Adjoint Solver Reference

Adjoint

The adjoint solver controls the adjoint acceleration selection as well as the solving progress through right-click actions.


Adjoint Solution Algorithm Selection	Selects the solver to use to obtain the adjoint solution.
	GMRES-DR	Selects the defect-correction algorithm in combination with the generalized minimal residual with deflated restarting (GMRES-DR) solution driver for simulations that are difficult to converge. The solution driver accelerates convergence of the adjoint flow algorithm. For more information, see GMRES-DR Solution Driver Properties. This is the default.
	Flexible GMRES-DR	Selects the defect-correction algorithm in combination with the flexible GMRES-DR solution driver for simulations that are difficult to converge. Use this option for adjoint simulations where the default GMRES-DR solution driver does not provide acceptable rates of convergence. For more information, see GMRES-DR Solution Driver Properties.
	Defect Correction	Selects the defect-correction algorithm. This algorithm iteratively advances the adjoint solution similar to the primal solution process. It requires no additional memory overhead but may fail to converge for complex applications.

Right-Click Actions

Step

Runs the adjoint solver for all the active cost functions for one iteration.

Run

Runs the adjoint solver for all the active cost functions until a stopping criterion for the adjoint solver is met.

Clear

Clears all the adjoint solution.

Compute Parameter Sensitivity

Calculates the sensitivity of global parameters that are associated with boundary conditions. Parameter sensitivity can be computed for the following boundary condition types and properties:


Property	Boundary/ Region Physics Condition
Static Temperature	Velocity Inlet Mass Flow Inlet Far Field Pressure Outlet Wall
Supersonic Pressure	Mass Flow Inlet Stagnation Inlet
Pressure	Pressure Outlet Far Field
Total Pressure	Stagnation Inlet
Total Temperature	Stagnation Inlet Mass Flow Inlet
Mach Number	Far Field
Corrected Mass Flow Rate	Outlet
Heat Flux	Wall Interface
Shear Stress Specification, Heat Source	Wall
Modified Diffusivity, Turbulence Intensity , Turbulence Length Scale, Turbulent Viscosity, Turbulent Viscosity Ratio	Velocity Inlet Mass Flow Inlet Far Field Pressure Outlet
Flow Direction (except Flow Angles), Reference Frame Specification	Velocity Inlet Mass Flow Inlet Far Field Stagnation Inlet Pressure Outlet Wall
Energy Source Option, Mass Source Option, Momentum Source Option	Region

For more details refer to Computing Adjoint Parameter Sensitivity.

Compute Mesh Sensitivity

Calculates the mesh sensitivity, which gives the sensitivity of the active cost functions associated with mesh deformation. For more details refer to Computing the Mesh Sensitivity.

Compute Surface Sensitivity

Computes approximate sensitivities with respect to surface position for the active cost functions. For more details refer to Computing the Surface Sensitivity. This action only appears when the surface sensitivity model is selected in the physics continuum.

Compute Error Estimates

Marks locations in the flow where high numerical inaccuracy impacts the accuracy of the active cost functions. For more details refer to Computing Adjoint Error Estimates.

GMRES Solution Driver Properties

The GMRES-DR and Flexible GMRES-DR solvers are able to converge the adjoint of complex flow solutions. However, these solvers have a higher memory overhead compared to the simple defect correction scheme.

If you select the GMRES-DR or the Flexible GMRES-DR option, the GMRES-DR(m,k) Driver node or the FGMRES-DR(m,k) Driver node, respectively, is added to the simulation tree.


Preconditioning Option	Preconditioning is a method for transforming a set of equations to make them easier to solve. For the adjoint solver, this preconditioning is achieved by applying a number of defect correction sweeps. See also: GMRES Preconditioning. There are two preconditioning methods: Left Preconditioning The preconditioning transformation is applied from the left side of each term of Eqn. (5082). Default acceleration method for GMRES-DR solver. For particularly difficult convergence, Right Preconditioning may be helpful. Right Preconditioning The preconditioning transformation is applied from the right side of each term of Eqn. (5082). Default acceleration method for the Flexible GMRES-DR solver.
Krylov Space Dimension	Specifies the number of orthogonal Krylov space vectors to use. Increase this number to enhance GMRES-driver convergence and robustness. However, increasing this number increases the memory requirement.
Recycled Krylov vectors percentage	Specifies the number of Krylov vectors that are extracted from the Krylov space at the end of a restart, and are used to generate a new Krylov space. This number is expressed as a percentage of the Krylov space dimension with the allowed range of 0 to 60%. The recommended value for this number is 25% to 50%. When the number of recycled vectors is set to zero, GMRES-DR reduces to the classic GMRES, and FGMRES-DR reduces to FGMRES.
Number of correction sweeps	Number of smoothing defect correction iterations. If the default value of 2 does not provide sufficient smoothing for the Krylov solver, you are advised to increase this number. A value of 3 smoothing defect corrections has proven efficient for cases with difficult convergence.
Verbosity	Provides additional information on the GMRES solver in the Output window.

The default Adjoint Solution Algorithm Selection is GMRES-DR. Its default settings are correspond to best practices:


Property	Setting
Preconditioning Option	Left Preconditioning
Krylov Space Dimension	50
Recycled Krylov vectors percentage	25
Number of Correction Sweeps	2
Verbosity	None

Adjoint Coupled Implicit

This solver controls the preconditioning applied to the linearized flow equations during the adjoint solution process.


Courant Number	Adjusts the Courant (CFL) number of the flow equation

The default solver settings are as follows:


Node	Property	Setting
Adjoint Coupled Implicit	Courant Number	500
AMG Linear Solver	Cycle Type	V Cycle
V Cycle	Pre-Sweeps	0
	Post-Sweeps	3
	Max Levels	50

Note	Usually, no changes to the default settings are required. If the convergence is not sufficient, refer to Troubleshooting the Adjoint Flow.

Surface Sensitivity

The surface sensitivity solver is available when the surface sensitivity model is selected in the physics continuum.


Node	Property	Setting
Surface Sensitivity	Maximum Points in Filter Query Return List Specifies the maximum number of boundary surface centroids to be filtered. Surface sensitivity filtering stops proceeding when this number is exceeded.	50000

Adjoint Cost Functions

Here you define new cost functions or edit the existing cost functions.

Right-Click Actions

New: Creates a new cost function. For more details refer to Adjoint Cost Functions Reference.

Edit: Opens Adjoint cost function manager to modify the existing cost function.

[cost function] > Properties

The adjoint run can be started for an individual cost function through right-click actions.

Active: Sets the cost function to active during adjoint step/run. Enable this property to exclude the cost function for adjoint solver.

[cost function] Report: Specifies an associated report for the cost function.

Right-Click Actions

The right-click actions available for the adjoint solver as a whole are also available for individual cost functions. In each case, the solver action operates for the individual cost function only.