Jetstream contains both monolithic and predictor-corrector methods for homotopy-based continuation. For more information regarding the theory, implementation, and performance of these algorithms, refer to David Brown's PhD thesis. To use the homotopy modules:
1) Set opt_method = 'flowsolve' and diablo%nk_global = 0 (predictor-corrector homotopy continuation), diablo%nk_global = -1 (monolithic homotopy continuation), or diablo%nk_global = -2 (explicit monolithic homotopy continuation) in the input file;
2) Set diablo%hom_method appropriately: 'convex' (default) or 'global' ;
3) Include the homotopy namelist &homot at the bottom of the input file;
4) Include any homotopy parameters according to preference.
Note that many solver parameters (diablo%) are not used in this module. Instead, we now use Hom type parameters (c_hom% or g_hom%) to make the options phase-dependent.
Description: Specifies the continuation function to use. Parameter Type: character Range of Acceptable values: 'diss', 'diss2' Default Value: 'diss' User Notes:
-'diss': Second order dissipation operator (without the pressure switch) as the homotopy function. The extra equation for the RANS formulation is the dissipation-like operator used to stabilize the convective term in the RANS equation (see Michal Osusky's Nashville AIAA paper, on Dr. Zingg's website).
-'diss2': This is exactly the same as 'diss' for Euler/NS, but for the RANS equations we use an extended version of the same operator to include the turbulent viscosity. Currently, 'diss2' is far superior to the RANS equations.
HOM% nls
HOM% nls% check_relres_glob Description: A flag to determine whether to check the relative residual at globalization. Parameter Type: logical Default Value: .false. User Notes:
The checks the relative residual of R at each iterate against the parameter HOM% nls% relres_glob. If it is below that value, we will switch directly to phase 3. This requires an extra L2 norm to be calculated at each iterate. We don't normally use this criterion, it is mainly just for comparison with the original DBC codes which did use this criterion. Default will become .false. at the next merge.
HOM% nls% tol_rel_embed Description: A flag to determine whether to take the relative residual relative to the embedding step or the actual predictor point. Parameter Type: logical Default Value: .true. User Notes:
Better to keep it on, since turning it off will actually solve the problem more when your predictor step is better, which is not logical.
HOM% nls% use_traceback Description: If set to true, the solution will be traced back if the nls fails to converge when max iterations are met. Otherwise, it will just continue on as normal. Parameter Type: logical Default Value: .false. User Notes:
You can turn this on for difficult flow solves, but expect high cost, and make sure to make nls%max_its(2) large enough so that you can be reasonably sure that failure to meet the tolerance indeed indicates a problem.
HOM% nls% traceback_max Description: Maximum number of traceback iterations if nls%use_traceback is on. Parameter Type: Integer Default Value: 4
HOM% nls% relres_glob Description: The relative residual that must be met as a requirement at globalization. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 1.d-3 User Notes:
See the description in HOM% nls% check_relres_glob for more info.
HOM% nls% fin_strt_relres Description: The relative residual at globalization must be less than this to be accepted. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 5.d-1 User Notes:
We check the relative residual (calculated based on the initial flow residual) at globalization (lambda = 0) against this parameter. If it is not lower than this parameter, the predictor step will be repeated with a factor of HOM% nls% fin_strt_red_fac applied to the current steplength and the resulting nonlinear subproblem will be solved to try to get a better estimate. This process is repeated until a suitable initial residual is acquired. Note that the problem becomes increasingly stiff near lambda=0, so this can add significant computation cost to a flow solve. Usually, we use the large default value to essentially turn this off.
HOM% nls% fsrr_tb_max Description: If the final starting relative residual tolerance nls%fin_strt_relres is not met, this parameter provides the upper bound on how many times traceback will be attempted. Parameter Type: Integer Range of Acceptable values: [0, inf] Default Value: 10
HOM% nls% traceback_red_fac Description: The traceback phase is activated if problems were encountered at the current subproblem or if nls%fin_strt_relres was not met. In the traceback phase, we repeat the previous predictor iterate with this factor applied to the steplength (so a larger value actually means less reduction). Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 0.5 User Notes:
There is probably no reason to change this from default.
HOM% nls% pc_its Description: Maximum allowable predictor iterations, after which the flow solve will quit. Parameter Type: integer Range of Acceptable values: [1, 400) Default Value: 50 User Notes:
A typical flow solve will take ~10 predictor steps. If it reaches 50, it is probably stuck above a stagnation point and will never converge. HOM% nls% mh_its Description: Maximum allowable iterations for monolithic homotopy, after which the flow solve will quit. Parameter Type: integer Default Value: 200
HOM% nls% abs_tol(1:3) Description: Absolute tolerance to check if the residual is converged at each phase. Note that the phase 1 and phase 3 values are taken as abs_tol(1)l and abs_tol(3), but the phase 2 value is actually interpolated between abs_tol(1) and abs_tol(2) values. Parameter Type: real(3) Range of Acceptable values: Should be small Default Value: (/ 1E-10, 1E-10, 1E-12 /) User Notes:
Note that the convergence criterion for each nonlinear subproblem is that either the relative tolerance or the absolute tolerance is met. While it seems like a good idea in principle to check absolute residuals, in practice we don't really know what these values should be. So, we typically set these small so as not to rely on them, preferring to use the relative residual.
HOM% nls% rel_tol(1:3) Description: Relative tolerance to check if the residual is converged at each phase. Unlike the absolute tolerance, nls(1), nls(2), and nls(3) do correspond exactly to the relative residual checked at each phase Like abs_tol, this value is also intepolated. Parameter Type: real(3) Range of Acceptable values: Should be small Default Value: (/ 1E-1, 1E-1, 1E-10 /) User Notes:
rel_tol(1) and rel_tol(2) are taken relative to the starting residual at each particular nonlinear subproblem. For phase 3, the relative residual is taken relative to the starting residual of the flow solve.
