hmap_frenet_eval_all_e

public pure subroutine hmap_frenet_eval_all_e(xv, q1, q2, dX1_dt, dX2_dt, dX1_dz, dX2_dz, Jh, g_tt, g_tz, g_zz, Jh_dq1, g_tt_dq1, g_tz_dq1, g_zz_dq1, Jh_dq2, g_tt_dq2, g_tz_dq2, g_zz_dq2, g_t1, g_t2, g_z1, g_z2, Gh11, Gh22)

evaluate all quantities at one given point (elemental)

Arguments

Type	Intent		Name
type(t_hmap_frenet_auxvar),	intent(in)	::	xv	precomputed auxiliary variables
real(kind=wp),	intent(in)	::	q1	solution variables q1,q2
real(kind=wp),	intent(in)	::	q2	solution variables q1,q2
real(kind=wp),	intent(in)	::	dX1_dt	theta derivative of solution variables q1,q2
real(kind=wp),	intent(in)	::	dX2_dt	theta derivative of solution variables q1,q2
real(kind=wp),	intent(in)	::	dX1_dz	zeta derivative of solution variables q1,q2
real(kind=wp),	intent(in)	::	dX2_dz	zeta derivative of solution variables q1,q2
real(kind=wp),	intent(out)	::	Jh	Jac,1/Jac,g_{ab} with a=theta/zeta b=theta/zeta
real(kind=wp),	intent(out)	::	g_tt	Jac,1/Jac,g_{ab} with a=theta/zeta b=theta/zeta
real(kind=wp),	intent(out)	::	g_tz	Jac,1/Jac,g_{ab} with a=theta/zeta b=theta/zeta
real(kind=wp),	intent(out)	::	g_zz	Jac,1/Jac,g_{ab} with a=theta/zeta b=theta/zeta
real(kind=wp),	intent(out)	::	Jh_dq1	and their variation vs q1
real(kind=wp),	intent(out)	::	g_tt_dq1	and their variation vs q1
real(kind=wp),	intent(out)	::	g_tz_dq1	and their variation vs q1
real(kind=wp),	intent(out)	::	g_zz_dq1	and their variation vs q1
real(kind=wp),	intent(out)	::	Jh_dq2	and their variation vs q2
real(kind=wp),	intent(out)	::	g_tt_dq2	and their variation vs q2
real(kind=wp),	intent(out)	::	g_tz_dq2	and their variation vs q2
real(kind=wp),	intent(out)	::	g_zz_dq2	and their variation vs q2
real(kind=wp),	intent(out)	::	g_t1	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}
real(kind=wp),	intent(out)	::	g_t2	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}
real(kind=wp),	intent(out)	::	g_z1	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}
real(kind=wp),	intent(out)	::	g_z2	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}
real(kind=wp),	intent(out)	::	Gh11	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}
real(kind=wp),	intent(out)	::	Gh22	dq^{i}/dthetaG^{i1}, dq^{i}/dthetaG^{i2}, and dq^{i}/dzetaG^{i1}, dq^{i}/dzetaG^{i2} and G^{11},G^{22}

