mixing_preconditioner_oct_m Module Reference

Functions/Subroutines
subroutine, public	dkerker_preconditioner (der, q_0, delta_f, f_out)
	Kerker preconditioner for the mixing operator in real space. More...
subroutine	dlaplacian_op (x, lx, userdata)
subroutine, public	zkerker_preconditioner (der, q_0, delta_f, f_out)
	Kerker preconditioner for the mixing operator in real space. More...
subroutine	zlaplacian_op (x, lx, userdata)

Function/Subroutine Documentation

dkerker_preconditioner()

subroutine, public mixing_preconditioner_oct_m::dkerker_preconditioner	(	type(derivatives_t), intent(in), target	der,
		real(real64), intent(in), target	q_0,
		real(real64), dimension(:), intent(in), contiguous	delta_f,
		real(real64), dimension(:), intent(out)	f_out
	)

Kerker preconditioner for the mixing operator in real space.

Computes the preconditioned residual:

\[ f_{out} = (\Delta - q_0^2)^{-1} \Delta \delta f \]

by multiplying through by \((\Delta - q_0^2)\) and solving the linear system:

\[ (\Delta - q_0^2) f_{out} = \Delta \delta f \]

for \(f_{out}\). The implementation follows [Shiihara et. al. 2008 Modelling Simul. Mater. Sci. Eng. 16 035004] (https: the mixing coefficient in the preconditioned residual.

If the starting density does not already integrate to the fully correct total charge, an additional charge correction treatment is necessary:

\[ f_{out} = f_{out} + \frac{a}{V} \int_{V} \delta f d\mathbr{r} \]

See [Winkelmann et. al.](https:

Parameters

[in]	der	Derivatives
[in]	q_0	Kerker parameter
[in]	delta_f	Residual
[out]	f_out	Preconditioned Residual

Definition at line 228 of file mixing_preconditioner.F90.

dlaplacian_op()

subroutine mixing_preconditioner_oct_m::dlaplacian_op ( real(real64), dimension(:), intent(in), contiguous  x, real(real64), dimension(:), intent(out), contiguous  lx, type(c_ptr), dimension(:), intent(in)  userdata  )

private

Parameters

[in]	x	Current guess for preconditioned residual
[out]	lx	The LHS product of CG: Ax, or (\Delta - q_0^2) f_out

Definition at line 281 of file mixing_preconditioner.F90.

zkerker_preconditioner()

subroutine, public mixing_preconditioner_oct_m::zkerker_preconditioner	(	type(derivatives_t), intent(in), target	der,
		real(real64), intent(in), target	q_0,
		complex(real64), dimension(:), intent(in), contiguous	delta_f,
		complex(real64), dimension(:), intent(out)	f_out
	)

Kerker preconditioner for the mixing operator in real space.

Computes the preconditioned residual:

\[ f_{out} = (\Delta - q_0^2)^{-1} \Delta \delta f \]

by multiplying through by \((\Delta - q_0^2)\) and solving the linear system:

\[ (\Delta - q_0^2) f_{out} = \Delta \delta f \]

for \(f_{out}\). The implementation follows [Shiihara et. al. 2008 Modelling Simul. Mater. Sci. Eng. 16 035004] (https: the mixing coefficient in the preconditioned residual.

If the starting density does not already integrate to the fully correct total charge, an additional charge correction treatment is necessary:

\[ f_{out} = f_{out} + \frac{a}{V} \int_{V} \delta f d\mathbr{r} \]

See [Winkelmann et. al.](https:

Parameters

[in]	der	Derivatives
[in]	q_0	Kerker parameter
[in]	delta_f	Residual
[out]	f_out	Preconditioned Residual

Definition at line 401 of file mixing_preconditioner.F90.

zlaplacian_op()

subroutine mixing_preconditioner_oct_m::zlaplacian_op ( complex(real64), dimension(:), intent(in), contiguous  x, complex(real64), dimension(:), intent(out), contiguous  lx, type(c_ptr), dimension(:), intent(in)  userdata  )

private

Parameters

[in]	x	Current guess for preconditioned residual
[out]	lx	The LHS product of CG: Ax, or (\Delta - q_0^2) f_out

Definition at line 454 of file mixing_preconditioner.F90.