HOM% nls% max_its(1:3) Description: Maximum allowable nonlinear iterations per subproblem at each phase. Parameter Type: integer(3) Range of Acceptable values: [1, inf) Default Value: (/ 15, 25, 75 /)
HOM% nls% updat_frq(1:3) Description: Frequency with which to update both the preconditioner matrix and its ILU factorization. Parameter Type: integer(3) Range of Acceptable values: [1, large] Default Value: (/ 3, 3, 1 /)
HOM% prec
HOM% prec(1:3)% opt Description: Choice of ILU factorization. Parameter Type: Character(3) Range of Acceptable values: 'iluk', 'ilut' Default Value: (/ 'iluk', 'iluk', 'iluk' /)
HOM% prec(1:3)% iluk% lev_fil Description: Fill level for ILUK Parameter Type: Integer(3) Range of Acceptable values: [0,1,2,3,...] Default Value: (/ 2, 2, 2 /)
HOM% l% inewt_s_params Description: That's a lower case 'ell', not an upper case 'eye'. The value of lamba below which we will use the matvecs and preconditioner parameters from the inexact Newton phase. For example, if inewt_s_params=0.1, then we can use Frechet matvecs and higher fill level when lambda is below 0.1. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 0.d0
HOM% l% init Description: This is the initial value of lambda. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 1.d0 User notes:
Usually we use the default.
HOM% l% tol Description: A tolerance on lambda. Lambda is considered to be essentially 1 or 0 if it is within this tolerance of it. Parameter Type: real Range of Acceptable values: should be small Default Value: 1.d-12 User notes:
Not a critical value; no reason to mess with it.
HOM% scl
HOM% scl% mu Description: mu scaling. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 User Notes:
Mu-scaling is an extra scaling factor that we apply to the homotopy function G. This parameter affects curvature and hence it affects predictor performance. The value from the input parameter is a front end to this; an appropriate value for mu is acquired from a numerical algorithm based on minimizing the H20norm of d||H||/dlam and hard-coded into the appropriate homotopy module. This value is an extra scaling factor that is applied afterwards. Smaller values tend to reduce the curvature near lambda=0 and increase it near lambda=1 and vice versa. Since the auto-scaling algorithm does not take into account problem stiffness, it may be useful to use mu ~(0.5-0.8). Or, just use the default.
HOM% scl% mu_turb Description: mu scaling. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 UserNotes:
An experimental extra mu-scaling factor in front of the RANS equation. Changing it from 1 usually causes the solver to fail.
HOM% scl% turb_fac Description: Scaling factor for the RANS equations, similar to what is used in Michal's RANS scaling. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d-3
HOM% scl% kappa Description: kappa-scaling value. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 UserNotes:
This parameter is only active when auto-scaling is turned off (HOM% scl% k_auto = .false.), which we typically do not use.
HOM% scl% k_auto Description: Turn kappa auto-scaling on? Parameter Type: logical Default Value: .true. User Notes:
Kappa-scaling is applied to the whole equation. It does not affect the predictor performance, but is critical for the orthogonal corrector method and important for steplength adaptation as well since it adjusts the relative scaling between ||dq| and dlambda.
HOM% scl% k_adapt Description: Turn adaptive kappa-scaling on? Parameter Type: logical Default Value: .false. User Notes:
This will determine the kappa-scaling based on the first nonlinear subproblem requiring at least one nonlinear iteration. This can be used when k_auto is on, in which case it will replace the auto-scaling once it becomes available. I generally don't use this.
HOM% scl% k_angle Description: The target angle between the orthogonal corrector and the constant-lambda corrector directions, used in determining the kappa-scaling. Parameter Type: real Range of Acceptable values: (0,90) Default Value: 8.d0 User Notes:
Degrees. Only active when HOM% scl% k_auto = .true.
HOM% scl% k_f_auto Description: Extra factor to multiply auto-acquired kappa by. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 User Notes:
Only active when HOM% scl% k_auto = .true.
HOM% scl% k_f_adapt Description: Extra factor to multiply adaptation-acquired kappa by. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 User Notes:
Only active when HOM% scl% k_adapt = .true.
HOM% a
HOM% a% m_on Description: Is this an auto-scaling run for mu? Parameter Type: logical Default Value: .false. User Notes:
This determines acceptable values for mu based on minimizing the H2-norm of d||H||/dlam. The integral is estimated over a variety of mu for a single flow solve by applying a local change of coordinates to lambda. Since the integration is in the lambda direction, the estimate of the integral is inaccurate for large changes in mu, so we limit ourselves to a factor of 10 in each direction per scaling run. The intended use is that we should run this several times, updating mu each time, until it converges. (Should only take a few runs.)
HOM% a% m_opt Description: Option for mu auto-scaling algorithm. Parameter Type: character Range of Acceptable values: 'error', 'resid' Default Value: 'error' User Notes:
The problem with using the residual is that it is biased by the relative scaling of ||R|| and ||G||, so we typically use the error in the H2-norm minimization described above, and not the residual. Only active when HOM% a% m_on = .true.
HOM% a% k_on Description: Is this and auto-scaling run for kappa? Parameter Type: logical Default Value: .false. User Notes:
Ideally, mu-scaling has been performed already. This determines acceptable values for kappa based on a target angle between the orthogonal corrector direction and the constant-lambda corrector direction. This should be run for a variety of Ma. We can then do some line-fitting and then hard-code the results into the appropriate homotopy module. (See HOM_C_Diss_Mod for an example of this.)
HOM% a% k_embed Description: During an auto-scaling run for kappa, should we over-write the input parameters with embedding parameters? Parameter Type: logical Default Value: .true.
HOM% sat
HOM% sat% on Description: Should we turn the SATs on? Parameter Type: logical Default Value: .true. User Notes:
Note that the linear system will be singular at lambda=1 if the SATs are turned off.
HOM% sat% opt Description: Different boundary conditions can be applied to the homotopy function. Parameter Type: character Range of Acceptable values: 'fstrm', 'flow' Default Value: 'fstrm' User Notes:
1) 'fstrm' - BC's imitate freestream conditions.
2) 'flow' - BC's imitate the flow BC's.
Both methods work, but the 'flow' option seems to result in higher curvature for viscous flows.
HOM% sat% fac Description: We can multiply the SAT terms by a factor Parameter Type: real Range of Acceptable values: (-inf, inf) Default Value: 1.d0 User Notes:
Mostly for debugging.
HOM% sat% sym Description: Should symmetry planes still be treated as such? Parameter Type: logical Default Value: .false. User Notes:
Works either way, but seems to exhibit slightly lower curvature with it off.
NOTE: This should be set to .true. for 2D flow.
HOM% h% opt Description: Options for how to modify the steplength. Parameter Type: character Range of Acceptable values: 'none', 'adapt', 'hob' Default Value: 'adapt' User Notes:
1) 'none' - Steplength is constant
2) 'adapt' - Applies any steplength adaptation routines, which must be activated individually. By default, ag_a and ag_d are turned on and wj and dhr are turned off. At each predictor step, all active steplength adaptations will be calculated and the most limiting one will be applied.
