1246 lines
64 KiB
Fortran
1246 lines
64 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Utilities used by the different spectral solver variants
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!--------------------------------------------------------------------------------------------------
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module spectral_utilities
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use, intrinsic :: iso_c_binding
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use prec, only: &
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pReal, &
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pInt
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use math, only: &
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math_I3
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implicit none
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private
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#include <petsc/finclude/petscsys.h>
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include 'fftw3-mpi.f03'
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logical, public :: cutBack =.false. !< cut back of BVP solver in case convergence is not achieved or a material point is terminally ill
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integer(pInt), public, parameter :: maxPhaseFields = 2_pInt
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integer(pInt), public :: nActiveFields = 0_pInt
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!--------------------------------------------------------------------------------------------------
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! field labels information
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enum, bind(c)
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enumerator :: FIELD_UNDEFINED_ID, &
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FIELD_MECH_ID, &
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FIELD_THERMAL_ID, &
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FIELD_DAMAGE_ID, &
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FIELD_VACANCYDIFFUSION_ID
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end enum
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!--------------------------------------------------------------------------------------------------
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! grid related information information
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real(pReal), public :: wgt !< weighting factor 1/Nelems
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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integer(pInt), public :: grid1Red !< grid(1)/2
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real (C_DOUBLE), public, dimension(:,:,:,:,:), pointer :: tensorField_real !< real representation (some stress or deformation) of field_fourier
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:,:), pointer :: tensorField_fourier !< field on which the Fourier transform operates
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real(C_DOUBLE), public, dimension(:,:,:,:), pointer :: vectorField_real !< vector field real representation for fftw
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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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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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!--------------------------------------------------------------------------------------------------
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! plans for FFTW
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type(C_PTR), private :: &
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planTensorForth, & !< FFTW MPI plan P(x) to P(k)
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planTensorBack, & !< FFTW MPI plan F(k) to F(x)
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planVectorForth, & !< FFTW MPI plan v(x) to v(k)
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planVectorBack, & !< FFTW MPI plan v(k) to v(x)
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planScalarForth, & !< FFTW MPI plan s(x) to s(k)
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planScalarBack !< FFTW MPI plan s(k) to s(x)
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!--------------------------------------------------------------------------------------------------
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! variables controlling debugging
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logical, private :: &
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debugGeneral, & !< general debugging of spectral solver
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debugRotation, & !< also printing out results in lab frame
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debugPETSc !< use some in debug defined options for more verbose PETSc solution
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!--------------------------------------------------------------------------------------------------
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! derived types
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type, public :: tSolutionState !< return type of solution from spectral solver variants
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logical :: converged = .true.
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logical :: regrid = .false.
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logical :: stagConverged = .true.
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logical :: termIll = .false.
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integer(pInt) :: iterationsNeeded = 0_pInt
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end type tSolutionState
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type, public :: tBoundaryCondition !< set of parameters defining a boundary condition
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real(pReal), dimension(3,3) :: values = 0.0_pReal
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real(pReal), dimension(3,3) :: maskFloat = 0.0_pReal
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logical, dimension(3,3) :: maskLogical = .false.
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character(len=64) :: myType = 'None'
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end type tBoundaryCondition
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type, public :: tLoadCase
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real(pReal), dimension (3,3) :: rotation = math_I3 !< rotation of BC
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type(tBoundaryCondition) :: P, & !< stress BC
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deformation !< deformation BC (Fdot or L)
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real(pReal) :: time = 0.0_pReal !< length of increment
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integer(pInt) :: incs = 0_pInt, & !< number of increments
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outputfrequency = 1_pInt, & !< frequency of result writes
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restartfrequency = 0_pInt, & !< frequency of restart writes
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logscale = 0_pInt !< linear/logarithmic time inc flag
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logical :: followFormerTrajectory = .true. !< follow trajectory of former loadcase
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integer(kind(FIELD_UNDEFINED_ID)), allocatable :: ID(:)
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end type tLoadCase
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type, public :: tSolutionParams !< @todo use here the type definition for a full loadcase including mask
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real(pReal), dimension(3,3) :: P_BC, rotation_BC
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real(pReal) :: timeinc
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real(pReal) :: timeincOld
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real(pReal) :: density
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end type tSolutionParams
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type, public :: phaseFieldDataBin !< set of parameters defining a phase field
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real(pReal) :: diffusion = 0.0_pReal, & !< thermal conductivity
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mobility = 0.0_pReal, & !< thermal mobility
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phaseField0 = 0.0_pReal !< homogeneous damage field starting condition
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logical :: active = .false.
