4.8. Control Damped Solve

Control damped solve is used to aid implicit quasistatic runs in convergence. With implicit quasistatic problems, it is sometimes very difficult to achieve convergence with the cg solver alone (even when used in combination with the FETI equation solver). Some problems where convergence is difficult to achieve includes: problems with unconstrained rigid body motion, problems that contain very nonlinear physics, implicit contact problems that involve rebound or bounce, implicit contact problems where sliding occurs, and implicit fracture problems where failure introduces rigid body motion or softening materials.

At a high level, CONTROL DAMPED SOLVE places artificial springs to ground on nodes to allow the problem to converge. Once the springs are placed, CONTROL DAMPED SOLVE will iterate until the artificial spring force is below the user defined tolerance. To achieve convergence, the ground position of the springs is moved to the last predicted position at the control level. If the next predicted position is the same, the spring applies no force.

The command block for control damped solve is as follows:

BEGIN CONTROL DAMPED SOLVE [<string>damped solve_name]
  # Convergence commands
  TARGET SPRING FORCE = <real>target_spring_force
  TARGET RELATIVE SPRING FORCE = <real>target_rel_spring_force
  ACCEPTABLE SPRING FORCE = <real>accept_spring_force
  ACCEPTABLE RELATIVE SPRING FORCE = <real>accept_rel_spring_force
  REFERENCE = EXTERNAL|INTERNAL(EXTERNAL)
  MAXIMUM ITERATIONS = <integer>max_iter
  MINIMUM ITERATIONS = <integer>min_iter
  #
  # level selection command
  LEVEL = <integer>damped_solve_level
  #
  # artificial spring commands
  STIFFNESS FORM = SHIFTED|SCALED(SCALED)
  STIFFNESS FACTOR = <REAL>stiffness_factor
  FORCE DECAY = NONE|ITERFRAC|HALVED|TENTHED(HALVED)
  EVERY NTH NODE = <integer>nth_node(1)
  #
  # diagnostic output commands, off by default.
  ITERATION PLOT = <integer>iter_plot
    [DURING <string list>period_names]
  ITERATION PLOT OUTPUT BLOCKS  = <string list>plot_blocks
END [CONTROL DAMPED SOLVE <string>damped solve_name]

To enable control damped solve, a CONTROL DAMPED SOLVE command block must exist in the SOLVER command block. The command lines within the CONTROL DAMPED SOLVE command block are used to establish convergence criteria, select the level for control damped solve within the multilevel solver, specify characteristics of the artificial springs, and output diagnostic information. These commands are described in detail in Section 4.8.1 and Section 4.1.1.

4.8.1. Convergence Command

The command lines listed in this section specify convergence criteria for the control damped solve level.

TARGET SPRING FORCE = <real>target_spring_force
TARGET RELATIVE SPRING FORCE = <real>target_rel_spring_force
ACCEPTABLE SPRING FORCE = <real>accept_spring_force
ACCEPTABLE RELATIVE SPRING FORCE = <real>accept_rel_spring_force
REFERENCE = EXTERNAL|INTERNAL(EXTERNAL)
MAXIMUM ITERATIONS = <integer>max_iter
MINIMUM ITERATIONS = <integer>min_iter

Solver convergence is monitored for control damped solve by examining the force in the artificial springs. Convergence is evaluated by computing the \(L^2\) norm of the spring forces and comparing that with a target convergence criteria specified by the user in the control damped solve block. The relative spring force is computed by dividing the spring force by a reference quantity that is indicative of the current loading conditions on the model. Note the spring force has units of force while the relative spring force is a dimensionless quantity where one or larger is an unconverged solution and the value moves towards zero for increasingly exact convergence. When using CONTROL DAMPED SOLVE, at least one of the following must be specified: TARGET SPRING FORCE, TARGET RELATIVE SPRING FORCE, ACCEPTABLE SPRING FORCE, or ACCEPTABLE RELATIVE SPRING FORCE.

The TARGET SPRING FORCE command specifies the target convergence force in terms of the actual spring force norm. The TARGET RELATIVE SPRING FORCE command specifies a convergence criterion in terms of the relative spring force norm. If both command lines are specified, the multilevel solver will accept the damped solve solution as converged if either the target spring force norm or the target relative spring force norm is below the specified values.