3) 'hob' - This imitates Hicken/Osusky/Buckley's 2011 AIAA paper. Mostly implemented for debugging and comparative purposes. Note that the scaling of the linear system is different.
HOM% h% dlam_init Description: Change in lambda at the first iteration. Parameter Type: real Range of Acceptable values: (0, h%max) Default Value: 1.d-1 User Notes:
This can generally be increased to about 0.2 without convergence problems.
HOM% h% min Description: Minimum acceptable value of the steplength. Parameter Type: real Range of Acceptable values: (h%min, inf) Default Value: 1.d-2 User Notes:
Better to rely on h%dlam_min, and to keep this small, since we really don't have a good idea of what it should be.
HOM% h% max Description: Maximum acceptable value of the steplength. Parameter Type: real Range of Acceptable values: (h%min, inf) Default Value: 4.d0 User Notes:
Better to rely on h%dlam_max, and to keep this large, since we really don't have a good idea of what it should be.
HOM% h% fmin Description: Minimum value to divide the steplength by during adaptation. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 0.5d0 User Notes:
Since we are dividing, this actually sets an upper bound on how much the steplength can increase.
HOM% h% fmax Description: Maximum value to divided the steplength by during adaptation. Parameter Type: real Range of Acceptable values: (1, inf) Default Value: 2.d0 User Notes:
Since we are dividing, this actually sets an upper bound on how much the steplength can be reduced by.
HOM% h% dlam_min Description: Minimum allowable increase in lambda at each predictor iterate. Parameter Type: real Range of Acceptable values: (0, h%dlam_max) Default Value: 4.d-2
HOM% h% dlam_max Description: Maximum allowable increase in lambda at each predictor iterate. Parameter Type: real Range of Acceptable values: (h%dlam_min, 1) Default Value: 2.5d-1
HOM% h% dlam_max_fin Description: Maximum allowable change in lambda at the final predictor step (towards globalization). Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 5.d-2 User Notes:
If this number is exceeded, the predictor step is scaled back.
HOM% ad% ag_d% on Description: Adaptation of Allgower and Georg (1990) based on asymptotic expansions: distance to the curve. Parameter Type: logical Default Value: .true. User Notes:
Increase the steplength if the initial predictor point was further from the solution than some target value, and decrease otherwise.
HOM% h% ad% ag_d% auto Description: Turn on to auto-acquire a target value, which can then be multiplied by the factor h%ad%ag_d%fac. Parameter Type: logical Default Value: .true. User Notes:
Unless you know specifically what a good distance to the curve is, you should turn this on.
HOM% h% ad% ag_d% fac Description: After auto-acquiring the target value for ag_d, we can then multiply it by a factor. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d0 User Notes:
Greater than 1 will result in larger steplengths and vice versa. Only active if h%ad%ag_d%auto = .true.
HOM% h% ad% ag_d% targ Description: Target value for the distance in ag_d. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 5.d-1 User Notes:
Only active if h%ad%ag_d%auto = .false.
HOM% h% ad% ag_a% on Description: Turn on Allgower and Georg's (1990) method of asymptotic expansions: angle between successive tangent vectors. Parameter Type: logical Default Value: .true. User Notes:
Essentially, a measure of curvature. This is affected by kappa-scaling. If no corrector iterates were performed this step, then ag_d results in 0 distance, which is not very useful. However, this algorithm still produces something useful. So, it is good to have them both active.
HOM% h% ad% ag_a% targ Description: Target angle between successive tangent vectors. Parameter Type: real Range of Acceptable values: (0,90) Default Value: 8.d0 User Notes:
Degrees.
HOM% h% ad% dhr% on Description: Steplength adaptation of Den Heijer and Rheinbodlt (1981). Parameter Type: logical Default Value: .false. User Notes:
This method is based on Newton-Kantorovich theory to try to predict the behaviour of Newton's method. The steplength is adjusted to try to achieve some target number of iterations per nonlinear subproblem. This method seems ideal since it addresses directly the issue of problem stiffness but in practice it suffers from a number of approximation errors resulting in the numerous relaxations that we use.
HOM% h% ad% dhr% psi Description: Psi are functions that are used in the Kantorovich approximation. There are two available. Parameter Type: integer Range of Acceptable values: 1,2 Default Value: 1 User Notes:
It doesn't make much difference which you use.
HOM% h% ad% dhr% targ Description: Target number of iterations for dhr. Parameter Type: integer Range of Acceptable values: [1,inf) Default Value: 5
HOM% h% ad% wgj% on Description: Turn on Wales, Gaitonde, Jones' (2012) stplength adaptation. Parameter Type: logical Default Value: .false. User Notes:
A very simplistic algorithm, where the target is again the number of iterations. Perhaps too simplistic to update the steplength in a useful way.
HOM% h% ad% wgj% targ Description: Target number of iterations for wgj steplength adaptation. Parameter Type: integer Range of Acceptable values: [1, inf) Default Value: 5
HOM% h% hob% l_init Description: For the hob method, lambda does not start at 1.d0 (in fact, it is impossible in the authors' coordinates), so we start from this value. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 15.d0 User Notes:
Input value is assumed to be in Hicken et al. (2011) coordinates.
HOM% h% hob% beta Description: See Hicken et al. (2011) AIAA paper. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.7d0
HOM% p
HOM% p% opt Description: Predictor method. Parameter Type: character Range of Acceptable values: 'euler' Default Value: 'euler' User Notes:
Hgiher order predictors may some day be supported.
HOM% p% safety Description: Turn on if you always want to check the predictor tangent. Parameter Type: logical Default Value: .true.
User Notes:
Checks the predicted residual against the embedding residual and picks which one is best.
HOM% p% prec_up Description: Update the preconditioner at each tangent calculation? Parameter Type: logical Default Value: .true.
HOM% p% check_full Description: This is a fun option the will check the predicted and embedded residual element-wise and replace elements accordingly. Parameter Type: logical Default Value: .false. User Notes:
I haven't tested this extensively. In the tests I've run, this results in a very large initial residual which is reduced very rapidly, making it hard to determine what the relative tolerances should be.