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character(len=64) :: label = ''
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end type phaseFieldDataBin
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enum, bind(c)
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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(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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utilities_updateGamma, &
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utilities_FFTtensorForward, &
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utilities_FFTtensorBackward, &
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utilities_FFTvectorForward, &
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utilities_FFTvectorBackward, &
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utilities_FFTscalarForward, &
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utilities_FFTscalarBackward, &
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utilities_fourierGammaConvolution, &
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utilities_fourierGreenConvolution, &
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utilities_divergenceRMS, &
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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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utilities_forwardField, &
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utilities_destroy, &
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utilities_updateIPcoords, &
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FIELD_UNDEFINED_ID, &
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FIELD_MECH_ID, &
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FIELD_THERMAL_ID, &
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FIELD_DAMAGE_ID
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private :: &
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utilities_getFreqDerivative
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief allocates all neccessary fields, sets debug flags, create plans for FFTW
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!> @details Sets the debug levels for general, divergence, restart and FFTW from the biwise coding
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!> provided by the debug module to logicals.
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!> Allocates all fields used by FFTW and create the corresponding plans depending on the debug
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!> level chosen.
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!> Initializes FFTW.
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!--------------------------------------------------------------------------------------------------
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subroutine utilities_init()
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
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use IO, only: &
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IO_error, &
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IO_warning, &
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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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petsc_defaultOptions, &
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petsc_options, &
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divergence_correction
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use debug, only: &
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debug_level, &
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debug_SPECTRAL, &
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debug_LEVELBASIC, &
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debug_SPECTRALDIVERGENCE, &
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debug_SPECTRALFFTW, &
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debug_SPECTRALPETSC, &
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debug_SPECTRALROTATION
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use debug, only: &
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PETSCDEBUG
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use math
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use mesh, only: &
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grid, &
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grid3, &
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grid3Offset, &
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geomSize
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implicit none
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external :: &
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PETScOptionsClear, &
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PETScOptionsInsertString, &
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MPI_Abort
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PetscErrorCode :: ierr
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integer(pInt) :: i, j, k
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integer(pInt), dimension(3) :: k_s
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type(C_PTR) :: &
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tensorField, & !< field containing data for FFTW in real and fourier space (in place)
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vectorField, & !< field containing data for FFTW in real space when debugging FFTW (no in place)
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scalarField !< field containing data for FFTW in real space when debugging FFTW (no in place)
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integer(C_INTPTR_T), dimension(3) :: gridFFTW
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integer(C_INTPTR_T) :: alloc_local, local_K, local_K_offset
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integer(C_INTPTR_T), parameter :: &
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scalarSize = 1_C_INTPTR_T, &
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vecSize = 3_C_INTPTR_T, &
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tensorSize = 9_C_INTPTR_T
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write(6,'(/,a)') ' <<<+- spectral_utilities init -+>>>'
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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#include "compilation_info.f90"
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!--------------------------------------------------------------------------------------------------
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! set debugging parameters
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debugGeneral = iand(debug_level(debug_SPECTRAL),debug_LEVELBASIC) /= 0
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debugRotation = iand(debug_level(debug_SPECTRAL),debug_SPECTRALROTATION) /= 0
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debugPETSc = iand(debug_level(debug_SPECTRAL),debug_SPECTRALPETSC) /= 0
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if(debugPETSc) write(6,'(3(/,a),/)') &
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' Initializing PETSc with debug options: ', &
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trim(PETScDebug), &
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' add more using the PETSc_Options keyword in numerics.config '; flush(6)
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call PetscOptionsClear(ierr); CHKERRQ(ierr)
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if(debugPETSc) call PetscOptionsInsertString(trim(PETSCDEBUG),ierr)
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CHKERRQ(ierr)
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call PetscOptionsInsertString(trim(petsc_defaultOptions),ierr)
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CHKERRQ(ierr)
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call PetscOptionsInsertString(trim(petsc_options),ierr)
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CHKERRQ(ierr)
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grid1Red = grid(1)/2_pInt + 1_pInt
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wgt = 1.0/real(product(grid),pReal)
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write(6,'(a,3(i12 ))') ' grid a b c: ', grid
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write(6,'(a,3(es12.5))') ' size x y z: ', geomSize
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select case (spectral_derivative)
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case ('continuous')
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spectral_derivative_ID = DERIVATIVE_CONTINUOUS_ID
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case ('central_difference')
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spectral_derivative_ID = DERIVATIVE_CENTRAL_DIFF_ID
