!-------------------------------------------------------------------------------------------------- !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @author Shaokang Zhang, Max-Planck-Institut für Eisenforschung GmbH !> @brief Spectral solver for thermal conduction !-------------------------------------------------------------------------------------------------- module grid_thermal_spectral #include #include use PETScdmda use PETScsnes use prec, only: & pReal use spectral_utilities, only: & tSolutionState, & tSolutionParams implicit none private !-------------------------------------------------------------------------------------------------- ! derived types type(tSolutionParams), private :: params !-------------------------------------------------------------------------------------------------- ! PETSc data SNES, private :: thermal_snes Vec, private :: solution_vec PetscInt, private :: xstart, xend, ystart, yend, zstart, zend real(pReal), private, dimension(:,:,:), allocatable :: & temperature_current, & !< field of current temperature temperature_lastInc, & !< field of previous temperature temperature_stagInc !< field of staggered temperature !-------------------------------------------------------------------------------------------------- ! reference diffusion tensor, mobility etc. integer, private :: totalIter = 0 !< total iteration in current increment real(pReal), dimension(3,3), private :: D_ref real(pReal), private :: mobility_ref public :: & grid_thermal_spectral_init, & grid_thermal_spectral_solution, & grid_thermal_spectral_forward private :: & formResidual contains !-------------------------------------------------------------------------------------------------- !> @brief allocates all neccessary fields and fills them with data ! ToDo: Restart not implemented !-------------------------------------------------------------------------------------------------- subroutine grid_thermal_spectral_init use spectral_utilities, only: & wgt use mesh, only: & grid, & grid3 use thermal_conduction, only: & thermal_conduction_getConductivity33, & thermal_conduction_getMassDensity, & thermal_conduction_getSpecificHeat use material, only: & material_homogenizationAt, & temperature, & thermalMapping use numerics, only: & worldrank, & worldsize, & petsc_options implicit none PetscInt, dimension(worldsize) :: localK integer :: i, j, k, cell DM :: thermal_grid PetscScalar, dimension(:,:,:), pointer :: x_scal PetscErrorCode :: ierr write(6,'(/,a)') ' <<<+- grid_thermal_spectral init -+>>>' write(6,'(/,a)') ' Shanthraj et al., Handbook of Mechanics of Materials, 2019' write(6,'(a)') ' https://doi.org/10.1007/978-981-10-6855-3_80' !-------------------------------------------------------------------------------------------------- ! set default and user defined options for PETSc call PETScOptionsInsertString(PETSC_NULL_OPTIONS,'-thermal_snes_type ngmres',ierr) CHKERRQ(ierr) call PETScOptionsInsertString(PETSC_NULL_OPTIONS,trim(petsc_options),ierr) CHKERRQ(ierr) !-------------------------------------------------------------------------------------------------- ! initialize solver specific parts of PETSc call SNESCreate(PETSC_COMM_WORLD,thermal_snes,ierr); CHKERRQ(ierr) call SNESSetOptionsPrefix(thermal_snes,'thermal_',ierr);CHKERRQ(ierr) localK = 0 localK(worldrank+1) = grid3 call MPI_Allreduce(MPI_IN_PLACE,localK,worldsize,MPI_INTEGER,MPI_SUM,PETSC_COMM_WORLD,ierr) call DMDACreate3D(PETSC_COMM_WORLD, & DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, & ! cut off stencil at boundary DMDA_STENCIL_BOX, & ! Moore (26) neighborhood around central point grid(1),grid(2),grid(3), & ! global grid 1, 1, worldsize, & 1, 0, & ! #dof (thermal phase field), ghost boundary width (domain overlap) [grid(1)],[grid(2)],localK, & ! local grid thermal_grid,ierr) ! handle, error CHKERRQ(ierr) call SNESSetDM(thermal_snes,thermal_grid,ierr); CHKERRQ(ierr) ! connect snes to da call DMsetFromOptions(thermal_grid,ierr); CHKERRQ(ierr) call DMsetUp(thermal_grid,ierr); CHKERRQ(ierr) call DMCreateGlobalVector(thermal_grid,solution_vec,ierr); CHKERRQ(ierr) ! global solution vector (grid x 1, i.e. every def grad tensor) call DMDASNESSetFunctionLocal(thermal_grid,INSERT_VALUES,formResidual,PETSC_NULL_SNES,ierr) ! residual vector of same shape as solution vector CHKERRQ(ierr) call SNESSetFromOptions(thermal_snes,ierr); CHKERRQ(ierr) ! pull it all together with additional CLI arguments !