HOM% p% res_max_i Description: Maximum allowable starting residual at lambda = 1.d0. Phase 2 values are interpolated from this and p%res_max_i. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d-1 User Notes:
If the residual after a predictor step exceeds the interpolated value, the predictor is scaled back until it is no longer exceeded.
HOM% p% res_max_f Description: Maximum allowable starting residual at lambda = 0.d0. Phase 2 values are interpolated from this and p%res_max_f. Parameter Type: real Range of Acceptable values: (0, inf) Default Value: 1.d-1 User Notes:
If the residual after a predictor step exceeds the interpolated values, the predictor is scaled back until it is no longer exceeded.
HOM% p% h_reduct_fac Description: If the predicted residual is larger than the interpolated value above, we reduce multiply the steplength by this factor and repeat the predictor step. Parameter Type: real Range of Acceptable values: (0, 1) Default Value: 0.6d0
HOM% p% h_reduct_max Description: If the predicted residual is larger than the interpolated value above, this is the maximum number of times we will try to reduce the steplength. Parameter Type: integer Range of Acceptable values: [1, inf) Default Value: 5
HOM% p% t% dlam_min_for_alge Description: Minimum change in lambda for which we use the algebraic method, less than this will use secant. Parameter Type: real Range of Acceptable values: (0,inf) Default Value: 5.d-2 User Notes:
Secant method is not very accurate for large step sizes. As the step size decreases, accuracy improves and it is very cheap, so we may want to use it for small step sizes.
HOM% p% t% opt Description: Options for calculating the tangent Parameter Type: character Range of Acceptable values: 'none', 'alge', 'seca' Default Value: 'alge' User Notes:
1) 'none' - Embedding algorithm
2) 'alge' - An accurate but expensive algebraic method, requiring the solution to a linear system of equations
3) 'seca' - Secant method; essentailly, first order backwards-differencing.
HOM% p% t% prec% opt Description: Choice of preconditioner for the algebraic tangent method. Parameter Type: Character Range of Acceptable values: 'iluk', 'ilut' Default Value: 'iluk' User Notes:
We only need to factor the preconditioner when p%t%opt = 'alge'.
HOM% p% t% prec% iluk% lev_fil Description: Fill level for the preconditioner. Parameter Type: integer Range of Acceptable values: [0, inf) Default Value: 2
HOM% p% t% s Description: Solver options for the tangent Parameter Type:LinSolvOpts Default Values:
p%t%s%solver = 'fgmrs'
p%t%s%matvec = 'frcht'
p%t%s%prec = 'schur'
p%t%s%rel_lin_tol = 1.d-2
p%t%s%krylv_size = 40
p%t%s%gcrot_k = 1
p%t%s%krylv_max = 100
p%t%s%sol_init = .true. User Notes:
Active only for HOM%t%opt = 'alge'
HOM% c
HOM% c% opt Description: Corrector option Parameter Type: character Range of Acceptable values: 'none', 'proj' Default Value: 'none' User Notes:
1) 'none' - lambda is treated as constant.
2) 'proj' - The system is solved in the minimum-norm sense, for the cost of some extra tangent calculations per predictor step.
HOM% c% tan_up_frq Description: Period with which to update the tangent. Parameter Type: integer Range of Acceptable values: (1, inf) Default Value: 100 (essentially, off by default) User Notes:
HOM%c%opt = 'proj' only.
HOM% c% dlam_max Description: Maximum allowable value that the corrector step can affect lambda by. Parameter Type: real Range of Acceptable values: (0,1) Default Value: 2.d-2 User Notes:
You shouldn't need to rely on this if the kappa-scaling is effective.
HOM%c%opt = 'proj' only.
HOM% c% t% opt Description: How to calculate the tangent for the corrector. Parameter Type: character Range of Acceptable values: 'alge' Default Value: 'alge' User Notes:
HOM%c%opt = 'proj' only. This should be left as 'alge'.
HOM% c% t% prec% opt Description: Choice of ILU factorization. Parameter Type: character Range of Acceptable values: 'iluk', 'ilut' Default Value: 'iluk'
HOM% c% t% prec% iluk% lev_fil Description: Fill level for the preconditioner. Parameter Type: integer Range of Acceptable values: [1, inf) Default Value: 2
Table of Contents
Jetstream contains both monolithic and predictor-corrector methods for homotopy-based continuation. For more information regarding the theory, implementation, and performance of these algorithms, refer to David Brown's PhD thesis. To use the homotopy modules:
1) Set opt_method = 'flowsolve' and diablo%nk_global = 0 (predictor-corrector homotopy continuation), diablo%nk_global = -1 (monolithic homotopy continuation), or diablo%nk_global = -2 (explicit monolithic homotopy continuation) in the input file;
2) Set diablo%hom_method appropriately: 'convex' (default) or 'global' ;
3) Include the homotopy namelist &homot at the bottom of the input file;
4) Include any homotopy parameters according to preference.
Note that many solver parameters (diablo%) are not used in this module. Instead, we now use Hom type parameters (c_hom% or g_hom%) to make the options phase-dependent.
Phases:1 --> lambda = 1.0;
2 --> 1.0 > lambda > 0.0
3 --> lambda = 0.0 (final phase)
HOM% convex_opt
Description: Specifies the continuation function to use.Parameter Type: character
Range of Acceptable values: 'diss', 'diss2'
Default Value: 'diss'
User Notes:
-'diss': Second order dissipation operator (without the pressure switch) as the homotopy function. The extra equation for the RANS formulation is the dissipation-like operator used to stabilize the convective term in the RANS equation (see Michal Osusky's Nashville AIAA paper, on Dr. Zingg's website).
-'diss2': This is exactly the same as 'diss' for Euler/NS, but for the RANS equations we use an extended version of the same operator to include the turbulent viscosity. Currently, 'diss2' is far superior to the RANS equations.
HOM% nls
HOM% nls% check_relres_glob
Description: A flag to determine whether to check the relative residual at globalization.
Parameter Type: logical
Default Value: .false.
User Notes:
The checks the relative residual of R at each iterate against the parameter HOM% nls% relres_glob. If it is below that value, we will switch directly to phase 3. This requires an extra L2 norm to be calculated at each iterate. We don't normally use this criterion, it is mainly just for comparison with the original DBC codes which did use this criterion. Default will become .false. at the next merge.
HOM% nls% tol_rel_embed
Description: A flag to determine whether to take the relative residual relative to the embedding step or the actual predictor point.
Parameter Type: logical
Default Value: .true.