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case ('fwbw_difference')
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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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if (divergence_correction == 1_pInt) then
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do j = 1_pInt, 3_pInt
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if (j /= minloc(geomSize,1) .and. j /= maxloc(geomSize,1)) &
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scaledGeomSize = geomSize/geomSize(j)
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enddo
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elseif (divergence_correction == 2_pInt) then
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do j = 1_pInt, 3_pInt
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if ( j /= int(minloc(geomSize/real(grid,pReal),1),pInt) &
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.and. j /= int(maxloc(geomSize/real(grid,pReal),1),pInt)) &
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scaledGeomSize = geomSize/geomSize(j)*real(grid(j),pReal)
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enddo
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else
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scaledGeomSize = geomSize
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endif
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!--------------------------------------------------------------------------------------------------
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! MPI allocation
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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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PETSC_COMM_WORLD, local_K, local_K_offset)
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allocate (xi1st (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, 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 for second derivatives, 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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call c_f_pointer(tensorField, tensorField_fourier, [3_C_INTPTR_T,3_C_INTPTR_T, &
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gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T , gridFFTW(2),local_K]) ! place a pointer for a fourier tensor representation
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vectorField = fftw_alloc_complex(vecSize*alloc_local)
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call c_f_pointer(vectorField, vectorField_real, [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 vector representation
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call c_f_pointer(vectorField, vectorField_fourier,[3_C_INTPTR_T,&
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gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T, gridFFTW(2),local_K]) ! place a pointer for a fourier vector representation
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scalarField = fftw_alloc_complex(scalarSize*alloc_local) ! allocate data for real representation (no in place transform)
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call c_f_pointer(scalarField, scalarField_real, &
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[2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1),gridFFTW(2),local_K]) ! place a pointer for a real scalar representation
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call c_f_pointer(scalarField, scalarField_fourier, &
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[ gridFFTW(1)/2_C_INTPTR_T + 1 ,gridFFTW(2),local_K]) ! place a pointer for a fourier scarlar representation
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!--------------------------------------------------------------------------------------------------
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! tensor MPI fftw plans
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planTensorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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tensorField_real, tensorField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planTensorForth)) call IO_error(810, ext_msg='planTensorForth')
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planTensorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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tensorField_fourier,tensorField_real, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! all processors, planer precision
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if (.not. C_ASSOCIATED(planTensorBack)) call IO_error(810, ext_msg='planTensorBack')
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!--------------------------------------------------------------------------------------------------
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! vector MPI fftw plans
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planVectorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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vectorField_real, vectorField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planVectorForth)) call IO_error(810, ext_msg='planVectorForth')
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planVectorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
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vectorField_fourier,vectorField_real, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! all processors, planer precision
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if (.not. C_ASSOCIATED(planVectorBack)) call IO_error(810, ext_msg='planVectorBack')
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!--------------------------------------------------------------------------------------------------
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! scalar MPI fftw plans
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planScalarForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
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scalarField_real, scalarField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planScalarForth)) call IO_error(810, ext_msg='planScalarForth')
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planScalarBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order, no. of transforms
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scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
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scalarField_fourier,scalarField_real, & ! input data, output data
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PETSC_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planScalarBack)) call IO_error(810, ext_msg='planScalarBack')
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!--------------------------------------------------------------------------------------------------
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! general initialization of FFTW (see manual on fftw.org for more details)
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if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(0_pInt,ext_msg='Fortran to C') ! check for correct precision in C
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call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
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if (debugGeneral) write(6,'(/,a)') ' FFTW initialized'; flush(6)
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!--------------------------------------------------------------------------------------------------
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! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
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do k = grid3Offset+1_pInt, grid3Offset+grid3
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k_s(3) = k - 1_pInt
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if(k > grid(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - grid(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do j = 1_pInt, grid(2)
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k_s(2) = j - 1_pInt
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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) = 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
|
|
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,grid1Red,grid(2),grid3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
|
|
endif
|
|
|
|
end subroutine utilities_init
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief updates references stiffness and potentially precalculated gamma operator
|
|
!> @details Sets the current reference stiffness to the stiffness given as an argument.
|
|
!> If the gamma operator is precalculated, it is calculated with this stiffness.
|
|
!> In case of a on-the-fly calculation, only the reference stiffness is updated.
