
if (bc(loadcase)%maskStressVector(k)) temp_valueVector(k) =&
IO_floatValue(line,positions,j+k) ! assign values for the bc(loadcase)%stress matrix
enddo
bc(loadcase)%maskStress = transpose(reshape(bc(loadcase)%maskStressVector,(/3,3/)))
bc(loadcase)%stress = math_plain9to33(temp_valueVector)
case('t','time','delta') ! increment time
bc(loadcase)%time = IO_floatValue(line,positions,j+1_pInt)
case('temp','temperature') ! starting temperature
bc(loadcase)%temperature = IO_floatValue(line,positions,j+1_pInt)
case('n','incs','increments','steps') ! number of increments
bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
case('logincs','logincrements','logsteps') ! number of increments (switch to log time scaling)
bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
bc(loadcase)%logscale = 1_pInt
case('f','freq','frequency','outputfreq') ! frequency of result writings
bc(loadcase)%outputfrequency = IO_intValue(line,positions,j+1_pInt)
case('r','restart','restartwrite') ! frequency of writing restart information
bc(loadcase)%restartfrequency = max(0_pInt,IO_intValue(line,positions,j+1_pInt))
case('guessreset','dropguessing')
bc(loadcase)%followFormerTrajectory = .false. ! do not continue to predict deformation along former trajectory
case('euler') ! rotation of loadcase given in euler angles
p = 0_pInt ! assuming values given in radians
l = 1_pInt ! assuming keyword indicating degree/radians
select case (IO_lc(IO_stringValue(line,positions,j+1_pInt)))
case('deg','degree')
p = 1_pInt ! for conversion from degree to radian
case('rad','radian')
case default
l = 0_pInt ! immediately reading in angles, assuming radians
end select
forall(k = 1_pInt:3_pInt) temp33_Real(k,1) = &
IO_floatValue(line,positions,j+l+k) * real(p,pReal) * inRad
bc(loadcase)%rotation = math_EulerToR(temp33_Real(:,1))
case('rotation','rot') ! assign values for the rotation of loadcase matrix
temp_valueVector = 0.0_pReal
forall (k = 1_pInt:9_pInt) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
bc(loadcase)%rotation = math_plain9to33(temp_valueVector)
end select
enddo; enddo
101 close(myUnit)
!-------------------------------------------------------------------------------------------------- ToDo: if temperature at CPFEM is treated properly, move this up immediately after interface init
! initialization of all related DAMASK modules (e.g. mesh.f90 reads in geometry)
call CPFEM_initAll(bc(1)%temperature,1_pInt,1_pInt)
if (update_gamma .and. .not. memory_efficient) call IO_error(error_ID = 47_pInt)
!--------------------------------------------------------------------------------------------------
! read header of geom file to get size information. complete geom file is intepretated by mesh.f90
path = getModelName()
if (.not. IO_open_file(myUnit,trim(path)//InputFileExtension))&
call IO_error(error_ID=101_pInt,ext_msg = trim(path)//InputFileExtension)
rewind(myUnit)
read(myUnit,'(a1024)') line
positions = IO_stringPos(line,2_pInt)
keyword = IO_lc(IO_StringValue(line,positions,2_pInt))
if (keyword(1:4) == 'head') then
headerLength = IO_intValue(line,positions,1_pInt) + 1_pInt
else
call IO_error(error_ID=42_pInt)
endif
rewind(myUnit)
do i = 1_pInt, headerLength
read(myUnit,'(a1024)') line
positions = IO_stringPos(line,maxNchunksGeom)
select case ( IO_lc(IO_StringValue(line,positions,1)) )
case ('dimension')
gotDimension = .true.
do j = 2_pInt,6_pInt,2_pInt
select case (IO_lc(IO_stringValue(line,positions,j)))
case('x')
geomdim(1) = IO_floatValue(line,positions,j+1_pInt)
case('y')
geomdim(2) = IO_floatValue(line,positions,j+1_pInt)
case('z')
geomdim(3) = IO_floatValue(line,positions,j+1_pInt)
end select
enddo
case ('homogenization')
gotHomogenization = .true.
homog = IO_intValue(line,positions,2_pInt)
case ('resolution')
gotResolution = .true.