User Notes:
Better to keep it on, since turning it off will actually solve the problem more when your predictor step is better, which is not logical.
HOM% nls% use_traceback
Description: If set to true, the solution will be traced back if the nls fails to converge when max iterations are met. Otherwise, it will just continue on as normal.
Parameter Type: logical
Default Value: .false.
User Notes:
You can turn this on for difficult flow solves, but expect high cost, and make sure to make nls%max_its(2) large enough so that you can be reasonably sure that failure to meet the tolerance indeed indicates a problem.
HOM% nls% traceback_max
Description: Maximum number of traceback iterations if nls%use_traceback is on.
Parameter Type: Integer
Default Value: 4
HOM% nls% relres_glob
Description: The relative residual that must be met as a requirement at globalization.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 1.d-3
User Notes:
See the description in HOM% nls% check_relres_glob for more info.
HOM% nls% fin_strt_relres
Description: The relative residual at globalization must be less than this to be accepted.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 5.d-1
User Notes:
We check the relative residual (calculated based on the initial flow residual) at globalization (lambda = 0) against this parameter. If it is not lower than this parameter, the predictor step will be repeated with a factor of HOM% nls% fin_strt_red_fac applied to the current steplength and the resulting nonlinear subproblem will be solved to try to get a better estimate. This process is repeated until a suitable initial residual is acquired. Note that the problem becomes increasingly stiff near lambda=0, so this can add significant computation cost to a flow solve. Usually, we use the large default value to essentially turn this off.
HOM% nls% fsrr_tb_max
Description: If the final starting relative residual tolerance nls%fin_strt_relres is not met, this parameter provides the upper bound on how many times traceback will be attempted.
Parameter Type: Integer
Range of Acceptable values: [0, inf]
Default Value: 10
HOM% nls% traceback_red_fac
Description: The traceback phase is activated if problems were encountered at the current subproblem or if nls%fin_strt_relres was not met. In the traceback phase, we repeat the previous predictor iterate with this factor applied to the steplength (so a larger value actually means less reduction).
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 0.5
User Notes:
There is probably no reason to change this from default.
HOM% nls% pc_its
Description: Maximum allowable predictor iterations, after which the flow solve will quit.
Parameter Type: integer
Range of Acceptable values: [1, 400)
Default Value: 50
User Notes:
A typical flow solve will take ~10 predictor steps. If it reaches 50, it is probably stuck above a stagnation point and will never converge.
HOM% nls% mh_its
Description: Maximum allowable iterations for monolithic homotopy, after which the flow solve will quit.
Parameter Type: integer
Default Value: 200
HOM% nls% abs_tol(1:3)
Description: Absolute tolerance to check if the residual is converged at each phase. Note that the phase 1 and phase 3 values are taken as abs_tol(1)l and abs_tol(3), but the phase 2 value is actually interpolated between abs_tol(1) and abs_tol(2) values.
Parameter Type: real(3)
Range of Acceptable values: Should be small
Default Value: (/ 1E-10, 1E-10, 1E-12 /)
User Notes:
Note that the convergence criterion for each nonlinear subproblem is that either the relative tolerance or the absolute tolerance is met. While it seems like a good idea in principle to check absolute residuals, in practice we don't really know what these values should be. So, we typically set these small so as not to rely on them, preferring to use the relative residual.
HOM% nls% rel_tol(1:3)
Description: Relative tolerance to check if the residual is converged at each phase. Unlike the absolute tolerance, nls(1), nls(2), and nls(3) do correspond exactly to the relative residual checked at each phase Like abs_tol, this value is also intepolated.
Parameter Type: real(3)
Range of Acceptable values: Should be small
Default Value: (/ 1E-1, 1E-1, 1E-10 /)
User Notes:
rel_tol(1) and rel_tol(2) are taken relative to the starting residual at each particular nonlinear subproblem. For phase 3, the relative residual is taken relative to the starting residual of the flow solve.
HOM% nls% max_its(1:3)
Description: Maximum allowable nonlinear iterations per subproblem at each phase.
Parameter Type: integer(3)
Range of Acceptable values: [1, inf)
Default Value: (/ 15, 25, 75 /)
HOM% nls% updat_frq(1:3)
Description: Frequency with which to update both the preconditioner matrix and its ILU factorization.
Parameter Type: integer(3)
Range of Acceptable values: [1, large]
Default Value: (/ 3, 3, 1 /)
HOM% prec
HOM% prec(1:3)% opt
Description: Choice of ILU factorization.
Parameter Type: Character(3)
Range of Acceptable values: 'iluk', 'ilut'
Default Value: (/ 'iluk', 'iluk', 'iluk' /)
HOM% prec(1:3)% iluk% lev_fil
Description: Fill level for ILUK
Parameter Type: Integer(3)
Range of Acceptable values: [0,1,2,3,...]
Default Value: (/ 2, 2, 2 /)
HOM% prec(1:3)% ilut
Description: Parameters for ILUT
Parameter Type: ilut_opt
Default Values:
ilut%lev_fil = (/ 10, 10, 10 /)
ilut%bnorm = (/ 2, 2, 2 /)
ilut%pivoting = (/ .false., .false., .false. /)
ilut%diagcomp = (/ .false., .false., .false. /)
ilut%rowave = (/ .false., .false., .false. /)
ilut%droptol = (/ 1.d-3, 1.d-3, 1.d-3 /)
ilut%adpfactor = (/ 0.d0, 0.d0, 0.d0 /)
HOM% ls(1:3)
Description: Parameters for line searchParameter Type: LineSearch
Default Values:
ls(:)%on = (/.false., .false., .false. /)
ls(:)%damp = (/ 0.9d0, 0.9d0, 0.9d0 /)
ls(:)%eta_in = (/ 1.d0, 1.d0, 1.d0 /)
ls(:)%eta_min = (/ 0.75d0, 0.75d0, 0.75d0 /)
ls(:)%rfac_tol = (/ 1.d0, 1.d0, 1.d0 /)
HOM% l
HOM% l% inewt_s_params
Description: That's a lower case 'ell', not an upper case 'eye'. The value of lamba below which we will use the matvecs and preconditioner parameters from the inexact Newton phase. For example, if inewt_s_params=0.1, then we can use Frechet matvecs and higher fill level when lambda is below 0.1.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 0.d0
HOM% l% init
Description: This is the initial value of lambda.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 1.d0
User notes:
Usually we use the default.