|
|
!> Also writes out the current reference stiffness for restart.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_updateGamma(C,saveReference)
|
|
use IO, only: &
|
|
IO_write_jobRealFile
|
|
use numerics, only: &
|
|
memory_efficient, &
|
|
worldrank
|
|
use mesh, only: &
|
|
grid3Offset, &
|
|
grid3,&
|
|
grid
|
|
use math, only: &
|
|
math_det33, &
|
|
math_invert
|
|
|
|
implicit none
|
|
real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness
|
|
logical , intent(in) :: saveReference !< save reference stiffness to file for restart
|
|
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
|
|
real(pReal), dimension(6,6) :: matA, matInvA
|
|
integer(pInt) :: &
|
|
i, j, k, &
|
|
l, m, n, o
|
|
logical :: err
|
|
|
|
C_ref = C
|
|
if (saveReference) then
|
|
if (worldrank == 0_pInt) then
|
|
write(6,'(/,a)') ' writing reference stiffness to file'
|
|
flush(6)
|
|
call IO_write_jobRealFile(777,'C_ref',size(C_ref))
|
|
write (777,rec=1) C_ref
|
|
close(777)
|
|
endif
|
|
endif
|
|
|
|
if(.not. memory_efficient) then
|
|
gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal) ! for the singular point and any non invertible A
|
|
do k = grid3Offset+1_pInt, grid3Offset+grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
|
|
if (any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
|
|
matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
|
|
matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
|
|
if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
|
|
call math_invert(6_pInt, matA, matInvA, err)
|
|
temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
|
|
gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_complex(l,n)* &
|
|
conjg(-xi1st(o,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
|
|
endif
|
|
endif
|
|
enddo; enddo; enddo
|
|
endif
|
|
|
|
end subroutine utilities_updateGamma
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief forward FFT of data in field_real to field_fourier
|
|
!> @details Does an unweighted filtered FFT transform from real to complex
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTtensorForward()
|
|
implicit none
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the tensor FFT
|
|
call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
|
|
|
|
end subroutine utilities_FFTtensorForward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief backward FFT of data in field_fourier to field_real
|
|
!> @details Does an weighted inverse FFT transform from complex to real
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTtensorBackward()
|
|
implicit none
|
|
|
|
call fftw_mpi_execute_dft_c2r(planTensorBack,tensorField_fourier,tensorField_real)
|
|
tensorField_real = tensorField_real * wgt ! normalize the result by number of elements
|
|
|
|
end subroutine utilities_FFTtensorBackward
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief forward FFT of data in scalarField_real to scalarField_fourier
|
|
!> @details Does an unweighted filtered FFT transform from real to complex
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTscalarForward()
|
|
implicit none
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the scalar FFT
|
|
call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
|
|
|
|
end subroutine utilities_FFTscalarForward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief backward FFT of data in scalarField_fourier to scalarField_real
|
|
!> @details Does an weighted inverse FFT transform from complex to real
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTscalarBackward()
|
|
implicit none
|
|
|
|
call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real)
|
|
scalarField_real = scalarField_real * wgt ! normalize the result by number of elements
|
|
|
|
end subroutine utilities_FFTscalarBackward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
|
|
!> @details Does an unweighted filtered FFT transform from real to complex.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTvectorForward()
|
|
implicit none
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the vector FFT
|
|
call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
|
|
|
|
end subroutine utilities_FFTvectorForward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief backward FFT of data in field_fourier to field_real
|
|
!> @details Does an weighted inverse FFT transform from complex to real
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_FFTvectorBackward()
|
|
implicit none
|
|
|
|
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
|
|
vectorField_real = vectorField_real * wgt ! normalize the result by number of elements
|
|
|
|
end subroutine utilities_FFTvectorBackward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief doing convolution gamma_hat * field_real, ensuring that average value = fieldAim
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierGammaConvolution(fieldAim)
|
|
use numerics, only: &
|
|
memory_efficient
|
|
use math, only: &
|
|
math_det33, &
|
|
math_invert
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid, &
|
|
grid3Offset
|
|
|
|
implicit none
|
|
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
|
|
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
|
|
real(pReal) :: matA(6,6), matInvA(6,6)
|
|
|
|
integer(pInt) :: &
|
|
i, j, k, &
|
|
l, m, n, o
|
|
logical :: err
|
|
|
|
|
|
write(6,'(/,a)') ' ... doing gamma convolution ...............................................'
|
|
flush(6)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! do the actual spectral method calculation (mechanical equilibrium)
|
|
memoryEfficient: if(memory_efficient) then
|
|
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
|
|
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
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
|
|
matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
|
|
matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
|
|
if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
|
|
call math_invert(6_pInt, matA, matInvA, err)
|
|
temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
|
|
gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*conjg(-xi1st(o,i,j,k))*xi1st(m,i,j,k)
|
|
else
|
|
gamma_hat(1:3,1:3,1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
endif
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
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
|
|
else memoryEfficient
|
|
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) = 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)
|
|
|
|
end subroutine utilities_fourierGammaConvolution
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief doing convolution DamageGreenOp_hat * field_real
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierGreenConvolution(D_ref, mobility_ref, deltaT)
|
|
|
|
use math, only: &
|
|
math_mul33x3, &
|
|
PI
|
|
use mesh, only: &
|
|
grid, &
|
|
grid3
|
|
|
|
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
|
|
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
|
|
GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ &
|
|
(cmplx(mobility_ref,0.0_pReal,pReal) + cmplx(deltaT,0.0_pReal)*&
|
|
sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal),xi1st(1:3,i,j,k)))) ! why not use dot_product
|
|
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine utilities_fourierGreenConvolution
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate root mean square of divergence of field_fourier
|
|
!--------------------------------------------------------------------------------------------------
|
|
real(pReal) function utilities_divergenceRMS()
|
|
use IO, only: &
|
|
IO_error
|
|
use mesh, only: &
|
|
geomSize, &
|
|
grid, &
|
|
grid3
|
|
|
|
implicit none
|
|
integer(pInt) :: i, j, k, ierr
|
|
complex(pReal), dimension(3) :: rescaledGeom
|
|
|
|
external :: &
|
|
MPI_Allreduce
|
|
|
|
write(6,'(/,a)') ' ... calculating divergence ................................................'