do j = 2_pInt,6_pInt,2_pInt
select case (IO_lc(IO_stringValue(line,positions,j)))
case('a')
res(1) = IO_intValue(line,positions,j+1_pInt)
case('b')
res(2) = IO_intValue(line,positions,j+1_pInt)
case('c')
res(3) = IO_intValue(line,positions,j+1_pInt)
end select
enddo
end select
enddo
close(myUnit)
!--------------------------------------------------------------------------------------------------
! sanity checks of geometry parameters
if (.not.(gotDimension .and. gotHomogenization .and. gotResolution))&
call IO_error(error_ID = 45_pInt)
if (any(geomdim<=0.0_pReal)) stop
if(mod(res(1),2_pInt)/=0_pInt .or.&
mod(res(2),2_pInt)/=0_pInt .or.&
(mod(res(3),2_pInt)/=0_pInt .and. res(3)/= 1_pInt))&
call IO_error(error_ID = 103_pInt)
!--------------------------------------------------------------------------------------------------
! variables derived from resolution
res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
Npoints = res(1)*res(2)*res(3)
wgt = 1.0_pReal/real(Npoints, pReal)
if (cut_off_value <0.0_pReal .or. cut_off_value >0.9_pReal) stop
cutting_freq = nint(real(res,pReal)*cut_off_value,pInt) ! for cut_off_value=0.0 just the highest freq. is removed
!--------------------------------------------------------------------------------------------------
! output of geometry
print '(a)', ''
print '(a)', '#############################################################'
print '(a)', 'DAMASK spectral:'
print '(a)', 'The spectral method boundary value problem solver for'
print '(a)', 'the Duesseldorf Advanced Material Simulation Kit'
print '(a)', '#############################################################'
print '(a,a)', 'geometry file: ',trim(path)//'.geom'
print '(a)', '============================================================='
print '(a,3(i12 ))','resolution a b c:', res
print '(a,3(f12.5))','dimension x y z:', geomdim
print '(a,i5)','homogenization: ',homog
if(cut_off_value/=0.0_pReal) print '(a,3(i12),a)', 'cutting away ', cutting_freq, ' frequencies'
print '(a)', '#############################################################'
print '(a,a)', 'loadcase file: ',trim(getLoadcaseName())
!--------------------------------------------------------------------------------------------------
! consistency checks and output of load case
bc(1)%followFormerTrajectory = .false. ! cannot guess along trajectory for first inc of first loadcase
errorID = 0_pInt
do loadcase = 1_pInt, N_Loadcases
write (loadcase_string, '(i6)' ) loadcase
print '(a)', '============================================================='
print '(a,i6)', 'loadcase: ', loadcase
if (.not. bc(loadcase)%followFormerTrajectory) print '(a)', 'drop guessing along trajectory'
if (bc(loadcase)%velGradApplied) then
do j = 1_pInt, 3_pInt
if (any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .true.) .and. &
any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .false.)) errorID = 32_pInt ! each row should be either fully or not at all defined
enddo
print '(a)','velocity gradient:'
else
print '(a)','deformation gradient rate:'
endif
write (*,'(3(3(f12.7,1x)/))',advance='no') merge(math_transpose33(bc(loadcase)%deformation),&
reshape(spread(DAMASK_NaN,1,9),(/3,3/)),transpose(bc(loadcase)%maskDeformation))
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' stress / GPa:',&
1e-9*merge(math_transpose33(bc(loadcase)%stress),reshape(spread(DAMASK_NaN,1,9),(/3,3/))&
,transpose(bc(loadcase)%maskStress))
if (any(bc(loadcase)%rotation /= math_I3)) &
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',&
math_transpose33(bc(loadcase)%rotation)
print '(a,f12.6)','temperature:',bc(loadcase)%temperature
print '(a,f12.6)','time: ',bc(loadcase)%time
print '(a,i5)' ,'increments: ',bc(loadcase)%incs
print '(a,i5)','output frequency: ',bc(loadcase)%outputfrequency
print '(a,i5)','restart frequency: ',bc(loadcase)%restartfrequency
if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 31 ! exclusive or masking only
if (any(bc(loadcase)%maskStress .and. transpose(bc(loadcase)%maskStress) .and. &
reshape((/.false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false./),(/3,3/)))) &
errorID = 38_pInt ! no rotation is allowed by stress BC
if (any(abs(math_mul33x33(bc(loadcase)%rotation,math_transpose33(bc(loadcase)%rotation))&
-math_I3) > reshape(spread(rotation_tol,1,9),(/3,3/)))&
.or. abs(math_det33(bc(loadcase)%rotation)) > 1.0_pReal + rotation_tol)&
errorID = 46_pInt ! given rotation matrix contains strain
if (bc(loadcase)%time < 0.0_pReal) errorID = 34_pInt ! negative time increment
if (bc(loadcase)%incs < 1_pInt) errorID = 35_pInt ! non-positive incs count
if (bc(loadcase)%outputfrequency < 1_pInt) errorID = 36_pInt ! non-positive result frequency
