dl_mg_convergence_params Module Reference

Store of convergence and iteration control parameters: More...

Data Types
type	conv_params_t

Functions/Subroutines
subroutine	dl_mg_set_conv_params (eps_half, eq_type, fd_order, tol_res_rel, tol_res_abs, tol_pot_rel, tol_pot_abs, tol_newton_res_rel, tol_newton_res_abs, tol_cg_res_rel, tol_cg_res_abs, tol_vcyc_res_rel, tol_vcyc_res_abs, tol_level_1_res_rel, tol_level_1_res_abs, tol_mu_rel, tol_mu_abs, mg_max_conv_rate, max_iters_defco, max_iters_newton, max_iters_cg, max_iters_vcyc, max_iters_level_1, v_iterations, omega_sor, use_cg)
subroutine	write_convergence_params (eps_half, eq_type, fd_order, tol_res_rel, tol_res_abs, tol_pot_rel, tol_pot_abs, tol_newton_res_rel, tol_newton_res_abs, tol_cg_res_rel, tol_cg_res_abs, tol_vcyc_res_rel, tol_vcyc_res_abs, tol_level_1_res_rel, tol_level_1_res_abs, tol_mu_rel, tol_mu_abs, mg_max_conv_rate, max_iters_defco, max_iters_newton, max_iters_cg, max_iters_vcyc, max_iters_level_1, v_iterations, omega_sor, use_cg)

Variables
real(wp)	tol_res_rel_ = 1.0e-2_wp
real(wp)	tol_res_abs_ = 1.0e-2_wp
real(wp)	tol_pot_rel_ = 1.0e-6_wp
real(wp)	tol_pot_abs_ = 1.0e-6_wp
real(wp)	tol_newton_res_rel_ = 1.0e-8_wp
real(wp)	tol_newton_res_abs_ = 1.0e-8_wp
real(wp)	tol_cg_res_rel_ = 1.0e-8_wp
real(wp)	tol_cg_res_abs_ = 1.0e-8_wp
real(wp)	tol_vcyc_res_rel_ = 1.0e-8_wp
real(wp)	tol_vcyc_res_abs_ = 1.0e-8_wp
real(wp)	tol_level_1_res_rel_
	initialisation is done in the subroutine from below More...
real(wp)	tol_level_1_res_abs_ = 1.0e-12_wp
real(wp)	tol_mu_rel_ = 1.0e-3_wp
real(wp)	tol_mu_abs_ = 1.0e-3_wp
integer	max_iters_defco_ = 30
	maximum number of iterations for the higher order correction More...
integer	max_iters_newton_ = 30
	.... Newton iteration More...
integer	max_iters_cg_ = 100
integer	max_iters_vcyc_ = 30
	maximum number of V cycles (recommended value not more that 50) if conjugate gradient is on this is reset to 1, unless set explicitly via input argument or envinroment variable More...
integer	max_iters_level_1_ = 100
	max number of iteration at the coarsest level More...
integer, dimension(2)	v_iterations_ = (/2, 1/)
	Number of smoother iteration to be applied at each level. First value is for the descending branch (coarsening), the second is for the ascending branch (prolongation). More...
real(wp)	omega_sor_ = 1.15
	SOR relaxation parameter, the default is set tp 1.15 as recommended in Trottenberg's book. More...
real(wp)	mg_max_conv_rate_ = 0.85_wp
	if consecutive residuals ratio is larger than the value below it is assumed that round-off limit was reached. i.e. the computation cannot progress becase of roundoff errors, or perhaps the problem is too hard for this algorithm More...
logical, save	use_cg_ = .false.
integer, parameter	tconv_level_1 =1
	convergence tags used in subroutine mg_convergence_test: MG coarse level, MG V-cycle, Cojugate Gradient, Newton More...
integer, parameter	tconv_vcycle =2
integer, parameter	tconv_cg =3
integer, parameter	tconv_newton =4
integer, parameter	nconv_tags =4
type(conv_params_t), dimension(nconv_tags), save	conv_params
	used in mg_convergence_test More...