|
|
flush(6)
|
|
|
|
rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
utilities_divergenceRMS = 0.0_pReal
|
|
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(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))*rescaledGeom))**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))*rescaledGeom))**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(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
|
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
|
|
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
|
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
|
|
+ sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
|
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) &
|
|
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
|
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**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)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='utilities_divergenceRMS')
|
|
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
|
|
|
|
|
|
end function utilities_divergenceRMS
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate max of curl of field_fourier
|
|
!--------------------------------------------------------------------------------------------------
|
|
real(pReal) function utilities_curlRMS()
|
|
use IO, only: &
|
|
IO_error
|
|
use mesh, only: &
|
|
geomSize, &
|
|
grid, &
|
|
grid3
|
|
|
|
implicit none
|
|
integer(pInt) :: i, j, k, l, ierr
|
|
complex(pReal), dimension(3,3) :: curl_fourier
|
|
complex(pReal), dimension(3) :: rescaledGeom
|
|
|
|
external :: &
|
|
MPI_Allreduce
|
|
|
|
write(6,'(/,a)') ' ... calculating curl ......................................................'
|
|
flush(6)
|
|
|
|
rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating max curl criterion in Fourier space
|
|
utilities_curlRMS = 0.0_pReal
|
|
|
|
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)*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))
|
|
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)*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))
|
|
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)*rescaledGeom(2) &
|
|
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3))
|
|
curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3) &
|
|
-tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1))
|
|
curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1) &
|
|
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(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)
|
|
enddo; enddo
|
|
|
|
call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='utilities_curlRMS')
|
|
utilities_curlRMS = sqrt(utilities_curlRMS) * wgt
|
|
if(grid(1) == 1_pInt) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
|
|
|
|
end function utilities_curlRMS
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates mask compliance tensor used to adjust F to fullfill stress BC
|
|
!--------------------------------------------------------------------------------------------------
|
|
function utilities_maskedCompliance(rot_BC,mask_stress,C)
|
|
use prec, only: &
|
|
prec_isNaN
|
|
use IO, only: &
|
|
IO_error
|
|
use math, only: &
|
|
math_Plain3333to99, &
|
|
math_plain99to3333, &
|
|
math_rotate_forward3333, &
|
|
math_rotate_forward33, &
|
|
math_invert
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3,3,3) :: utilities_maskedCompliance !< masked compliance
|
|
real(pReal), intent(in) , dimension(3,3,3,3) :: C !< current average stiffness
|
|
real(pReal), intent(in) , dimension(3,3) :: rot_BC !< rotation of load frame
|
|
logical, intent(in), dimension(3,3) :: mask_stress !< mask of stress BC
|
|
integer(pInt) :: j, k, m, n
|
|
logical, dimension(9) :: mask_stressVector
|
|
real(pReal), dimension(9,9) :: temp99_Real
|
|
integer(pInt) :: size_reduced = 0_pInt
|
|
real(pReal), dimension(:,:), allocatable :: &
|
|
s_reduced, & !< reduced compliance matrix (depending on number of stress BC)
|
|
c_reduced, & !< reduced stiffness (depending on number of stress BC)
|
|
sTimesC !< temp variable to check inversion
|
|
logical :: errmatinv
|
|
character(len=1024):: formatString
|
|
|
|
mask_stressVector = reshape(transpose(mask_stress), [9])
|
|
size_reduced = int(count(mask_stressVector), pInt)
|
|
if(size_reduced > 0_pInt )then
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (sTimesC(size_reduced,size_reduced), source =0.0_pReal)
|
|
temp99_Real = math_Plain3333to99(math_rotate_forward3333(C,rot_BC))
|
|
|
|
if(debugGeneral) then
|
|
write(6,'(/,a)') ' ... updating masked compliance ............................................'