if (errorID > 0_pInt) call IO_error(error_ID = errorID, ext_msg = loadcase_string)
enddo
!--------------------------------------------------------------------------------------------------
! debugging parameters
debugGeneral = iand(debug_spectral,debug_spectralGeneral) > 0_pInt
debugDivergence = iand(debug_spectral,debug_spectralDivergence) > 0_pInt
debugRestart = iand(debug_spectral,debug_spectralRestart) > 0_pInt
debugFFTW = iand(debug_spectral,debug_spectralFFTW) > 0_pInt
!##################################################################################################
! Loop over loadcases defined in the loadcase file
!##################################################################################################
do loadcase = 1_pInt, N_Loadcases
time0 = time ! loadcase start time
if (bc(loadcase)%followFormerTrajectory) then ! continue to guess along former trajectory where applicable
guessmode = 1.0_pReal
else
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
endif
!--------------------------------------------------------------------------------------------------
! arrays for mixed boundary conditions
mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
size_reduced = count(bc(loadcase)%maskStressVector)
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
fDot = bc(loadcase)%deformation ! only valid for given fDot. will be overwritten later in case L is given
!##################################################################################################
! loop oper incs defined in input file for current loadcase
!##################################################################################################
do inc = 1_pInt, bc(loadcase)%incs
!--------------------------------------------------------------------------------------------------
! forwarding time
if (bc(loadcase)%logscale == 1_pInt) then ! logarithmic scale
if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
else ! not-1st inc of 1st loadcase of logarithmic scale
timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
endif
else ! not-1st loadcase of logarithmic scale
timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
real(bc(loadcase)%incs ,pReal))&
-(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
real(bc(loadcase)%incs ,pReal)) )
endif
endif
time = time + timeinc
totalIncsCounter = totalIncsCounter + 1_pInt
!##################################################################################################
! initialization start after forwarding to restart step
!##################################################################################################
if(totalIncsCounter == restartReadInc+1_pInt) then ! Initialize values
guessmode = 0.0_pReal ! no old values
allocate (defgrad ( res(1), res(2),res(3),3,3)); defgrad = 0.0_pReal
allocate (defgradold ( res(1), res(2),res(3),3,3)); defgradold = 0.0_pReal
allocate (coordinates( res(1), res(2),res(3),3)); coordinates = 0.0_pReal
allocate (temperature( res(1), res(2),res(3))); temperature = bc(1)%temperature ! start out isothermally
allocate (xi (3,res1_red,res(2),res(3))); xi = 0.0_pReal
tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
call c_f_pointer(tensorField, tensorField_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation
call c_f_pointer(tensorField, tensorField_complex, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
!--------------------------------------------------------------------------------------------------
! general initialization of fftw (see manual on fftw.org for more details)
if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=102) ! check for correct precision in C
#ifdef _OPENMP
if(DAMASK_NumThreadsInt > 0_pInt) then
ierr = fftw_init_threads()
if (ierr == 0_pInt) call IO_error(error_ID = 104_pInt)
call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
endif
#endif
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! creating plans
plan_stress = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),9,& ! dimensions , length in each dimension in reversed order
tensorField_real,(/res(3),res(2) ,res(1)+2_pInt/),& ! input data , physical length in each dimension in reversed order
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
tensorField_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
plan_correction =fftw_plan_many_dft_c2r(3,(/res(3),res(2) ,res(1)/),9,&
tensorField_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,&
tensorField_real,(/res(3),res(2) ,res(1)+2_pInt/),&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
!--------------------------------------------------------------------------------------------------
! depending on (debug) options, allocate more memory and create additional plans