HOM% l% tol
Description: A tolerance on lambda. Lambda is considered to be essentially 1 or 0 if it is within this tolerance of it.
Parameter Type: real
Range of Acceptable values: should be small
Default Value: 1.d-12
User notes:
Not a critical value; no reason to mess with it.
HOM% scl
HOM% scl% mu
Description: mu scaling.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
Mu-scaling is an extra scaling factor that we apply to the homotopy function G. This parameter affects curvature and hence it affects predictor performance. The value from the input parameter is a front end to this; an appropriate value for mu is acquired from a numerical algorithm based on minimizing the H20norm of d||H||/dlam and hard-coded into the appropriate homotopy module. This value is an extra scaling factor that is applied afterwards. Smaller values tend to reduce the curvature near lambda=0 and increase it near lambda=1 and vice versa. Since the auto-scaling algorithm does not take into account problem stiffness, it may be useful to use mu ~(0.5-0.8). Or, just use the default.
HOM% scl% mu_turb
Description: mu scaling.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
An experimental extra mu-scaling factor in front of the RANS equation. Changing it from 1 usually causes the solver to fail.
HOM% scl% turb_fac
Description: Scaling factor for the RANS equations, similar to what is used in Michal's RANS scaling.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d-3
HOM% scl% kappa
Description: kappa-scaling value.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
This parameter is only active when auto-scaling is turned off (HOM% scl% k_auto = .false.), which we typically do not use.
HOM% scl% k_auto
Description: Turn kappa auto-scaling on?
Parameter Type: logical
Default Value: .true.
User Notes:
Kappa-scaling is applied to the whole equation. It does not affect the predictor performance, but is critical for the orthogonal corrector method and important for steplength adaptation as well since it adjusts the relative scaling between ||dq| and dlambda.
HOM% scl% k_adapt
Description: Turn adaptive kappa-scaling on?
Parameter Type: logical
Default Value: .false.
User Notes:
This will determine the kappa-scaling based on the first nonlinear subproblem requiring at least one nonlinear iteration. This can be used when k_auto is on, in which case it will replace the auto-scaling once it becomes available. I generally don't use this.
HOM% scl% k_angle
Description: The target angle between the orthogonal corrector and the constant-lambda corrector directions, used in determining the kappa-scaling.
Parameter Type: real
Range of Acceptable values: (0,90)
Default Value: 8.d0
User Notes:
Degrees. Only active when HOM% scl% k_auto = .true.
HOM% scl% k_f_auto
Description: Extra factor to multiply auto-acquired kappa by.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
Only active when HOM% scl% k_auto = .true.
HOM% scl% k_f_adapt
Description: Extra factor to multiply adaptation-acquired kappa by.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
Only active when HOM% scl% k_adapt = .true.
HOM% a
HOM% a% m_on
Description: Is this an auto-scaling run for mu?
Parameter Type: logical
Default Value: .false.
User Notes:
This determines acceptable values for mu based on minimizing the H2-norm of d||H||/dlam. The integral is estimated over a variety of mu for a single flow solve by applying a local change of coordinates to lambda. Since the integration is in the lambda direction, the estimate of the integral is inaccurate for large changes in mu, so we limit ourselves to a factor of 10 in each direction per scaling run. The intended use is that we should run this several times, updating mu each time, until it converges. (Should only take a few runs.)
HOM% a% m_opt
Description: Option for mu auto-scaling algorithm.
Parameter Type: character
Range of Acceptable values: 'error', 'resid'
Default Value: 'error'
User Notes:
The problem with using the residual is that it is biased by the relative scaling of ||R|| and ||G||, so we typically use the error in the H2-norm minimization described above, and not the residual. Only active when HOM% a% m_on = .true.
HOM% a% k_on
Description: Is this and auto-scaling run for kappa?
Parameter Type: logical
Default Value: .false.
User Notes:
Ideally, mu-scaling has been performed already. This determines acceptable values for kappa based on a target angle between the orthogonal corrector direction and the constant-lambda corrector direction. This should be run for a variety of Ma. We can then do some line-fitting and then hard-code the results into the appropriate homotopy module. (See HOM_C_Diss_Mod for an example of this.)
HOM% a% k_embed
Description: During an auto-scaling run for kappa, should we over-write the input parameters with embedding parameters?
Parameter Type: logical
Default Value: .true.
HOM% sat
HOM% sat% on
Description: Should we turn the SATs on?
Parameter Type: logical
Default Value: .true.
User Notes:
Note that the linear system will be singular at lambda=1 if the SATs are turned off.
HOM% sat% opt
Description: Different boundary conditions can be applied to the homotopy function.
Parameter Type: character
Range of Acceptable values: 'fstrm', 'flow'
Default Value: 'fstrm'
User Notes:
1) 'fstrm' - BC's imitate freestream conditions.
2) 'flow' - BC's imitate the flow BC's.
Both methods work, but the 'flow' option seems to result in higher curvature for viscous flows.
HOM% sat% fac
Description: We can multiply the SAT terms by a factor
Parameter Type: real
Range of Acceptable values: (-inf, inf)
Default Value: 1.d0
User Notes:
Mostly for debugging.
HOM% sat% sym
Description: Should symmetry planes still be treated as such?
Parameter Type: logical
Default Value: .false.
User Notes:
Works either way, but seems to exhibit slightly lower curvature with it off.
NOTE: This should be set to .true. for 2D flow.
HOM% sat% roe_avg
Description: Turn Roe averaging on?
Parameter Type: logical
Default Value: .false.
HOM% h
HOM% h% opt
Description: Options for how to modify the steplength.
Parameter Type: character
Range of Acceptable values: 'none', 'adapt', 'hob'
Default Value: 'adapt'
User Notes:
1) 'none' - Steplength is constant
2) 'adapt' - Applies any steplength adaptation routines, which must be activated individually. By default, ag_a and ag_d are turned on and wj and dhr are turned off. At each predictor step, all active steplength adaptations will be calculated and the most limiting one will be applied.
3) 'hob' - This imitates Hicken/Osusky/Buckley's 2011 AIAA paper. Mostly implemented for debugging and comparative purposes. Note that the scaling of the linear system is different.
HOM% h% dlam_init
Description: Change in lambda at the first iteration.
Parameter Type: real
Range of Acceptable values: (0, h%max)
Default Value: 1.d-1
User Notes:
This can generally be increased to about 0.2 without convergence problems.
HOM% h% min
Description: Minimum acceptable value of the steplength.