|
|
write(6,'(/,a,/,9(9(2x,f12.7,1x)/))',advance='no') ' Stiffness C (load) / GPa =',&
|
|
transpose(temp99_Real)/1.e9_pReal
|
|
flush(6)
|
|
endif
|
|
k = 0_pInt ! calculate reduced stiffness
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector(m)) then
|
|
j = j + 1_pInt
|
|
c_reduced(k,j) = temp99_Real(n,m)
|
|
endif; enddo; endif; enddo
|
|
|
|
call math_invert(size_reduced, c_reduced, s_reduced, errmatinv) ! invert reduced stiffness
|
|
if (any(prec_isNaN(s_reduced))) errmatinv = .true.
|
|
if(errmatinv) call IO_error(error_ID=400_pInt,ext_msg='utilities_maskedCompliance')
|
|
temp99_Real = 0.0_pReal ! fill up compliance with zeros
|
|
k = 0_pInt
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector(m)) then
|
|
j = j + 1_pInt
|
|
temp99_Real(n,m) = s_reduced(k,j)
|
|
endif; enddo; endif; enddo
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! check if inversion was successful
|
|
sTimesC = matmul(c_reduced,s_reduced)
|
|
do m=1_pInt, size_reduced
|
|
do n=1_pInt, size_reduced
|
|
if(m==n .and. abs(sTimesC(m,n)) > (1.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! diagonal elements of S*C should be 1
|
|
if(m/=n .and. abs(sTimesC(m,n)) > (0.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! off diagonal elements of S*C should be 0
|
|
enddo
|
|
enddo
|
|
if(debugGeneral .or. errmatinv) then
|
|
write(formatString, '(I16.16)') size_reduced
|
|
formatString = '(/,a,/,'//trim(formatString)//'('//trim(formatString)//'(2x,es9.2,1x)/))'
|
|
write(6,trim(formatString),advance='no') ' C * S (load) ', &
|
|
transpose(matmul(c_reduced,s_reduced))
|
|
write(6,trim(formatString),advance='no') ' S (load) ', transpose(s_reduced)
|
|
endif
|
|
if(errmatinv) call IO_error(error_ID=400_pInt,ext_msg='utilities_maskedCompliance')
|
|
deallocate(c_reduced)
|
|
deallocate(s_reduced)
|
|
deallocate(sTimesC)
|
|
else
|
|
temp99_real = 0.0_pReal
|
|
endif
|
|
if(debugGeneral) &
|
|
write(6,'(/,a,/,9(9(2x,f12.7,1x)/),/)',advance='no') ' Masked Compliance (load) * GPa =', &
|
|
transpose(temp99_Real*1.e9_pReal)
|
|
flush(6)
|
|
utilities_maskedCompliance = math_Plain99to3333(temp99_Real)
|
|
|
|
end function utilities_maskedCompliance
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate scalar gradient in fourier field
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierScalarGradient()
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid
|
|
|
|
implicit none
|
|
integer(pInt) :: i, j, k
|
|
|
|
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
|
|
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)
|
|
|
|
end subroutine utilities_fourierScalarGradient
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate vector divergence in fourier field
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierVectorDivergence()
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid
|
|
|
|
implicit none
|
|
integer(pInt) :: i, j, k
|
|
|
|
scalarField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
|
|
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k) + &
|
|
sum(vectorField_fourier(1:3,i,j,k)*conjg(-xi1st(1:3,i,j,k)))
|
|
|
|
end subroutine utilities_fourierVectorDivergence
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate vector gradient in fourier field
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierVectorGradient()
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid
|
|
|
|
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
|
|
|
|
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
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_constitutiveResponse(F_lastInc,F,timeinc, &
|
|
P,C_volAvg,C_minmaxAvg,P_av,forwardData,rotation_BC)
|
|
use IO, only: &
|
|
IO_error
|
|
use debug, only: &
|
|
debug_reset, &
|
|
debug_info
|
|
use math, only: &
|
|
math_transpose33, &
|
|
math_rotate_forward33, &
|
|
math_det33
|
|
use mesh, only: &
|
|
grid,&
|
|
grid3
|
|
use FEsolving, only: &
|
|
restartWrite
|
|
use CPFEM2, only: &
|
|
CPFEM_general
|
|
use homogenization, only: &
|
|
materialpoint_F0, &
|
|
materialpoint_F, &
|
|
materialpoint_P, &
|
|
materialpoint_dPdF
|
|
|
|
implicit none
|
|
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
|
|
F_lastInc, & !< target deformation gradient
|
|
F !< previous deformation gradient
|
|
real(pReal), intent(in) :: timeinc !< loading time
|
|
logical, intent(in) :: forwardData !< age results
|
|
real(pReal), intent(in), dimension(3,3) :: rotation_BC !< rotation of load frame
|
|
|
|
real(pReal),intent(out), dimension(3,3,3,3) :: C_volAvg, C_minmaxAvg !< average stiffness
|
|
real(pReal),intent(out), dimension(3,3) :: P_av !< average PK stress
|
|
real(pReal),intent(out), dimension(3,3,grid(1),grid(2),grid3) :: P !< PK stress
|
|
|
|
logical :: &
|
|
age
|
|
|
|
integer(pInt) :: &
|
|
j,k,ierr
|
|
real(pReal), dimension(3,3,3,3) :: max_dPdF, min_dPdF
|
|
real(pReal) :: max_dPdF_norm, min_dPdF_norm, defgradDetMin, defgradDetMax, defgradDet
|
|
|
|
write(6,'(/,a)') ' ... evaluating constitutive response ......................................'