if (.not. simplified_algorithm) then
stop 'long algorithm is not working yet'
tau = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T))
call c_f_pointer(tau, tau_real, [ res(1)+2_pInt,res(2),res(3),3,3])
call c_f_pointer(tau, tau_complex, [ res1_red, res(2),res(3),3,3])
plan_tau = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),9,&
tau_real,(/res(3),res(2) ,res(1)+2_pInt/),&
1, res(3)*res(2)*(res(1)+2_pInt),&
tau_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
endif
if (debugDivergence) then
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
call c_f_pointer(divergence, divergence_complex, [ res1_red, res(2),res(3),3])
allocate (divergence_postProc(res(1),res(2),res(3),3)); divergence_postProc= 0.0_pReal
plan_divergence = fftw_plan_many_dft_c2r(3,(/res(3),res(2) ,res(1)/),3,&
divergence_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,&
divergence_real,(/res(3),res(2) ,res(1)+2_pInt/),&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
endif
if (debugFFTW) then
scalarField_realPointer = fftw_alloc_complex(int(res(1) *res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
scalarField_complexPointer = fftw_alloc_complex(int(res1_red*res(2)*res(3),C_SIZE_T))
call c_f_pointer(scalarField_realPointer, scalarField_real, [res(1), res(2),res(3)])
call c_f_pointer(scalarField_complexPointer, scalarField_complex, [res1_red,res(2),res(3)])
plan_scalarField_forth = fftw_plan_dft_r2c_3d(res(3),res(2),res(1),& !reversed order
scalarField_real,scalarField_complex,fftw_planner_flag)
plan_scalarField_back = fftw_plan_dft_c2r_3d(res(3),res(2),res(1),& !reversed order
scalarField_complex,scalarField_real,fftw_planner_flag)
endif
if (debugGeneral) print '(a)' , 'FFTW initialized'
!--------------------------------------------------------------------------------------------------
! calculate initial deformation
if (restartReadInc==0_pInt) then ! not restarting, no deformation at the beginning
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
defgrad(i,j,k,1:3,1:3) = math_I3
defgradold(i,j,k,1:3,1:3) = math_I3
enddo; enddo; enddo
else ! using old values from file
if (debugRestart) print '(a,i6,a)' , 'Reading values of increment ',&
restartReadInc ,' from file'
if (IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
trim(getSolverJobName()),size(defgrad))) then
read (777,rec=1) defgrad
close (777)
endif
defgradold = defgrad
defgradAim = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
defgradAim = defgradAim + defgrad(i,j,k,1:3,1:3) ! calculating old average deformation
enddo; enddo; enddo
defgradAim = defgradAim * wgt
defgradAimOld = defgradAim
guessmode=0.0_pInt
endif
call deformed_fft(res,geomdim,defgradAimOld,1.0_pReal,defgrad,coordinates) ! calculate current coordinates
ielem = 0_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
ielem = ielem + 1_pInt
call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c_current = c_current + dPdF
enddo; enddo; enddo
c0_reference = c_current * wgt ! linear reference material stiffness
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) and remove the given highest frequencies
if (debugGeneral) print '(a)' , 'first call to CPFEM_general finished'
do k = 1_pInt, res(3)
k_s(3) = k - 1_pInt
if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
do j = 1_pInt, res(2)
k_s(2) = j - 1_pInt
if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
do i = 1, res1_red
k_s(1) = i - 1_pInt
xi(1:3,i,j,k) = real(k_s, pReal)/geomdim
enddo; enddo; enddo
xi(1,res1_red-cutting_freq(1):res1_red , 1:res(2) , 1:res(3)) = 0.0_pReal
xi(2,1:res1_red, res(2)/2_pInt+1_pInt-cutting_freq(2):res(2)/2_pInt+1_pInt+cutting_freq(2),&
1:res(3)) = 0.0_pReal
xi(3,1:res1_red, 1:res(2) ,&
res(3)/2_pInt+1_pInt-cutting_freq(3):res(3)/2_pInt+1_pInt+cutting_freq(3)) = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! calculate the gamma operator
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal
else ! precalculation of gamma_hat field
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3)); gamma_hat = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then
do l = 1_pInt ,3_pInt; do m = 1_pInt,3_pInt
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
enddo; enddo
temp33_Real = math_inv33(math_mul3333xx33(c0_reference, xiDyad))
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt; do p=1_pInt,3_pInt
gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
(xiDyad(m,p)+xiDyad(p,m))
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! empirical factor for making divergence resolution and dimension indpendent
divergence_correction =.false.
if (divergence_correction) then
if (res(3) == 1_pInt) then
correctionFactor = minval(geomdim(1:2))*wgt**(-1.0_pReal/4.0_pReal) ! 2D case, ToDo: correct?
