!-------------------------------------------------------------------------------------------------- !> @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 #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY) use MPI_f08 #endif use prec use parallelization use IO use spectral_utilities use discretization_grid use homogenization use YAML_types use config implicit none private type :: tNumerics integer :: & itmax !< maximum number of iterations real(pReal) :: & eps_thermal_atol, & !< absolute tolerance for thermal equilibrium eps_thermal_rtol !< relative tolerance for thermal equilibrium end type tNumerics type(tNumerics) :: num type(tSolutionParams) :: params !-------------------------------------------------------------------------------------------------- ! PETSc data SNES :: thermal_snes Vec :: solution_vec PetscInt :: xstart, xend, ystart, yend, zstart, zend real(pReal), dimension(:,:,:), allocatable :: & T_current, & !< field of current temperature T_lastInc, & !< field of previous temperature T_stagInc !< field of staggered temperature !-------------------------------------------------------------------------------------------------- ! reference diffusion tensor, mobility etc. integer :: totalIter = 0 !< total iteration in current increment real(pReal), dimension(3,3) :: K_ref real(pReal) :: mu_ref public :: & grid_thermal_spectral_init, & grid_thermal_spectral_solution, & grid_thermal_spectral_forward contains !-------------------------------------------------------------------------------------------------- !> @brief allocates all neccessary fields and fills them with data ! ToDo: Restart not implemented !-------------------------------------------------------------------------------------------------- subroutine grid_thermal_spectral_init(T_0) real(pReal), intent(in) :: T_0 PetscInt, dimension(0:worldsize-1) :: localK integer :: i, j, k, ce DM :: thermal_grid PetscScalar, dimension(:,:,:), pointer :: T_PETSc integer(MPI_INTEGER_KIND) :: err_MPI PetscErrorCode :: err_PETSc class(tNode), pointer :: & num_grid print'(/,1x,a)', '<<<+- grid_thermal_spectral init -+>>>' print'(/,1x,a)', 'P. Shanthraj et al., Handbook of Mechanics of Materials, 2019' print'( 1x,a)', 'https://doi.org/10.1007/978-981-10-6855-3_80' !------------------------------------------------------------------------------------------------- ! read numerical parameters and do sanity checks num_grid => config_numerics%get('grid',defaultVal=emptyDict) num%itmax = num_grid%get_asInt ('itmax', defaultVal=250) num%eps_thermal_atol = num_grid%get_asFloat ('eps_thermal_atol',defaultVal=1.0e-2_pReal) num%eps_thermal_rtol = num_grid%get_asFloat ('eps_thermal_rtol',defaultVal=1.0e-6_pReal) if (num%itmax <= 1) call IO_error(301,ext_msg='itmax') if (num%eps_thermal_atol <= 0.0_pReal) call IO_error(301,ext_msg='eps_thermal_atol') if (num%eps_thermal_rtol <= 0.0_pReal) call IO_error(301,ext_msg='eps_thermal_rtol') !-------------------------------------------------------------------------------------------------- ! set default and user defined options for PETSc call PetscOptionsInsertString(PETSC_NULL_OPTIONS,'-thermal_snes_type newtonls -thermal_snes_mf & &-thermal_snes_ksp_ew -thermal_ksp_type fgmres',err_PETSc) CHKERRQ(err_PETSc) call PetscOptionsInsertString(PETSC_NULL_OPTIONS,num_grid%get_asString('petsc_options',defaultVal=''),err_PETSc) CHKERRQ(err_PETSc) !-------------------------------------------------------------------------------------------------- ! initialize solver specific parts of PETSc call SNESCreate(PETSC_COMM_WORLD,thermal_snes,err_PETSc); CHKERRQ(err_PETSc) call SNESSetOptionsPrefix(thermal_snes,'thermal_',err_PETSc);CHKERRQ(err_PETSc) localK = 0_pPetscInt localK(worldrank) = int(grid3,pPetscInt) call MPI_Allreduce(MPI_IN_PLACE,localK,worldsize,MPI_INTEGER,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' 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 int(grid(1),pPetscInt),int(grid(2),pPetscInt),int(grid(3),pPetscInt), & ! global grid 1_pPetscInt, 1_pPetscInt, int(worldsize,pPetscInt), & 1_pPetscInt, 0_pPetscInt, & ! #dof (T, scalar), ghost boundary width (domain overlap) [int(grid(1),pPetscInt)],[int(grid(2),pPetscInt)],localK, & ! local grid thermal_grid,err_PETSc) ! handle, error CHKERRQ(err_PETSc) call SNESSetDM(thermal_snes,thermal_grid,err_PETSc); CHKERRQ(err_PETSc) ! connect snes to da call DMsetFromOptions(thermal_grid,err_PETSc); CHKERRQ(err_PETSc) call DMsetUp(thermal_grid,err_PETSc); CHKERRQ(err_PETSc) call DMCreateGlobalVector(thermal_grid,solution_vec,err_PETSc) ! global solution vector (grid x 1, i.e. every def grad tensor) CHKERRQ(err_PETSc) call DMDASNESSetFunctionLocal(thermal_grid,INSERT_VALUES,formResidual,PETSC_NULL_SNES,err_PETSc) ! residual vector of same shape as solution vector CHKERRQ(err_PETSc) call SNESSetFromOptions(thermal_snes,err_PETSc); CHKERRQ(err_PETSc) ! pull it all together with additional CLI arguments !-------------------------------------------------------------------------------------------------- ! init fields call DMDAGetCorners(thermal_grid,xstart,ystart,zstart,xend,yend,zend,err_PETSc) CHKERRQ(err_PETSc) xend = xstart + xend - 1 yend = ystart + yend - 1 zend = zstart + zend - 1 allocate(T_current(grid(1),grid(2),grid3), source=0.0_pReal) allocate(T_lastInc(grid(1),grid(2),grid3), source=0.0_pReal) allocate(T_stagInc(grid(1),grid(2),grid3), source=0.0_pReal) ce = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) ce = ce + 1 T_current(i,j,k) = T_0 T_lastInc(i,j,k) = T_current(i,j,k) T_stagInc(i,j,k) = T_current(i,j,k) call homogenization_thermal_setField(T_0,0.0_pReal,ce) end do; end do; end do call DMDAVecGetArrayF90(thermal_grid,solution_vec,T_PETSc,err_PETSc) CHKERRQ(err_PETSc) T_PETSc(xstart:xend,ystart:yend,zstart:zend) = T_current call DMDAVecRestoreArrayF90(thermal_grid,solution_vec,T_PETSc,err_PETSc) CHKERRQ(err_PETSc) call updateReference end subroutine grid_thermal_spectral_init !-------------------------------------------------------------------------------------------------- !> @brief solution for the spectral thermal scheme with internal iterations !-------------------------------------------------------------------------------------------------- function grid_thermal_spectral_solution(Delta_t) result(solution) real(pReal), intent(in) :: & Delta_t !< increment in time for current solution integer :: i, j, k, ce type(tSolutionState) :: solution PetscInt :: devNull PetscReal :: T_min, T_max, stagNorm integer(MPI_INTEGER_KIND) :: err_MPI PetscErrorCode :: err_PETSc SNESConvergedReason :: reason solution%converged =.false. !-------------------------------------------------------------------------------------------------- ! set module wide availabe data params%Delta_t = Delta_t call SNESSolve(thermal_snes,PETSC_NULL_VEC,solution_vec,err_PETSc) CHKERRQ(err_PETSc) call SNESGetConvergedReason(thermal_snes,reason,err_PETSc) CHKERRQ(err_PETSc) if (reason < 1) then solution%converged = .false. solution%iterationsNeeded = num%itmax else solution%converged = .true. solution%iterationsNeeded = totalIter end if stagNorm = maxval(abs(T_current - T_stagInc)) call MPI_Allreduce(MPI_IN_PLACE,stagNorm,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_MAX,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' solution%stagConverged = stagNorm < max(num%eps_thermal_atol, num%eps_thermal_rtol*maxval(T_current)) call MPI_Allreduce(MPI_IN_PLACE,solution%stagConverged,1_MPI_INTEGER_KIND,MPI_LOGICAL,MPI_LAND,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' T_stagInc = T_current !-------------------------------------------------------------------------------------------------- ! updating thermal state ce = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) ce = ce + 1 call homogenization_thermal_setField(T_current(i,j,k),(T_current(i,j,k)-T_lastInc(i,j,k))/params%Delta_t,ce) end do; end do; end do call VecMin(solution_vec,devNull,T_min,err_PETSc); CHKERRQ(err_PETSc) call VecMax(solution_vec,devNull,T_max,err_PETSc); CHKERRQ(err_PETSc) if (solution%converged) & print'(/,1x,a)', '... thermal conduction converged ..................................' print'(/,1x,a,f8.4,2x,f8.4,2x,f8.4)', 'Minimum|Maximum|Delta Temperature / K = ', T_min, T_max, stagNorm print'(/,1x,a)', '===========================================================================' flush(IO_STDOUT) end function grid_thermal_spectral_solution !