MODgvec_MHD3D_evalFunc Module

Module MHD3D Evalfunc

Evaluate the MHD3D functional and its derivative


Uses

  • module~~modgvec_mhd3d_evalfunc~~UsesGraph module~modgvec_mhd3d_evalfunc MODgvec_MHD3D_evalFunc module~modgvec_globals MODgvec_Globals module~modgvec_mhd3d_evalfunc->module~modgvec_globals module~sll_m_spline_matrix sll_m_spline_matrix module~modgvec_mhd3d_evalfunc->module~sll_m_spline_matrix module~sll_m_spline_matrix_banded sll_m_spline_matrix_banded module~modgvec_mhd3d_evalfunc->module~sll_m_spline_matrix_banded iso_fortran_env iso_fortran_env module~modgvec_globals->iso_fortran_env module~sll_m_spline_matrix->module~sll_m_spline_matrix_banded module~sll_m_errors sll_m_errors module~sll_m_spline_matrix->module~sll_m_errors module~sll_m_spline_matrix_base sll_m_spline_matrix_base module~sll_m_spline_matrix->module~sll_m_spline_matrix_base module~sll_m_spline_matrix_dense sll_m_spline_matrix_dense module~sll_m_spline_matrix->module~sll_m_spline_matrix_dense module~sll_m_working_precision sll_m_working_precision module~sll_m_spline_matrix->module~sll_m_working_precision module~sll_m_spline_matrix_banded->iso_fortran_env module~sll_m_assert sll_m_assert module~sll_m_spline_matrix_banded->module~sll_m_assert module~sll_m_spline_matrix_banded->module~sll_m_errors module~sll_m_spline_matrix_banded->module~sll_m_spline_matrix_base module~sll_m_spline_matrix_banded->module~sll_m_working_precision module~sll_m_errors->iso_fortran_env module~sll_m_spline_matrix_base->module~sll_m_working_precision module~sll_m_spline_matrix_dense->iso_fortran_env module~sll_m_spline_matrix_dense->module~sll_m_assert module~sll_m_spline_matrix_dense->module~sll_m_errors module~sll_m_spline_matrix_dense->module~sll_m_spline_matrix_base module~sll_m_spline_matrix_dense->module~sll_m_working_precision

Used by

  • module~~modgvec_mhd3d_evalfunc~~UsedByGraph module~modgvec_mhd3d_evalfunc MODgvec_MHD3D_evalFunc proc~finalizemhd3d t_functional_mhd3d%FinalizeMHD3D proc~finalizemhd3d->module~modgvec_mhd3d_evalfunc proc~initmhd3d t_functional_mhd3d%InitMHD3D proc~initmhd3d->module~modgvec_mhd3d_evalfunc proc~initsolutionmhd3d t_functional_mhd3d%InitSolutionMHD3D proc~initsolutionmhd3d->module~modgvec_mhd3d_evalfunc proc~minimizemhd3d_descent t_minimizer_mhd3d%MinimizeMHD3D_descent proc~minimizemhd3d_descent->module~modgvec_mhd3d_evalfunc proc~minimizemhd3d_resetdescent t_minimizer_mhd3d%MinimizeMHD3d_ResetDescent proc~minimizemhd3d_resetdescent->module~modgvec_mhd3d_evalfunc proc~new_minimizer new_minimizer proc~new_minimizer->module~modgvec_mhd3d_evalfunc proc~writestatetoascii WriteStateToASCII proc~writestatetoascii->module~modgvec_mhd3d_evalfunc program~gvec_post GVEC_POST program~gvec_post->module~modgvec_mhd3d_evalfunc

Variables

Type Visibility Attributes Name Initial
real(kind=wp), private, ALLOCATABLE :: pres_GP(:)

mass profile
real(kind=wp), private, ALLOCATABLE :: chiPrime_GP(:)

s derivative of poloidal flux
real(kind=wp), private, ALLOCATABLE :: phiPrime_GP(:)

s derivative of toroidal flux
real(kind=wp), private, ALLOCATABLE :: phiPrime2_GP(:)

s derivative of toroidal flux : |Phi'(s)|^2
real(kind=wp), private, ALLOCATABLE :: X1_IP_GP(:,:)

evaluation of X1
real(kind=wp), private, ALLOCATABLE :: X2_IP_GP(:,:)

evaluation of X2
real(kind=wp), private, ALLOCATABLE :: J_h(:,:)

Jacobian of the mapping h (X1,X2,zeta) -->(x,y,z)
real(kind=wp), private, ALLOCATABLE :: J_p(:,:)

Jacobian of poloidal mapping: dX1_dsdX2_dtheta - dX2_dsdX1_theta
real(kind=wp), private, ALLOCATABLE :: sJ_h(:,:)

1/J_h
real(kind=wp), private, ALLOCATABLE :: sJ_p(:,:)