else
correctionFactor = minval(geomdim(1:3))*wgt**(-1.0_pReal/4.0_pReal) ! multiplying by minimum dimension to get rid of dimension dependency and phenomenologigal factor wgt**(-1/4) to get rid of resolution dependency
endif
else
correctionFactor = 1.0_pReal
endif
!--------------------------------------------------------------------------------------------------
! write header of output file
open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
//'.spectralOut',form='UNFORMATTED',status='REPLACE')
write(538) 'load', trim(getLoadcaseName())
write(538) 'workingdir', trim(getSolverWorkingDirectoryName())
write(538) 'geometry', trim(getSolverJobName())//InputFileExtension
write(538) 'resolution', res
write(538) 'dimension', geomdim
write(538) 'materialpoint_sizeResults', materialpoint_sizeResults
write(538) 'loadcases', N_Loadcases
write(538) 'frequencies', bc(1:N_Loadcases)%outputfrequency ! one entry per loadcase
write(538) 'times', bc(1:N_Loadcases)%time ! one entry per loadcase
write(538) 'logscales', bc(1:N_Loadcases)%logscale
bc(1)%incs = bc(1)%incs + 1_pInt ! additional for zero deformation
write(538) 'increments', bc(1:N_Loadcases)%incs ! one entry per loadcase
bc(1)%incs = bc(1)%incs - 1_pInt
write(538) 'startingIncrement', restartReadInc ! start with writing out the previous inc
write(538) 'eoh' ! end of header
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! initial (non-deformed or read-in) results
if (debugGeneral) print '(a)' , 'Header of result file written out'
endif
if(totalIncsCounter > restartReadInc) then ! Do calculations (otherwise just forwarding)
if(bc(loadcase)%restartFrequency>0_pInt) &
restartWrite = ( mod(inc - 1_pInt,bc(loadcase)%restartFrequency)==0_pInt) ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
if (bc(loadcase)%velGradApplied) & ! calculate fDot from given L and current F
fDot = math_mul33x33(bc(loadcase)%deformation, defgradAim)
!--------------------------------------------------------------------------------------------------
! winding forward of deformation aim in loadcase system
temp33_Real = defgradAim
defgradAim = defgradAim &
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
+ mask_defgrad * fDot * timeinc
defgradAimOld = temp33_Real
!--------------------------------------------------------------------------------------------------
! update local deformation gradient
if (any(bc(loadcase)%rotation/=math_I3)) then ! lab and loadcase coordinate system are NOT the same
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc(loadcase)%velGradApplied) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc(loadcase)%deformation,&
math_rotate_forward33(defgradold(i,j,k,1:3,1:3),bc(loadcase)%rotation))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ math_rotate_backward33((1.0_pReal-guessmode) * mask_defgrad * fDot,&
bc(loadcase)%rotation) *timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
else ! one coordinate system for lab and loadcase, save some multiplications
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc(loadcase)%velGradApplied) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc(loadcase)%deformation,defgradold(i,j,k,1:3,1:3))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ (1.0_pReal-guessmode) * mask_defgrad * fDot * timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! calculate reduced compliance
c_prev = math_rotate_forward3333(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former inc
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
c_prev99 = math_Plain3333to99(c_prev)
k = 0_pInt ! build reduced stiffness
do n = 1_pInt,9_pInt
if(bc(loadcase)%maskStressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(bc(loadcase)%maskStressVector(m)) then
j = j + 1_pInt
c_reduced(k,j) = c_prev99(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(error_ID=799)
s_prev99 = 0.0_pReal ! build full compliance
k = 0_pInt
do n = 1_pInt,9_pInt
if(bc(loadcase)%maskStressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(bc(loadcase)%maskStressVector(m)) then
j = j + 1_pInt
s_prev99(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
s_prev = (math_Plain99to3333(s_prev99))
endif
!--------------------------------------------------------------------------------------------------
! report begin of new increment
print '(a)', '##################################################################'
print '(A,I5.5,A,es12.6)', 'Increment ', totalIncsCounter, ' Time ',time
if (restartWrite ) then
print '(A)', 'writing converged results of previous increment for restart'
if(IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(defgrad))) then ! writing deformation gradient field to file
write (777,rec=1) defgrad
close (777)
endif
writtenRestart=totalIncsCounter-1_pInt
endif
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
CPFEM_mode = 1_pInt ! winding forward
iter = 0_pInt
err_div = 2.0_pReal * err_div_tol ! go into loop
!##################################################################################################
! convergence loop (looping over iterations)
!##################################################################################################
do while(iter < itmax .and. &
(err_div > err_div_tol .or. &
err_stress > err_stress_tol))
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
! report begin of new iteration
print '(a)', ''
print '(a)', '=================================================================='
print '(5(a,i6.6))', 'Loadcase ',loadcase,' Increment ',inc,'/',bc(loadcase)%incs,&
' @ Iteration ',iter,'/',itmax
do n = 1_pInt,3_pInt; do m = 1_pInt,3_pInt
defgrad_av_lab(m,n) = sum(defgrad(1:res(1),1:res(2),1:res(3),m,n)) * wgt
enddo; enddo
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient:',&
math_transpose33(math_rotate_forward33(defgrad_av_lab,bc(loadcase)%rotation))
print '(a)', ''
print '(a)', '... update stress field P(F) .....................................'