Called by

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Source Code

PURE SUBROUTINE hmap_frenet_eval_all_e(xv,q1,q2,dX1_dt,dX2_dt,dX1_dz,dX2_dz, &
                                       Jh,    g_tt,    g_tz,    g_zz,     &
                                       Jh_dq1,g_tt_dq1,g_tz_dq1,g_zz_dq1, &
                                       Jh_dq2,g_tt_dq2,g_tz_dq2,g_zz_dq2, &
                                       g_t1,g_t2,g_z1,g_z2,Gh11,Gh22  )
! MODULES
  IMPLICIT NONE
!-----------------------------------------------------------------------------------------------------------------------------------
! INPUT VARIABLES
  TYPE(t_hmap_frenet_auxvar),INTENT(IN) :: xv    !! precomputed auxiliary variables
  REAL(wp),INTENT(IN)  :: q1,q2       !! solution variables q1,q2
  REAL(wp),INTENT(IN)  :: dX1_dt,dX2_dt  !! theta derivative of solution variables q1,q2
  REAL(wp),INTENT(IN)  :: dX1_dz,dX2_dz  !!  zeta derivative of solution variables q1,q2
!-----------------------------------------------------------------------------------------------------------------------------------
! OUTPUT VARIABLES
  REAL(wp),INTENT(OUT) :: Jh,g_tt,g_tz,g_zz              !! Jac,1/Jac,g_{ab} with a=theta/zeta b=theta/zeta
  REAL(wp),INTENT(OUT) :: Jh_dq1,g_tt_dq1,g_tz_dq1,g_zz_dq1  !! and their variation vs q1
  REAL(wp),INTENT(OUT) :: Jh_dq2,g_tt_dq2,g_tz_dq2,g_zz_dq2  !! and their variation vs q2
  REAL(wp),INTENT(OUT) :: g_t1,g_t2,g_z1,g_z2,Gh11,Gh22  !! dq^{i}/dtheta*G^{i1}, dq^{i}/dtheta*G^{i2}, and dq^{i}/dzeta*G^{i1}, dq^{i}/dzeta*G^{i2} and G^{11},G^{22}
!-----------------------------------------------------------------------------------------------------------------------------------
! LOCAL VARIABLES
  REAL(wp) :: Gh31,Gh32,Gh33
!===================================================================================================================================
  ASSOCIATE(  lp=>xv%lp, tau=>xv%tau, sigma=>xv%sigma, kappa=>xv%kappa)
  Gh11=1.0_wp
  !Gh21=0.0_wp
  Gh22=1.0_wp
  Gh31 =-lp*tau*q2
  Gh32 = lp*tau*q1

  !Jh=lp*(1.0_wp-sigma*kappa*q1)
  Jh_dq1=-lp*sigma*kappa
  Jh_dq2=0.0_wp

  Jh=lp+Jh_dq1*q1
  ! Gh33 = (lp**2)*((1.0_wp-sigma*kappa*q1)**2+tau**2*(q1**2+q2**2))
  Gh33 = Jh*Jh + Gh31*Gh31 + Gh32*Gh32

  g_t1 = dX1_dt
  g_t2 = dX2_dt
  g_z1 = dX1_dz + Gh31
  g_z2 = dX2_dz + Gh32

  g_tt =   dX1_dt *  g_t1         +  dX2_dt *  g_t2
  g_tz =   dX1_dt *  g_z1         +  dX2_dt *  g_z2
  g_zz =   dX1_dz * (g_z1 + Gh31) +  dX2_dz * (g_z2 + Gh32)  + Gh33

  !Gh11/dq1 =0 Gh12/dq1 =0 Gh13/dq1 = 0
  !            Gh22/dq1 =0 Gh23/dq1 = lp*tau
  !                        Gh33/dq1 = 2*(lp**2)*((1.0_wp-sigma*kappa*q1)*(-sigma*kappa)+tau**2 *(q1))
  !Gh11/dq2 =0 Gh12/dq2 =0 Gh13/dq2 = -lp*tau
  !            Gh22/dq2 =0 Gh23/dq2 = 0
  !                        Gh33/dq2 = 2*(lp*tau)**2*(q2)
  ! => g_t1 /dq1 =0, g_t1/dq2 =0, g_t2/dq1 =0, g_t2/dq2 =0
  ! => g_z1 /dq1 = Gh31/dq1, g_z1/dq2 =Gh31/dq2, g_z2/dq1 =Gh32/dq1, g_z2/dq2 =Gh32/dq2
  g_tt_dq1 = 0.0_wp
  g_tt_dq2 = 0.0_wp

  g_tz_dq1 =  lp*tau*dX2_dt
  g_tz_dq2 = -lp*tau*dX1_dt

  g_zz_dq1 =  2.0_wp*(lp*tau*(dX2_dz + Gh32)+Jh*Jh_dq1)
  g_zz_dq2 = -2.0_wp*lp*tau*(dX1_dz + Gh31)
  END ASSOCIATE
END SUBROUTINE hmap_frenet_eval_all_e

hmap_frenet_eval_all_e Subroutine

Contents

Source Code

public pure subroutine hmap_frenet_eval_all_e(xv, q1, q2, dX1_dt, dX2_dt, dX1_dz, dX2_dz, Jh, g_tt, g_tz, g_zz, Jh_dq1, g_tt_dq1, g_tz_dq1, g_zz_dq1, Jh_dq2, g_tt_dq2, g_tz_dq2, g_zz_dq2, g_t1, g_t2, g_z1, g_z2, Gh11, Gh22)

Arguments

Called by

Source Code