1/J_p
real(kind=wp), private, ALLOCATABLE :: detJ(:,:)

global Jacobian: detJ=sqrt(det g)=J_h*J_p )
real(kind=wp), private, ALLOCATABLE :: sdetJ(:,:)

1/detJ
real(kind=wp), private, ALLOCATABLE :: dX1_ds(:,:)

radial derivative of X1
real(kind=wp), private, ALLOCATABLE :: dX2_ds(:,:)

radial derivative of X2
real(kind=wp), private, ALLOCATABLE :: dX1_dthet(:,:)

theta derivative of X1
real(kind=wp), private, ALLOCATABLE :: dX2_dthet(:,:)

theta derivative of X2
real(kind=wp), private, ALLOCATABLE :: dLA_dthet(:,:)

theta derivative of lambda
real(kind=wp), private, ALLOCATABLE :: dX1_dzeta(:,:)

zeta derivative of X1
real(kind=wp), private, ALLOCATABLE :: dX2_dzeta(:,:)

zeta derivative of X2
real(kind=wp), private, ALLOCATABLE :: dLA_dzeta(:,:)

zeta derivative of lambda
real(kind=wp), private, ALLOCATABLE :: b_thet(:,:)

b_thet=(iota-dlamba_dzeta,1+dlambda_dtheta), normalized contravariant magnetic field
real(kind=wp), private, ALLOCATABLE :: b_zeta(:,:)

b_zeta=1+dlambda_dtheta, normalized contravariant magnetic field
real(kind=wp), private, ALLOCATABLE :: sJ_bcov_thet(:,:)

covariant normalized magnetic field, scaled with 1/J:
real(kind=wp), private, ALLOCATABLE :: sJ_bcov_zeta(:,:)

sJ_bcov_alpha=1/detJ (g_{alpha,theta} b_theta + g_{alpha,zeta) b_zeta)
real(kind=wp), private, ALLOCATABLE :: bbcov_sJ(:,:)

(b^alphag_{alpha,beta}b^beta)/(detJ)
real(kind=wp), private, ALLOCATABLE :: g_tt(:,:)

metric tensor g_(theta,theta)
real(kind=wp), private, ALLOCATABLE :: g_tz(:,:)

metric tensor g_(theta,zeta )=g_(zeta,theta)
real(kind=wp), private, ALLOCATABLE :: g_zz(:,:)

metric tensor g_(zeta ,zeta )
real(kind=wp), private, ALLOCATABLE :: g_t1(:,:)

metric tensor dq^i_dthet G^i1 (sum over i=1,2,3)
real(kind=wp), private, ALLOCATABLE :: g_t2(:,:)

metric tensor dq^i_dthet G^i2
real(kind=wp), private, ALLOCATABLE :: g_z1(:,:)

metric tensor dq^i_dzeta G^i1
real(kind=wp), private, ALLOCATABLE :: g_z2(:,:)

metric tensor dq^i_dzeta G^i2
real(kind=wp), private, ALLOCATABLE :: Jh_dq1(:,:)

hmap dJh/dq1
real(kind=wp), private, ALLOCATABLE :: Jh_dq2(:,:)

hmap dJh/dq2
real(kind=wp), private, ALLOCATABLE :: gtt_dq1(:,:)

hmap dg_{thet,theta}/dq1
real(kind=wp), private, ALLOCATABLE :: gtz_dq1(:,:)

hmap dg_{theta,zeta}/dq1
real(kind=wp), private, ALLOCATABLE :: gzz_dq1(:,:)

hmap dg_{zeta,zeta}/dq1
real(kind=wp), private, ALLOCATABLE :: gtt_dq2(:,:)

hmap dg_{thet,theta}/dq2
real(kind=wp), private, ALLOCATABLE :: gtz_dq2(:,:)

hmap dg_{theta,zeta}/dq2
real(kind=wp), private, ALLOCATABLE :: gzz_dq2(:,:)

hmap dg_{zeta,zeta}/dq2
real(kind=wp), private, ALLOCATABLE :: Gh11(:,:)

hmap G_{11}
real(kind=wp), private, ALLOCATABLE :: Gh22(:,:)

hmap G_{22}
integer, private :: nGP
integer, private :: nGP_str
integer, private :: nGP_end
integer, private :: mn_IP
real(kind=wp), private :: dthet_dzeta
real(kind=wp), private, ALLOCATABLE :: w_GP(:)
integer, private :: nElems
integer, private :: nElems_str
integer, private :: nElems_end
integer, private :: degGP
real(kind=wp), private, ALLOCATABLE :: s_GP(:)
real(kind=wp), private, ALLOCATABLE :: zeta_IP(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX1_tt(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX1_tz(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX1_zz(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX1(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX1_ss(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX2_tt(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX2_tz(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX2_zz(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX2(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DX2_ss(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DLA_tt(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DLA_tz(:)
real(kind=wp), private, CONTIGUOUS, POINTER :: DLA_zz(:)
real(kind=wp), private, ALLOCATABLE, TARGET :: D_buf(:,:)