Detailed Description

Store of convergence and iteration control parameters:

• defect correction
• conjugate gradient
• multigrid V cycle
• multigirid coarse level ieration
• Newton iteration

The governing convergence criteria is as follow:

A. if defect correction order is > 2 the following applies:

defect norm < MAX(tol_rel_res * (initial defect norm), tol_res_abs)

AND

||pot^(n) -pot^(n-1)|| < MAX(tol_res_pot * ||pot^(n-1)||, tol_abs_pot)

These two conditions try to ensure that the iteration process does not stops too early because of a norm reduction stall or small defect. The tol_abs_{res,pot} values ensure stopping in the case of zero solution or account for roundoff errors.

B. defect correction == 2

In this case the standard the multigrid convergence algorithm is used

residual norm < MAX(tol_rel_res * || f||, tol_res_abs)

where tol_res_rel, and tol_res_abs are transferrend to the selected equation (Poisson or or PB flavor) and their tolerance parameters are ignored if not present in the argument list. Also, tol_rel_pot and tol_abs_pot are ignored in this cases.

When the PBE equation is solved with periodic boundary conditions the chemical potential convergence is tested with the following condition:

abs(mu^(i) - mu^(i-1)) < MAX(tol_mu_rel * abs(mu^(i), tol_mu_abs)

Convergece is reached if the above condition and the Newton converge test are satisfied

Function/Subroutine Documentation

dl_mg_set_conv_params()

subroutine dl_mg_convergence_params::dl_mg_set_conv_params	(	real(wp), dimension(:,:,:,:), intent(in)	eps_half,
		integer, intent(in)	eq_type,
		integer, intent(in)	fd_order,
		real(wp), intent(in), optional	tol_res_rel,
		real(wp), intent(in), optional	tol_res_abs,
		real(wp), intent(in), optional	tol_pot_rel,
		real(wp), intent(in), optional	tol_pot_abs,
		real(wp), intent(in), optional	tol_newton_res_rel,
		real(wp), intent(in), optional	tol_newton_res_abs,
		real(wp), intent(in), optional	tol_cg_res_rel,
		real(wp), intent(in), optional	tol_cg_res_abs,
		real(wp), intent(in), optional	tol_vcyc_res_rel,
		real(wp), intent(in), optional	tol_vcyc_res_abs,
		real(wp), intent(in), optional	tol_level_1_res_rel,
		real(wp), intent(in), optional	tol_level_1_res_abs,
		real(wp), intent(in), optional	tol_mu_rel,
		real(wp), intent(in), optional	tol_mu_abs,
		real(wp), intent(in), optional	mg_max_conv_rate,
		integer, intent(in), optional	max_iters_defco,
		integer, intent(in), optional	max_iters_newton,
		integer, intent(in), optional	max_iters_cg,
		integer, intent(in), optional	max_iters_vcyc,
		integer, intent(in), optional	max_iters_level_1,
		integer, dimension(2), intent(in), optional	v_iterations,
		real(wp), intent(in), optional	omega_sor,
		logical, intent(in), optional	use_cg
	)

Parameters

[in]

eps_half

to check for internal

set more convergence parameters if provided

write_convergence_params()

subroutine dl_mg_convergence_params::write_convergence_params	(	real(wp), dimension(:,:,:,:), intent(in)	eps_half,
		integer, intent(in)	eq_type,
		integer, intent(in)	fd_order,
		real(wp), intent(in)	tol_res_rel,
		real(wp), intent(in)	tol_res_abs,
		real(wp), intent(in)	tol_pot_rel,
		real(wp), intent(in)	tol_pot_abs,
		real(wp), intent(in)	tol_newton_res_rel,
		real(wp), intent(in)	tol_newton_res_abs,
		real(wp), intent(in)	tol_cg_res_rel,
		real(wp), intent(in)	tol_cg_res_abs,
		real(wp), intent(in)	tol_vcyc_res_rel,
		real(wp), intent(in)	tol_vcyc_res_abs,
		real(wp), intent(in)	tol_level_1_res_rel,
		real(wp), intent(in)	tol_level_1_res_abs,
		real(wp), intent(in)	tol_mu_rel,
		real(wp), intent(in)	tol_mu_abs,
		real(wp), intent(in)	mg_max_conv_rate,
		integer, intent(in)	max_iters_defco,
		integer, intent(in)	max_iters_newton,
		integer, intent(in)	max_iters_cg,
		integer, intent(in)	max_iters_vcyc,
		integer, intent(in)	max_iters_level_1,
		integer, dimension(2), intent(in)	v_iterations,
		real(wp), intent(in)	omega_sor,
		logical, intent(in)	use_cg
	)