|
|
flush(6)
|
|
age = .False.
|
|
|
|
if (forwardData) then ! aging results
|
|
age = .True.
|
|
materialpoint_F0 = reshape(F_lastInc, [3,3,1,product(grid(1:2))*grid3])
|
|
endif
|
|
if (cutBack) age = .False. ! restore saved variables
|
|
|
|
materialpoint_F = reshape(F,[3,3,1,product(grid(1:2))*grid3])
|
|
call debug_reset() ! this has no effect on rank >0
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate bounds of det(F) and report
|
|
if(debugGeneral) then
|
|
defgradDetMax = -huge(1.0_pReal)
|
|
defgradDetMin = +huge(1.0_pReal)
|
|
do j = 1_pInt, product(grid(1:2))*grid3
|
|
defgradDet = math_det33(materialpoint_F(1:3,1:3,1,j))
|
|
defgradDetMax = max(defgradDetMax,defgradDet)
|
|
defgradDetMin = min(defgradDetMin,defgradDet)
|
|
end do
|
|
|
|
write(6,'(a,1x,es11.4)') ' max determinant of deformation =', defgradDetMax
|
|
write(6,'(a,1x,es11.4)') ' min determinant of deformation =', defgradDetMin
|
|
flush(6)
|
|
endif
|
|
|
|
call CPFEM_general(age,timeinc)
|
|
|
|
max_dPdF = 0.0_pReal
|
|
max_dPdF_norm = 0.0_pReal
|
|
min_dPdF = huge(1.0_pReal)
|
|
min_dPdF_norm = huge(1.0_pReal)
|
|
do k = 1_pInt, product(grid(1:2))*grid3
|
|
if (max_dPdF_norm < sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)) then
|
|
max_dPdF = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)
|
|
max_dPdF_norm = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)
|
|
endif
|
|
if (min_dPdF_norm > sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)) then
|
|
min_dPdF = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)
|
|
min_dPdF_norm = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)
|
|
endif
|
|
end do
|
|
|
|
call MPI_Allreduce(MPI_IN_PLACE,max_dPdF,81,MPI_DOUBLE,MPI_MAX,PETSC_COMM_WORLD,ierr)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='MPI_Allreduce max')
|
|
call MPI_Allreduce(MPI_IN_PLACE,min_dPdF,81,MPI_DOUBLE,MPI_MIN,PETSC_COMM_WORLD,ierr)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='MPI_Allreduce min')
|
|
|
|
C_minmaxAvg = 0.5_pReal*(max_dPdF + min_dPdF)
|
|
C_volAvg = sum(sum(materialpoint_dPdF,dim=6),dim=5) * wgt
|
|
|
|
call MPI_Allreduce(MPI_IN_PLACE,C_volAvg,81,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
|
|
|
call debug_info() ! this has no effect on rank >0
|
|
|
|
restartWrite = .false. ! reset restartWrite status
|
|
cutBack = .false. ! reset cutBack status
|
|
|
|
P = reshape(materialpoint_P, [3,3,grid(1),grid(2),grid3])
|
|
P_av = sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt ! average of P
|
|
call MPI_Allreduce(MPI_IN_PLACE,P_av,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
|
if (debugRotation) &
|
|
write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress (lab) / MPa =',&
|
|
math_transpose33(P_av)*1.e-6_pReal
|
|
P_av = math_rotate_forward33(P_av,rotation_BC)
|
|
write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress / MPa =',&
|
|
math_transpose33(P_av)*1.e-6_pReal
|
|
flush(6)
|
|
|
|
end subroutine utilities_constitutiveResponse
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates forward rate, either guessing or just add delta/timeinc
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function utilities_calculateRate(avRate,timeinc_old,guess,field_lastInc,field)
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid
|
|
|
|
implicit none
|
|
real(pReal), intent(in), dimension(3,3) :: avRate !< homogeneous addon
|
|
real(pReal), intent(in) :: &
|
|
timeinc_old !< timeinc of last step
|
|
logical, intent(in) :: &
|
|
guess !< guess along former trajectory
|
|
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
|
|
field_lastInc, & !< data of previous step
|
|
field !< data of current step
|
|
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: &
|
|
utilities_calculateRate
|
|
|
|
if (guess) then
|
|
utilities_calculateRate = (field-field_lastInc) / timeinc_old
|
|
else
|
|
utilities_calculateRate = spread(spread(spread(avRate,3,grid(1)),4,grid(2)),5,grid3)
|
|
endif
|
|
|
|
end function utilities_calculateRate