-------------------------------------------------------------------------------------------------- !> @brief forwarding routine !-------------------------------------------------------------------------------------------------- subroutine grid_thermal_spectral_forward(cutBack) logical, intent(in) :: cutBack integer :: i, j, k, ce DM :: dm_local PetscScalar, dimension(:,:,:), pointer :: x_scal PetscErrorCode :: err_PETSc if (cutBack) then T_current = T_lastInc T_stagInc = T_lastInc !-------------------------------------------------------------------------------------------------- ! reverting thermal field state call SNESGetDM(thermal_snes,dm_local,err_PETSc) CHKERRQ(err_PETSc) call DMDAVecGetArrayF90(dm_local,solution_vec,x_scal,err_PETSc) !< get the data out of PETSc to work with CHKERRQ(err_PETSc) x_scal(xstart:xend,ystart:yend,zstart:zend) = T_current call DMDAVecRestoreArrayF90(dm_local,solution_vec,x_scal,err_PETSc) CHKERRQ(err_PETSc) ce = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) ce = ce + 1 call homogenization_thermal_setField(T_current(i,j,k),(T_current(i,j,k)-T_lastInc(i,j,k))/params%Delta_t,ce) end do; end do; end do else T_lastInc = T_current call updateReference end if end subroutine grid_thermal_spectral_forward !-------------------------------------------------------------------------------------------------- !> @brief forms the spectral thermal residual vector !-------------------------------------------------------------------------------------------------- subroutine formResidual(in,x_scal,f_scal,dummy,dummy_err) 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 :: dummy_err integer :: i, j, k, ce T_current = x_scal !-------------------------------------------------------------------------------------------------- ! evaluate polarization field scalarField_real = 0.0_pReal scalarField_real(1:grid(1),1:grid(2),1:grid3) = T_current call utilities_FFTscalarForward call utilities_fourierScalarGradient !< calculate gradient of temperature field call utilities_FFTvectorBackward ce = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) ce = ce + 1 vectorField_real(1:3,i,j,k) = matmul(homogenization_K_T(ce) - K_ref, vectorField_real(1:3,i,j,k)) end do; end do; end do call utilities_FFTvectorForward call utilities_fourierVectorDivergence !< calculate temperature divergence in fourier field call utilities_FFTscalarBackward ce = 0 do k = 1, grid3; do j = 1, grid(2); do i = 1,grid(1) ce = ce + 1 scalarField_real(i,j,k) = params%Delta_t*(scalarField_real(i,j,k) + homogenization_f_T(ce)) & + homogenization_mu_T(ce) * (T_lastInc(i,j,k) - T_current(i,j,k)) & + mu_ref*T_current(i,j,k) end do; end do; end do !-------------------------------------------------------------------------------------------------- ! convolution of temperature field with green operator call utilities_FFTscalarForward call utilities_fourierGreenConvolution(K_ref, mu_ref, params%Delta_t) call utilities_FFTscalarBackward !-------------------------------------------------------------------------------------------------- ! constructing residual f_scal = T_current - scalarField_real(1:grid(1),1:grid(2),1:grid3) end subroutine formResidual !-------------------------------------------------------------------------------------------------- !> @brief update reference viscosity and conductivity !-------------------------------------------------------------------------------------------------- subroutine updateReference() integer :: ce integer(MPI_INTEGER_KIND) :: err_MPI K_ref = 0.0_pReal mu_ref = 0.0_pReal do ce = 1, product(grid(1:2))*grid3 K_ref = K_ref + homogenization_K_T(ce) mu_ref = mu_ref + homogenization_mu_T(ce) end do K_ref = K_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,K_ref,9_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' mu_ref = mu_ref*wgt call MPI_Allreduce(MPI_IN_PLACE,mu_ref,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' end subroutine updateReference end module grid_thermal_spectral