-------------------------------------------------------------------------------------------------- ! init fields call DMDAGetCorners(thermal_grid,xstart,ystart,zstart,xend,yend,zend,ierr) CHKERRQ(ierr) xend = xstart + xend - 1 yend = ystart + yend - 1 zend = zstart + zend - 1 allocate(temperature_current(grid(1),grid(2),grid3), source=0.0_pReal) allocate(temperature_lastInc(grid(1),grid(2),grid3), source=0.0_pReal) allocate(temperature_stagInc(grid(1),grid(2),grid3), source=0.0_pReal) cell = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 temperature_current(i,j,k) = temperature(material_homogenizationAt(cell))% & p(thermalMapping(material_homogenizationAt(cell))%p(1,cell)) temperature_lastInc(i,j,k) = temperature_current(i,j,k) temperature_stagInc(i,j,k) = temperature_current(i,j,k) enddo; enddo; enddo call DMDAVecGetArrayF90(thermal_grid,solution_vec,x_scal,ierr); CHKERRQ(ierr) !< get the data out of PETSc to work with x_scal(xstart:xend,ystart:yend,zstart:zend) = temperature_current call DMDAVecRestoreArrayF90(thermal_grid,solution_vec,x_scal,ierr); CHKERRQ(ierr) !-------------------------------------------------------------------------------------------------- ! thermal reference diffusion update cell = 0 D_ref = 0.0_pReal mobility_ref = 0.0_pReal do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 D_ref = D_ref + thermal_conduction_getConductivity33(1,cell) mobility_ref = mobility_ref + thermal_conduction_getMassDensity(1,cell)* & thermal_conduction_getSpecificHeat(1,cell) enddo; enddo; enddo D_ref = D_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,D_ref,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) mobility_ref = mobility_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,mobility_ref,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) end subroutine grid_thermal_spectral_init !-------------------------------------------------------------------------------------------------- !> @brief solution for the spectral thermal scheme with internal iterations !-------------------------------------------------------------------------------------------------- function grid_thermal_spectral_solution(timeinc,timeinc_old,loadCaseTime) result(solution) use numerics, only: & itmax, & err_thermal_tolAbs, & err_thermal_tolRel use mesh, only: & grid, & grid3 use thermal_conduction, only: & thermal_conduction_putTemperatureAndItsRate implicit none real(pReal), intent(in) :: & timeinc, & !< increment in time for current solution timeinc_old, & !< increment in time of last increment loadCaseTime !< remaining time of current load case integer :: i, j, k, cell type(tSolutionState) :: solution PetscInt :: position PetscReal :: minTemperature, maxTemperature, stagNorm, solnNorm PetscErrorCode :: ierr SNESConvergedReason :: reason solution%converged =.false. !-------------------------------------------------------------------------------------------------- ! set module wide availabe data params%timeinc = timeinc params%timeincOld = timeinc_old call SNESSolve(thermal_snes,PETSC_NULL_VEC,solution_vec,ierr); CHKERRQ(ierr) call SNESGetConvergedReason(thermal_snes,reason,ierr); CHKERRQ(ierr) if (reason < 1) then solution%converged = .false. solution%iterationsNeeded = itmax else solution%converged = .true. solution%iterationsNeeded = totalIter endif stagNorm = maxval(abs(temperature_current - temperature_stagInc)) solnNorm = maxval(abs(temperature_current)) call MPI_Allreduce(MPI_IN_PLACE,stagNorm,1,MPI_DOUBLE,MPI_MAX,PETSC_COMM_WORLD,ierr) call MPI_Allreduce(MPI_IN_PLACE,solnNorm,1,MPI_DOUBLE,MPI_MAX,PETSC_COMM_WORLD,ierr) temperature_stagInc = temperature_current solution%stagConverged = stagNorm < min(err_thermal_tolAbs, err_thermal_tolRel*solnNorm) !-------------------------------------------------------------------------------------------------- ! updating thermal state cell = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 call thermal_conduction_putTemperatureAndItsRate(temperature_current(i,j,k), & (temperature_current(i,j,k)-temperature_lastInc(i,j,k))/params%timeinc, & 1,cell) enddo; enddo; enddo call VecMin(solution_vec,position,minTemperature,ierr); CHKERRQ(ierr) call VecMax(solution_vec,position,maxTemperature,ierr); CHKERRQ(ierr) if (solution%converged) & write(6,'(/,a)') ' ... thermal conduction converged ..................................' write(6,'(/,a,f8.4,2x,f8.4,2x,f8.4,/)',advance='no') ' Minimum|Maximum|Delta Temperature / K = ',& minTemperature, maxTemperature, stagNorm write(6,'(/,a)') ' ===========================================================================' flush(6) end function grid_thermal_spectral_solution !-------------------------------------------------------------------------------------------------- !> @brief forwarding routine !-------------------------------------------------------------------------------------------------- subroutine grid_thermal_spectral_forward use mesh, only: & grid, & grid3 use spectral_utilities, only: & cutBack, & wgt use thermal_conduction, only: & thermal_conduction_putTemperatureAndItsRate, & thermal_conduction_getConductivity33, & thermal_conduction_getMassDensity, & thermal_conduction_getSpecificHeat implicit none integer :: i, j, k, cell DM :: dm_local PetscScalar, dimension(:,:,:), pointer :: x_scal PetscErrorCode :: ierr if (cutBack) then temperature_current = temperature_lastInc temperature_stagInc = temperature_lastInc !