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
call deformed_fft(res,geomdim,defgrad_av_lab,1.0_pReal,defgrad,coordinates) ! calculate current coordinates
ielem = 0_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
ielem = ielem + 1_pInt
call CPFEM_general(3_pInt,& ! collect cycle
coordinates(i,j,k,1:3), defgradold(i,j,k,1:3,1:3), defgrad(i,j,k,1:3,1:3),&
temperature(i,j,k),timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
tensorField_real = 0.0_pReal ! needed because of the padding for FFTW
c_current = 0.0_pReal
ielem = 0_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
ielem = ielem + 1_pInt
call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
coordinates(i,j,k,1:3),&
defgradold(i,j,k,1:3,1:3), defgrad(i,j,k,1:3,1:3),& ! others get 2 (saves winding forward effort)
temperature(i,j,k),timeinc,ielem,1_pInt,&
cstress,dsde, pstress,dPdF)
CPFEM_mode = 2_pInt
tensorField_real(i,j,k,1:3,1:3) = pstress
c_current = c_current + dPdF
enddo; enddo; enddo
!--------------------------------------------------------------------------------------------------
! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
scalarField_real = 0.0_pReal
row = (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
column = (mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
tensorField_real(1:res(1),1:res(2),1:res(3),row,column)
endif
!--------------------------------------------------------------------------------------------------
! build polarization field
if (.not. simplified_algorithm) then
tau_real = 0.0_pReal ! padding
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
tau_real(i,j,k,1:3,1:3)&
= tensorField_real(i,j,k,1:3,1:3) &
- math_mul3333xx33(c0_reference,defgrad(i,j,k,1:3,1:3)-math_I3)!-defgrad_av_lab)
enddo; enddo; enddo
call fftw_execute_dft_r2c(plan_tau,tau_real,tau_complex)
endif
!--------------------------------------------------------------------------------------------------
! call function to calculate divergence from math (for post processing) to check results
if (debugDivergence) &
call divergence_fft(res,geomdim,3_pInt,&
tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_postProc) !padding
!--------------------------------------------------------------------------------------------------
! doing the FT because it simplifies calculation of average stress in real space also
call fftw_execute_dft_r2c(plan_stress,tensorField_real,tensorField_complex)
pstress_av_lab = real(tensorField_complex(1,1,1,1:3,1:3),pReal)*wgt
pstress_av = math_rotate_forward33(pstress_av_lab,bc(loadcase)%rotation)
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa:',&
math_transpose33(pstress_av)/1.e6
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (pstress_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = maxval(abs(pstress_av)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
print '(a)', ''
print '(a)', '... correcting deformation gradient to fulfill BCs ...............'
print '(a,es10.4,a,f6.2)', 'error stress = ',err_stress, ', rel. error = ',&
err_stress/err_stress_tol
defgradAim = defgradAim - math_mul3333xx33(s_prev, ((pstress_av - bc(loadcase)%stress))) ! residual on given stress components
if(debugGeneral) write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'new deformation aim:',&
math_transpose33(defgradAim)
print '(a,1x,es10.4)' , 'determinant of new deformation: ', math_det33(defgradAim)
else
err_stress_tol = 0.0_pReal
endif
defgradAim_lab = math_rotate_backward33(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
!--------------------------------------------------------------------------------------------------
! actual spectral method
print '(a)', ''
print '(a)', '... calculating equilibrium with spectral method .................'