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief forwards a field with a pointwise given rate, if aim is given,
|
|
!> ensures that the average matches the aim
|
|
!--------------------------------------------------------------------------------------------------
|
|
function utilities_forwardField(timeinc,field_lastInc,rate,aim)
|
|
use mesh, only: &
|
|
grid3, &
|
|
grid
|
|
|
|
implicit none
|
|
real(pReal), intent(in) :: &
|
|
timeinc !< timeinc of current step
|
|
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
|
|
field_lastInc, & !< initial field
|
|
rate !< rate by which to forward
|
|
real(pReal), intent(in), optional, dimension(3,3) :: &
|
|
aim !< average field value aim
|
|
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: &
|
|
utilities_forwardField
|
|
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
|
|
PetscErrorCode :: ierr
|
|
|
|
external :: &
|
|
MPI_Allreduce
|
|
|
|
utilities_forwardField = field_lastInc + rate*timeinc
|
|
if (present(aim)) then !< correct to match average
|
|
fieldDiff = sum(sum(sum(utilities_forwardField,dim=5),dim=4),dim=3)*wgt
|
|
call MPI_Allreduce(MPI_IN_PLACE,fieldDiff,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
|
fieldDiff = fieldDiff - aim
|
|
utilities_forwardField = utilities_forwardField - &
|
|
spread(spread(spread(fieldDiff,3,grid(1)),4,grid(2)),5,grid3)
|
|
endif
|
|
|
|
end function utilities_forwardField
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
|
|
!> @details this is the full operator to calculate derivatives, i.e. 2 \pi i k for the
|
|
! standard approach
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function utilities_getFreqDerivative(k_s)
|
|
use math, only: &
|
|
PI
|
|
use mesh, only: &
|
|
geomSize, &
|
|
grid
|
|
|
|
implicit none
|
|
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)
|
|
|
|
end select
|
|
|
|
end function utilities_getFreqDerivative
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate coordinates in current configuration for given defgrad field
|
|
! using integration in Fourier space. Similar as in mesh.f90, but using data already defined for
|
|
! convolution
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_updateIPcoords(F)
|
|
use prec, only: &
|
|
cNeq
|
|
use IO, only: &
|
|
IO_error
|
|
use math, only: &
|
|
math_mul33x3
|
|
use mesh, only: &
|
|
grid, &
|
|
grid3, &
|
|
grid3Offset, &
|
|
geomSize, &
|
|
mesh_ipCoordinates
|
|
implicit none
|
|
|
|
real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F
|
|
integer(pInt) :: i, j, k, m, ierr
|
|
real(pReal), dimension(3) :: step, offset_coords
|
|
real(pReal), dimension(3,3) :: Favg
|
|
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()
|
|
|
|
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
|
|
if (any(cNeq(xi1st(1:3,i,j,k),cmplx(0.0_pReal,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)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='update_IPcoords')
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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)
|
|
if(ierr /=0_pInt) call IO_error(894_pInt, ext_msg='update_IPcoords')
|
|
offset_coords = math_mul33x3(Favg,step/2.0_pReal) - offset_coords
|
|
m = 1_pInt
|
|
do k = 1_pInt,grid3; do j = 1_pInt,grid(2); do i = 1_pInt,grid(1)
|
|
mesh_ipCoordinates(1:3,1,m) = vectorField_real(1:3,i,j,k) &
|
|
+ offset_coords &
|
|
+ math_mul33x3(Favg,step*real([i,j,k+grid3Offset]-1_pInt,pReal))
|
|
m = m+1_pInt
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine utilities_updateIPcoords
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief cleans up
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_destroy()
|
|
implicit none
|
|
|
|
call fftw_destroy_plan(planTensorForth)
|
|
call fftw_destroy_plan(planTensorBack)
|
|
call fftw_destroy_plan(planVectorForth)
|
|
call fftw_destroy_plan(planVectorBack)
|
|
call fftw_destroy_plan(planScalarForth)
|
|
call fftw_destroy_plan(planScalarBack)
|
|
|
|
end subroutine utilities_destroy
|
|
|
|
|
|
end module spectral_utilities
|