Variable Documentation

conv_params

type(conv_params_t), dimension(nconv_tags), save dl_mg_convergence_params::conv_params

used in mg_convergence_test

max_iters_cg_

integer dl_mg_convergence_params::max_iters_cg_ = 100

max_iters_defco_

integer dl_mg_convergence_params::max_iters_defco_ = 30

maximum number of iterations for the higher order correction

max_iters_level_1_

integer dl_mg_convergence_params::max_iters_level_1_ = 100

max number of iteration at the coarsest level

max_iters_newton_

integer dl_mg_convergence_params::max_iters_newton_ = 30

.... Newton iteration

max_iters_vcyc_

integer dl_mg_convergence_params::max_iters_vcyc_ = 30

maximum number of V cycles (recommended value not more that 50) if conjugate gradient is on this is reset to 1, unless set explicitly via input argument or envinroment variable

mg_max_conv_rate_

real(wp) dl_mg_convergence_params::mg_max_conv_rate_ = 0.85_wp

if consecutive residuals ratio is larger than the value below it is assumed that round-off limit was reached. i.e. the computation cannot progress becase of roundoff errors, or perhaps the problem is too hard for this algorithm

nconv_tags

integer, parameter dl_mg_convergence_params::nconv_tags =4

omega_sor_

real(wp) dl_mg_convergence_params::omega_sor_ = 1.15

SOR relaxation parameter, the default is set tp 1.15 as recommended in Trottenberg's book.

tconv_cg

integer, parameter dl_mg_convergence_params::tconv_cg =3

tconv_level_1

integer, parameter dl_mg_convergence_params::tconv_level_1 =1

convergence tags used in subroutine mg_convergence_test: MG coarse level, MG V-cycle, Cojugate Gradient, Newton

tconv_newton

integer, parameter dl_mg_convergence_params::tconv_newton =4

tconv_vcycle

integer, parameter dl_mg_convergence_params::tconv_vcycle =2

tol_cg_res_abs_

real(wp) dl_mg_convergence_params::tol_cg_res_abs_ = 1.0e-8_wp

tol_cg_res_rel_

real(wp) dl_mg_convergence_params::tol_cg_res_rel_ = 1.0e-8_wp

tol_level_1_res_abs_

real(wp) dl_mg_convergence_params::tol_level_1_res_abs_ = 1.0e-12_wp

tol_level_1_res_rel_

real(wp) dl_mg_convergence_params::tol_level_1_res_rel_

initialisation is done in the subroutine from below

tol_mu_abs_

real(wp) dl_mg_convergence_params::tol_mu_abs_ = 1.0e-3_wp

tol_mu_rel_

real(wp) dl_mg_convergence_params::tol_mu_rel_ = 1.0e-3_wp

tol_newton_res_abs_

real(wp) dl_mg_convergence_params::tol_newton_res_abs_ = 1.0e-8_wp

tol_newton_res_rel_

real(wp) dl_mg_convergence_params::tol_newton_res_rel_ = 1.0e-8_wp

tol_pot_abs_

real(wp) dl_mg_convergence_params::tol_pot_abs_ = 1.0e-6_wp

tol_pot_rel_

real(wp) dl_mg_convergence_params::tol_pot_rel_ = 1.0e-6_wp

tol_res_abs_

real(wp) dl_mg_convergence_params::tol_res_abs_ = 1.0e-2_wp

tol_res_rel_

real(wp) dl_mg_convergence_params::tol_res_rel_ = 1.0e-2_wp

tol_vcyc_res_abs_

real(wp) dl_mg_convergence_params::tol_vcyc_res_abs_ = 1.0e-8_wp

tol_vcyc_res_rel_

real(wp) dl_mg_convergence_params::tol_vcyc_res_rel_ = 1.0e-8_wp

use_cg_

logical, save dl_mg_convergence_params::use_cg_ = .false.

v_iterations_

integer, dimension(2) dl_mg_convergence_params::v_iterations_ = (/2, 1/)

Number of smoother iteration to be applied at each level. First value is for the descending branch (coarsening), the second is for the ascending branch (prolongation).