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
call fftw_execute_dft_r2c(plan_scalarField_forth,scalarField_real,scalarField_complex)
print '(a,i1,1x,i1)', 'checking FT results of compontent ', row, column
print '(a,2(es10.4,1x))', 'max FT relative error ',&
maxval( real((scalarField_complex(1:res1_red,1:res(2),1:res(3))-&
tensorField_complex(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_complex(1:res1_red,1:res(2),1:res(3)))), &
maxval(aimag((scalarField_complex(1:res1_red,1:res(2),1:res(3))-&
tensorField_complex(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_complex(1:res1_red,1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
p_hat_avg = sqrt(maxval (math_eigenvalues33(math_mul33x33(real(tensorField_complex(1,1,1,1:3,1:3)),& ! L_2 norm of average stress (freq 0,0,0) in fourier space,
math_transpose33(real(tensorField_complex(1,1,1,1:3,1:3))))))) ! ignore imaginary part as it is always zero for real only input
err_div_RMS = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2)
do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
err_div_RMS = err_div_RMS &
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_complex(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(tensorField_complex(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal))
enddo
err_div_RMS = err_div_RMS & ! Those two layers do not have a conjugate complex counterpart
+ sum(real(math_mul33x3_complex(tensorField_complex(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(tensorField_complex(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
+ sum(real(math_mul33x3_complex(tensorField_complex(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(tensorField_complex(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)
enddo; enddo
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
err_div = err_div_RMS/p_hat_avg/sqrt(wgt) * correctionFactor ! criterion to stop iterations
!--------------------------------------------------------------------------------------------------
! calculate additional divergence criteria and report
if(debugDivergence) then ! calculate divergence again
err_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
temp3_Complex = math_mul33x3_complex(tensorField_complex(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*two_pi_img
err_div_max = max(err_div_max,sqrt(sum(abs(temp3_Complex)**2.0_pReal)))
divergence_complex(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_execute_dft_c2r(plan_divergence,divergence_complex,divergence_real)
divergence_real = divergence_real*wgt
err_real_div_RMS = 0.0_pReal
err_real_div_max = 0.0_pReal
max_div_error = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
max_div_error= max(max_div_error,maxval((divergence_real(i,j,k,1:3)&
-divergence_postProc(i,j,k,1:3))/divergence_real(i,j,k,1:3)))
err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of L_2 norm of div(stress) in real space
err_real_div_max = max(err_real_div_max, sqrt(sum(divergence_real(i,j,k,1:3)**2.0_pReal))) ! maximum of L two norm of div(stress) in real space
enddo; enddo; enddo
p_real_avg = sqrt(maxval (math_eigenvalues33(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space,
math_transpose33(pstress_av_lab)))))
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
err_div_max = err_div_max*sqrt(wgt)
print '(a,es10.4)', 'error divergence FT RMS = ',err_div_RMS
print '(a,es10.4)', 'error divergence FT max = ',err_div_max
print '(a,es10.4)', 'error divergence Real RMS = ',err_real_div_RMS
print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max
print '(a,es10.4)', 'divergence RMS FT/real = ',err_div_RMS/err_real_div_RMS
print '(a,es10.4)', 'divergence max FT/real = ',err_div_max/err_real_div_max
print '(a,es10.4)', 'avg stress FT/real = ',p_hat_avg*wgt/p_real_avg
print '(a,es10.4)', 'max deviat. from postProc = ',max_div_error
endif
print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', rel. error = ', err_div/err_div_tol
!--------------------------------------------------------------------------------------------------
! divergence is calculated from FT(stress), depending on algorithm use field for spectral method
if (.not. simplified_algorithm) tensorField_complex = tau_complex
!--------------------------------------------------------------------------------------------------
! to the actual spectral method calculation (mechanical equilibrium)
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then
do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
enddo; enddo
temp33_Real = math_inv33(math_mul3333xx33(c0_reference, xiDyad))
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt; do p=1_pInt,3_pInt
gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
(xiDyad(m,p) +xiDyad(p,m))
enddo; enddo; enddo; enddo
do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
temp33_Complex(m,n) = sum(gamma_hat(1,1,1, m,n, 1:3,1:3) * tensorField_complex(i,j,k,1:3,1:3))