Parameter Type: real
Range of Acceptable values: (h%min, inf)
Default Value: 1.d-2
User Notes:
Better to rely on h%dlam_min, and to keep this small, since we really don't have a good idea of what it should be.
HOM% h% max
Description: Maximum acceptable value of the steplength.
Parameter Type: real
Range of Acceptable values: (h%min, inf)
Default Value: 4.d0
User Notes:
Better to rely on h%dlam_max, and to keep this large, since we really don't have a good idea of what it should be.
HOM% h% fmin
Description: Minimum value to divide the steplength by during adaptation.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 0.5d0
User Notes:
Since we are dividing, this actually sets an upper bound on how much the steplength can increase.
HOM% h% fmax
Description: Maximum value to divided the steplength by during adaptation.
Parameter Type: real
Range of Acceptable values: (1, inf)
Default Value: 2.d0
User Notes:
Since we are dividing, this actually sets an upper bound on how much the steplength can be reduced by.
HOM% h% dlam_min
Description: Minimum allowable increase in lambda at each predictor iterate.
Parameter Type: real
Range of Acceptable values: (0, h%dlam_max)
Default Value: 4.d-2
HOM% h% dlam_max
Description: Maximum allowable increase in lambda at each predictor iterate.
Parameter Type: real
Range of Acceptable values: (h%dlam_min, 1)
Default Value: 2.5d-1
HOM% h% dlam_max_fin
Description: Maximum allowable change in lambda at the final predictor step (towards globalization).
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 5.d-2
User Notes:
If this number is exceeded, the predictor step is scaled back.
HOM% ad% ag_d% on
Description: Adaptation of Allgower and Georg (1990) based on asymptotic expansions: distance to the curve.
Parameter Type: logical
Default Value: .true.
User Notes:
Increase the steplength if the initial predictor point was further from the solution than some target value, and decrease otherwise.
HOM% h% ad% ag_d% auto
Description: Turn on to auto-acquire a target value, which can then be multiplied by the factor h%ad%ag_d%fac.
Parameter Type: logical
Default Value: .true.
User Notes:
Unless you know specifically what a good distance to the curve is, you should turn this on.
HOM% h% ad% ag_d% fac
Description: After auto-acquiring the target value for ag_d, we can then multiply it by a factor.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d0
User Notes:
Greater than 1 will result in larger steplengths and vice versa. Only active if h%ad%ag_d%auto = .true.
HOM% h% ad% ag_d% targ
Description: Target value for the distance in ag_d.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 5.d-1
User Notes:
Only active if h%ad%ag_d%auto = .false.
HOM% h% ad% ag_a% on
Description: Turn on Allgower and Georg's (1990) method of asymptotic expansions: angle between successive tangent vectors.
Parameter Type: logical
Default Value: .true.
User Notes:
Essentially, a measure of curvature. This is affected by kappa-scaling. If no corrector iterates were performed this step, then ag_d results in 0 distance, which is not very useful. However, this algorithm still produces something useful. So, it is good to have them both active.
HOM% h% ad% ag_a% targ
Description: Target angle between successive tangent vectors.
Parameter Type: real
Range of Acceptable values: (0,90)
Default Value: 8.d0
User Notes:
Degrees.
HOM% h% ad% dhr% on
Description: Steplength adaptation of Den Heijer and Rheinbodlt (1981).
Parameter Type: logical
Default Value: .false.
User Notes:
This method is based on Newton-Kantorovich theory to try to predict the behaviour of Newton's method. The steplength is adjusted to try to achieve some target number of iterations per nonlinear subproblem. This method seems ideal since it addresses directly the issue of problem stiffness but in practice it suffers from a number of approximation errors resulting in the numerous relaxations that we use.
HOM% h% ad% dhr% psi
Description: Psi are functions that are used in the Kantorovich approximation. There are two available.
Parameter Type: integer
Range of Acceptable values: 1,2
Default Value: 1
User Notes:
It doesn't make much difference which you use.
HOM% h% ad% dhr% targ
Description: Target number of iterations for dhr.
Parameter Type: integer
Range of Acceptable values: [1,inf)
Default Value: 5
HOM% h% ad% wgj% on
Description: Turn on Wales, Gaitonde, Jones' (2012) stplength adaptation.
Parameter Type: logical
Default Value: .false.
User Notes:
A very simplistic algorithm, where the target is again the number of iterations. Perhaps too simplistic to update the steplength in a useful way.
HOM% h% ad% wgj% targ
Description: Target number of iterations for wgj steplength adaptation.
Parameter Type: integer
Range of Acceptable values: [1, inf)
Default Value: 5
HOM% h% hob% l_init
Description: For the hob method, lambda does not start at 1.d0 (in fact, it is impossible in the authors' coordinates), so we start from this value.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 15.d0
User Notes:
Input value is assumed to be in Hicken et al. (2011) coordinates.
HOM% h% hob% beta
Description: See Hicken et al. (2011) AIAA paper.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.7d0
HOM% p
HOM% p% opt
Description: Predictor method.
Parameter Type: character
Range of Acceptable values: 'euler'
Default Value: 'euler'
User Notes:
Hgiher order predictors may some day be supported.
HOM% p% safety
Description: Turn on if you always want to check the predictor tangent.
Parameter Type: logical
Default Value: .true.
User Notes:
Checks the predicted residual against the embedding residual and picks which one is best.
HOM% p% prec_up
Description: Update the preconditioner at each tangent calculation?
Parameter Type: logical
Default Value: .true.
HOM% p% check_full
Description: This is a fun option the will check the predicted and embedded residual element-wise and replace elements accordingly.
Parameter Type: logical
Default Value: .false.
User Notes:
I haven't tested this extensively. In the tests I've run, this results in a very large initial residual which is reduced very rapidly, making it hard to determine what the relative tolerances should be.
HOM% p% res_max_i
Description: Maximum allowable starting residual at lambda = 1.d0. Phase 2 values are interpolated from this and p%res_max_i.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d-1
User Notes:
If the residual after a predictor step exceeds the interpolated value, the predictor is scaled back until it is no longer exceeded.
HOM% p% res_max_f
Description: Maximum allowable starting residual at lambda = 0.d0. Phase 2 values are interpolated from this and p%res_max_f.
Parameter Type: real
Range of Acceptable values: (0, inf)
Default Value: 1.d-1
User Notes:
If the residual after a predictor step exceeds the interpolated values, the predictor is scaled back until it is no longer exceeded.