Acceptable convergence criteria can also be used for damped solve convergence. If the solution has not converged to the specified target before the maximum number of iterations is reached, the spring force is checked against the acceptable convergence criteria. These criteria are specified via the ACCEPTABLE SPRING FORCE and ACCEPTABLE RELATIVE SPRING FORCE command lines. The concepts of acceptable spring force and acceptable relative spring force are the same as those used for the targets. If the solution has not met the target criteria but has met the acceptable criteria, the solution is allowed to proceed. The defaults for each of these acceptable criteria are 10 times the corresponding target criteria defaults.

If relative spring forces are given in the convergence criteria, the REFERENCE command line can be used to select the method for computing the reference load. This command line has two options: EXTERNAL and INTERNAL. When using the default option (EXTERNAL), the reference value is taken as the maximum of the \(L^2\) norm of either the current externally applied or reaction loads. The INTERNAL option uses the norm of the internal forces as the reference load. These criteria are further explained in Section 4.2.1.

The MAXIMUM ITERATIONS and MINIMUM ITERATIONS command lines specify the maximum and minimum number of damped solve updates, respectively. The default minimum number of iterations, min_iter, is 0. If a number greater than 0 is specified, the multilevel solver will update the damped solve at least that many times, regardless of whether the convergence criteria have been met.

For an explanation of commands common to all controls, see Section 4.1.1.

4.8.2. Level Command

When used in a multilevel solver the CONTROL DAMPED SOLVE command block is recommended to be at level 1 and be the only control acting at that level. This allows the artificial spring force to be minimized before considering other controls. For more details on the LEVEL command see Section 4.1.1.

4.8.3. Control Damped Solve Artificial Spring Commands

STIFFNESS FORM = SHIFTED|SCALED(SCALED)
STIFFNESS FACTOR = <REAL>stiffness_factor
FORCE DECAY = NONE|ITERFRAC|HALVED|TENTHED(HALVED)
EVERY NTH NODE = <integer>nth_node(1)

Commands directly relating to the artificial springs created by CONTROL DAMPED SOLVE are described in this section. STIFFNESS FORM specifies how the stiffness of the artificial springs is determined. If option SHIFTED is used all artificial springs added have the same stiffness. That spring’s stiffness is the maximum value of the nodal stiffness from the element stiffness contributions then scaled by the STIFFNESS FACTOR. If the option SCALED is used the artificial springs stiffness is the node’s nodal stiffness scaled by the STIFFNESS FACTOR.

The STIFFNESS FACTOR command specifies the scale factor for which to scale the spring stiffness. This scale factor can be between 0.0 and 1.0.

The FORCE DECAY command is used to decrease the stiffness used in the internal force routine (but not the preconditioner) with each control level iteration. The option NONE does nothing to the stiffness. The option ITERFRAC decreases the stiffness by 1 over the current iteration number. The option HALVED decreases the stiffness by half with each iteration. The option TENTHED decreases the stiffness by a factor of 10 with each iteration. The current FORCE DECAY FACTOR is echoed in the log file.

The EVERY NTH NODE command specifies the nodes for which the artificial springs are applied to. If EVERY NTH NODE = 1, springs will be applied to every node in the model. If EVERY NTH NODE = 5, springs will be applied to every 5th node in the model and then perturbed by 1 every CONTROL DAMPED SOLVE iteration.

Currently, there is not an automated method of deciding which nodes need springs. More advanced options for spring placement are currently in-development.

When a CONTROL DAMPED SOLVE block is included in the input deck, an integer field named Control_NodeMask is created. A node with an integer value of Control_NodeMask greater than 0 will have a spring added to ground. This field is what Sierra/SM uses to determine which nodes should have artificial springs. If desired, a user can set this field manually either by using a script like exodus.py or by setting the field with an initial condition block. To keep the field at the user defined value set EVERY NTH NODE = 0 to avoid the internals from resetting the field.

4.8.4. Other Commands

For an explanation of commands related to iteration plot, see Section 4.1.1.

4.8.5. Control Damped Solve Input Example

The following example shows the setup for a general multilevel solver involving control contact and control damped solve. Each load step first a multilevel control damped solve model problem is solved. Once the control damped solve force converges to the specified value, control contact is then solved at the next control level. Control damped solve again solves the model problem with the contact forces included, and the process continues until both levels converge to their specified criteria.

Begin solver

  Begin cg
    target relative residual = 1.0
  end cg

  Begin control damped solve
    level = 1
    target relative spring force = 1.0e-3
    stiffness shift factor = 1.0e-2
    maximum iterations = 100
  end control damped solve

  Begin control contact
    level = 2
    target relative residual = 1.0e-6
  end control contact
End