-------------------------------------------------------------------------------------------------- ! reverting thermal field state cell = 0 call SNESGetDM(thermal_snes,dm_local,ierr); CHKERRQ(ierr) call DMDAVecGetArrayF90(dm_local,solution_vec,x_scal,ierr); CHKERRQ(ierr) !< get the data out of PETSc to work with x_scal(xstart:xend,ystart:yend,zstart:zend) = temperature_current call DMDAVecRestoreArrayF90(dm_local,solution_vec,x_scal,ierr); CHKERRQ(ierr) do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 call thermal_conduction_putTemperatureAndItsRate(temperature_current(i,j,k), & (temperature_current(i,j,k) - & temperature_lastInc(i,j,k))/params%timeinc, & 1,cell) enddo; enddo; enddo else !-------------------------------------------------------------------------------------------------- ! update rate and forward last inc temperature_lastInc = temperature_current cell = 0 D_ref = 0.0_pReal mobility_ref = 0.0_pReal do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 D_ref = D_ref + thermal_conduction_getConductivity33(1,cell) mobility_ref = mobility_ref + thermal_conduction_getMassDensity(1,cell)* & thermal_conduction_getSpecificHeat(1,cell) enddo; enddo; enddo D_ref = D_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,D_ref,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) mobility_ref = mobility_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,mobility_ref,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) endif end subroutine grid_thermal_spectral_forward !-------------------------------------------------------------------------------------------------- !> @brief forms the spectral thermal residual vector !-------------------------------------------------------------------------------------------------- subroutine formResidual(in,x_scal,f_scal,dummy,ierr) use mesh, only: & grid, & grid3 use math, only: & math_mul33x3 use spectral_utilities, only: & scalarField_real, & vectorField_real, & utilities_FFTvectorForward, & utilities_FFTvectorBackward, & utilities_FFTscalarForward, & utilities_FFTscalarBackward, & utilities_fourierGreenConvolution, & utilities_fourierScalarGradient, & utilities_fourierVectorDivergence use thermal_conduction, only: & thermal_conduction_getSourceAndItsTangent, & thermal_conduction_getConductivity33, & thermal_conduction_getMassDensity, & thermal_conduction_getSpecificHeat implicit none DMDALocalInfo, dimension(DMDA_LOCAL_INFO_SIZE) :: & in PetscScalar, dimension( & XG_RANGE,YG_RANGE,ZG_RANGE), intent(in) :: & x_scal PetscScalar, dimension( & X_RANGE,Y_RANGE,Z_RANGE), intent(out) :: & f_scal PetscObject :: dummy PetscErrorCode :: ierr integer :: i, j, k, cell real(pReal) :: Tdot, dTdot_dT temperature_current = x_scal !-------------------------------------------------------------------------------------------------- ! evaluate polarization field scalarField_real = 0.0_pReal scalarField_real(1:grid(1),1:grid(2),1:grid3) = temperature_current call utilities_FFTscalarForward call utilities_fourierScalarGradient !< calculate gradient of damage field call utilities_FFTvectorBackward cell = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 vectorField_real(1:3,i,j,k) = math_mul33x3(thermal_conduction_getConductivity33(1,cell) - D_ref, & vectorField_real(1:3,i,j,k)) enddo; enddo; enddo call utilities_FFTvectorForward call utilities_fourierVectorDivergence !< calculate damage divergence in fourier field call utilities_FFTscalarBackward cell = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) cell = cell + 1 call thermal_conduction_getSourceAndItsTangent(Tdot, dTdot_dT, temperature_current(i,j,k), 1, cell) scalarField_real(i,j,k) = params%timeinc*scalarField_real(i,j,k) + & params%timeinc*Tdot + & thermal_conduction_getMassDensity (1,cell)* & thermal_conduction_getSpecificHeat(1,cell)*(temperature_lastInc(i,j,k) - & temperature_current(i,j,k)) + & mobility_ref*temperature_current(i,j,k) enddo; enddo; enddo !-------------------------------------------------------------------------------------------------- ! convolution of damage field with green operator call utilities_FFTscalarForward call utilities_fourierGreenConvolution(D_ref, mobility_ref, params%timeinc) call utilities_FFTscalarBackward !-------------------------------------------------------------------------------------------------- ! constructing residual f_scal = temperature_current - scalarField_real(1:grid(1),1:grid(2),1:grid3) end subroutine formResidual end module grid_thermal_spectral