HOM% p% h_reduct_fac
Description: If the predicted residual is larger than the interpolated value above, we reduce multiply the steplength by this factor and repeat the predictor step.
Parameter Type: real
Range of Acceptable values: (0, 1)
Default Value: 0.6d0
HOM% p% h_reduct_max
Description: If the predicted residual is larger than the interpolated value above, this is the maximum number of times we will try to reduce the steplength.
Parameter Type: integer
Range of Acceptable values: [1, inf)
Default Value: 5
HOM% p% t% dlam_min_for_alge
Description: Minimum change in lambda for which we use the algebraic method, less than this will use secant.
Parameter Type: real
Range of Acceptable values: (0,inf)
Default Value: 5.d-2
User Notes:
Secant method is not very accurate for large step sizes. As the step size decreases, accuracy improves and it is very cheap, so we may want to use it for small step sizes.
HOM% p% t% opt
Description: Options for calculating the tangent
Parameter Type: character
Range of Acceptable values: 'none', 'alge', 'seca'
Default Value: 'alge'
User Notes:
1) 'none' - Embedding algorithm
2) 'alge' - An accurate but expensive algebraic method, requiring the solution to a linear system of equations
3) 'seca' - Secant method; essentailly, first order backwards-differencing.
HOM% p% t% prec% opt
Description: Choice of preconditioner for the algebraic tangent method.
Parameter Type: Character
Range of Acceptable values: 'iluk', 'ilut'
Default Value: 'iluk'
User Notes:
We only need to factor the preconditioner when p%t%opt = 'alge'.
HOM% p% t% prec% iluk% lev_fil
Description: Fill level for the preconditioner.
Parameter Type: integer
Range of Acceptable values: [0, inf)
Default Value: 2
HOM% p% t% prec% ilut
Description: Options for ILUT preconditioner for algebraic tangent.
Parameter Type: ilut_opts
Default Values:
p%t%prec%ilut%lev_fil = 10
p%t%prec%ilut%bnorm = 2
p%t%prec%ilut%pivoting = .false.
p%t%prec%ilut%diagcomp = .false.
p%t%prec%ilut%rowave = .false.
p%t%prec%ilut%droptol = 1.d-3
p%t%prec%ilut%adpfactor = 0.d0
HOM% p% t% s
Description: Solver options for the tangent
Parameter Type: LinSolvOpts
Default Values:
p%t%s%solver = 'fgmrs'
p%t%s%matvec = 'frcht'
p%t%s%prec = 'schur'
p%t%s%rel_lin_tol = 1.d-2
p%t%s%krylv_size = 40
p%t%s%gcrot_k = 1
p%t%s%krylv_max = 100
p%t%s%sol_init = .true.
User Notes:
Active only for HOM%t%opt = 'alge'
HOM% c
HOM% c% opt
Description: Corrector option
Parameter Type: character
Range of Acceptable values: 'none', 'proj'
Default Value: 'none'
User Notes:
1) 'none' - lambda is treated as constant.
2) 'proj' - The system is solved in the minimum-norm sense, for the cost of some extra tangent calculations per predictor step.
HOM% c% tan_up_frq
Description: Period with which to update the tangent.
Parameter Type: integer
Range of Acceptable values: (1, inf)
Default Value: 100 (essentially, off by default)
User Notes:
HOM%c%opt = 'proj' only.
HOM% c% dlam_max
Description: Maximum allowable value that the corrector step can affect lambda by.
Parameter Type: real
Range of Acceptable values: (0,1)
Default Value: 2.d-2
User Notes:
You shouldn't need to rely on this if the kappa-scaling is effective.
HOM%c%opt = 'proj' only.
HOM% c% t% opt
Description: How to calculate the tangent for the corrector.
Parameter Type: character
Range of Acceptable values: 'alge'
Default Value: 'alge'
User Notes:
HOM%c%opt = 'proj' only. This should be left as 'alge'.
HOM% c% t% prec% opt
Description: Choice of ILU factorization.
Parameter Type: character
Range of Acceptable values: 'iluk', 'ilut'
Default Value: 'iluk'
HOM% c% t% prec% iluk% lev_fil
Description: Fill level for the preconditioner.
Parameter Type: integer
Range of Acceptable values: [1, inf)
Default Value: 2
HOM% c% t% prec% ilut
Description: ILUT options for the corrector tangent preconditioner.
Parameter Type: ilut_opts
Range of Acceptable values: [0, inf)
Default Values:
c%t%prec%ilut%lev_fil = 10
c%t%prec%ilut%bnorm = 2
c%t%prec%ilut%pivoting = .false.
c%t%prec%ilut%diagcomp = .false.
c%t%prec%ilut%rowave = .false.
c%t%prec%ilut%droptol = 1.d-3
c%t%prec%ilut%adpfactor = 0.d0
HOM% c% t% s
Description: Solver options for the corrector tangent.
Parameter Type: LinSolvOpts
Default Values:
c%t%s%solver = 'fgmrs'
c%t%s%matvec = 'apprx'
c%t%s%prec = 'schur'
c%t%s%rel_lin_tol = 1.d-2
c%t%s%krylv_size = 40
c%t%s%gcrot_k = 1
c%t%s%krylv_max = 100
c%t%s%sol_init = .false.
User Notes:
HOM%c%opt = 'proj' only.
HOM% s(1:3)
Description: Solver options for phases 1, 2, and 3.Parameter Type: LinSolvOpts
Default Values:
s(1:3)%solver = (/ 'fgmrs', 'fgmrs', 'fgmrs' /)
s(1:3)%matvec = (/ 'apprx', 'frcht', 'frcht' /)
s(1:3)%prec = (/ 'schur', 'schur', 'schur' /)
s(1:3)%rel_lin_tol = (/ 1.d-2, 1.d-2, 1.d-2 /)
s(1:3)%kryl_size = (/ 40, 40, 40 /)
s(1:3)%gcrot_k = (/ 1, 1, 1 /)
s(1:3)%krylv_max = (/40, 60, 100 /)
s(1:3)%sol_init = (/ .false., .false., .false. /)
HOM% debug
HOM% debug% on
Description: Turns debugging on.
Parameter Type: logical
Default Value: .false.
User Notes: Don't touch.
HOM% debug% print_lev
Description: Controls some printing.
Parameter Type: integer
Default Value: 11
User Notes: Don't touch.