2d array container for all 1d array abpove (is the one allocated)
class(sll_c_spline_matrix), private, ALLOCATABLE :: precond_X1(:)

container for preconditioner matrices
class(sll_c_spline_matrix), private, ALLOCATABLE :: precond_X2(:)

container for preconditioner matrices
class(sll_c_spline_matrix), private, ALLOCATABLE :: precond_LA(:)

container for preconditioner matrices

Functions

public function EvalEnergy(dofs_in, callEvalAux, JacCheck) result(W_MHD3D)

Evaluate 3D MHD energy NOTE: set callEvalaux >0 if not called before for the same dofs_in !!

Arguments

Type IntentOptional Attributes Name
class(t_sol_var_MHD3D), intent(in) :: dofs_in

input solution
logical, intent(in) :: callEvalAux

set True if evalAux was not called on dofs_in
integer, intent(inout) :: JacCheck

if 1 on input: abort if detJ<0. if 2 on input, no abort, unchanged if detJ>0 ,return <=-1 if detJ<=0

Return Value real(kind=wp)

total integral of MHD3D energy W_MHD3D= int ( p/(gamma-1) + 1/(2mu_0) |B|^2) detJ ds dtheta dzeta


Subroutines

public subroutine InitializeMHD3D_evalFunc()

Initialize Module

Arguments

None

public subroutine InitProfilesGP()

Initialize Profiles at GP!!!

Arguments

None

public subroutine EvalAux(dofs_in, JacCheck)

Evaluate auxiliary variables at input state, writes onto module variables!!! This includes the check of the Jacobian, which is crucial for the validity of the computations. only a positive Jacobian is accepted.

Arguments

Type IntentOptional Attributes Name
class(t_sol_var_MHD3D), intent(in) :: dofs_in

input solution
integer, intent(inout) :: JacCheck

if 1 on input: abort if detJ<1e-12max|detJ|. if 2 on input, no abort, unchanged if min(detJ)>=1e-12max|detJ|, else return -3 negative Jacobian everywhere (left-handed coordinates), -2 relative Jacobian too small, -1 Jacobian with sign change.

public subroutine EvalTotals(dofs_in, vol, surfAvg)

Evaluate total volume and average surface

Arguments

Type IntentOptional Attributes Name
class(t_sol_var_MHD3D), intent(in) :: dofs_in

input solution
real(kind=wp), intent(out) :: vol

total integral of the volume
real(kind=wp), intent(out) :: surfAvg

average polodial surface

public subroutine EvalForce(dofs_in, callEvalAux, JacCheck, F_MHD3D, noBC)

Evaluate the variation of the Energy = Force... F_j=-(D_U W(U))_j = -DW(u_h)*testfunc_j NOTE: set callEvalaux TRUE if not called before for the same dofs_in !!

Read more…

Arguments

Type IntentOptional Attributes Name
class(t_sol_var_MHD3D), intent(in) :: dofs_in

input solution
logical, intent(in) :: callEvalAux

set True if evalAux was not called on dofs_in
integer, intent(inout) :: JacCheck

if 1 on input: abort if detJ<0. if 2 on input, no abort, unchanged if detJ>0 ,return -1 if detJ<=0
class(t_sol_var_MHD3D), intent(inout) :: F_MHD3D

variation of the energy projected onto the basis functions of dofs_in
logical, intent(in), optional :: noBC

private subroutine ApplyBC_Fstrong(whichVar, F_MHD3D)

Applies strong boundary condition to force DOF

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: whichVar

=1: X1, =2: X2, =3: LA
class(t_sol_var_MHD3D), intent(inout) :: F_MHD3D

variation of the energy projected onto the basis functions of dofs_in

private subroutine BuildPrecond()

Build preconditioner matrices for X1,X2,LA and factorize, for all modes the matrix is only radially dependent, and has the form K_ij = int(s,0,1) d/ds sbase_i(s) (s) d/ds sbase_j(s) + sbase_i(s) ((s) + |Phi'(s)|^2 (-m^2 (s) - n^2 (s) ) ) sbase_j(s) where < > denote an average over the angular coordinates

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Arguments

None

private subroutine ApplyPrecond(nBase, precond, F_inout)

Apply preconditioner matrix for single mode of one variable

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: nBase

length of inout vector
type(sll_t_spline_matrix_banded), intent(in) :: precond

preconditioner matrix (factorized!)
real(kind=wp), intent(inout) :: F_inout(1:nBase)

apply preconditioner on this force vector

public subroutine FinalizeMHD3D_EvalFunc()

Finalize Module

Arguments

None