enddo; enddo
tensorField_complex(i,j,k,1:3,1:3) = temp33_Complex
enddo; enddo; enddo
else ! use precalculated gamma-operator
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) * tensorField_complex(i,j,k,1:3,1:3))
enddo; enddo
tensorField_complex(i,j,k,1:3,1:3) = temp33_Complex
enddo; enddo; enddo
endif
tensorField_complex(1,1,1,1:3,1:3) = (defgradAim_lab - defgrad_av_lab)& ! assign average deformation gradient change to zero frequency (real part)
* real(Npoints,pReal)
if (debugFFTW) then
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
scalarField_complex(i,j,k) = tensorField_complex(i,j,k,row,column)
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! doing the inverse FT
call fftw_execute_dft_c2r(plan_correction,tensorField_complex,tensorField_real) ! back transform of fluct deformation gradient
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 inverse FT results
if (debugFFTW) then
print '(a,i1,1x,i1)', 'checking iFT results of compontent ', row, column
call fftw_execute_dft_c2r(plan_scalarField_back,scalarField_complex,scalarField_real)
print '(a,es10.4)', 'max iFT relative error ',&
maxval((scalarField_real(1:res(1),1:res(2),1:res(3))-&
tensorField_real(1:res(1),1:res(2),1:res(3),row,column))/&
scalarField_real(1:res(1),1:res(2),1:res(3)))
endif
!--------------------------------------------------------------------------------------------------
! calculate some additional output
if(debugGeneral) then
maxCorrectionSkew = 0.0_pReal
maxCorrectionSym = 0.0_pReal
temp33_Real = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
maxCorrectionSym = max(maxCorrectionSym,&
maxval(math_symmetric33(tensorField_real(i,j,k,1:3,1:3))))
maxCorrectionSkew = max(maxCorrectionSkew,&
maxval(math_skew33(tensorField_real(i,j,k,1:3,1:3))))
temp33_Real = temp33_Real + tensorField_real(i,j,k,1:3,1:3)
enddo; enddo; enddo
print '(a,1x,es10.4)' , 'max symmetrix correction of deformation:',&
maxCorrectionSym*wgt
print '(a,1x,es10.4)' , 'max skew correction of deformation:',&
maxCorrectionSkew*wgt
print '(a,1x,es10.4)' , 'max sym/skew of avg correction: ',&
maxval(math_symmetric33(temp33_real))/&
maxval(math_skew33(temp33_real))
endif
!--------------------------------------------------------------------------------------------------
! updated deformation gradient
defgrad = defgrad + tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
!--------------------------------------------------------------------------------------------------
! updated deformation gradient in case of fluctuation field algorithm
if (.not.simplified_algorithm) then
defgrad = tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3) * wgt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) + defgrad_av_lab
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
if(debugGeneral) then
defgradDetMax = -huge(1.0_pReal)
defgradDetMin = +huge(1.0_pReal)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
defgradDet = math_det33(defgrad(i,j,k,1:3,1:3))
defgradDetMax = max(defgradDetMax,defgradDet)
defgradDetMin = min(defgradDetMin,defgradDet)
enddo; enddo; enddo
print '(a,1x,es10.4)' , 'max determinant of deformation:', defgradDetMax
print '(a,1x,es10.4)' , 'min determinant of deformation:', defgradDetMin
endif
enddo ! end looping when convergency is achieved
print '(a)', ''
print '(a)', '=================================================================='
if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' NOT converged'
notConvergedCounter = notConvergedCounter + 1_pInt
else
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' converged'
endif
if (mod(totalIncsCounter -1_pInt,bc(loadcase)%outputfrequency) == 0_pInt) then ! at output frequency
print '(a)', ''
print '(a)', '... writing results to file ......................................'
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
endif
if (update_gamma) then
print*, 'update c0_reference '
c0_reference = c_current*wgt
endif
endif ! end calculation/forwarding
enddo ! end looping over incs in current loadcase
deallocate(c_reduced)
deallocate(s_reduced)
enddo ! end looping over loadcases
print '(a)', ''
print '(a)', '##################################################################'
print '(i6.6,a,i6.6,a)', notConvergedCounter, ' out of ', &
totalIncsCounter - restartReadInc, ' increments did not converge!'
close(538)
call fftw_destroy_plan(plan_stress); call fftw_destroy_plan(plan_correction)
if (debugDivergence) call fftw_destroy_plan(plan_divergence)
if (debugFFTW) then
call fftw_destroy_plan(plan_scalarField_forth)
call fftw_destroy_plan(plan_scalarField_back)
endif
stop 0
end program DAMASK_spectral
!********************************************************************
! quit subroutine to satisfy IO_error
!
!********************************************************************
subroutine quit(id)
use prec
implicit none
integer(pInt) id
stop
end subroutine