# Parameters: Transient Solver

Command ElementParam_Transient defines the simulation control parameters for a time-domain-based nonlinear dynamic analysis.

## Description

- The choice of the integrator.
- The integration error tolerance (or the accuracy of the solution).
- Integrator performance during the simulation.

Dynamic simulations are performed on systems with one or more degrees of freedom. The dynamic simulation accounts for all inertia effects, all applied forces, and internal constraints. This enables you to run accurate system level simulations of complex mechanical systems.

- The Ordinary Differential Equations (ODE) form of the equations.
- The Differential Algebraic Equations (DAE) form of the equations.

The settings for each formulation are documented separately.

## Format

ODE form | DAE form |
---|---|

<Param_Transient
[
integrator_type = " real"
]
[
h_max = " real"
]
[
vel_tol_factor = " integer"]
[
rel_abs_tol_ratio = " /> |
<Param_Transient
[
integrator_type = " real"
]
[
h_max = " real"
]
[
h0_max = " real"
]
[
max_order = " real"
]
[
dae_index = " real"
]
[
dae_corrector_maxit = " real"
]
[
dae_vel_ctrl = "TRUE|FALSE integer"]
[
dae_eval_expiry = " [ dae_interpolation = "TRUE|FALSE"] /> |

## Attributes (ODE)

`integrator_type`- Defines the integrator to be used with the ODE form of the equations of
motion. Select one of the following:
- VSTIFF
- MSTIFF
- ABAM

`integrator_type`is VSTIFF. See the Comments below for a more detailed explanation of these integrators. `integr_tol`- Represents the maximum absolute error per step that the integrator is allowed in computing the displacement, velocity, and differential equations states. Differential equation states include those found in <Control_Diff>, <Control_SISO>, and the <Control_StateEqn> modeling entities.
`h_max`- Defines the maximum step size the integrator is allowed to take. You can
also use this parameter to control the accuracy of the results. Generally, a
smaller time step leads to more accurate results. For models with
discontinuities, such as contact, a smaller value of
`h_max`should be specified. `h_min`- Defines the minimum step size the integrator is allowed to take.
`h0_max`- The maximum initial step size. The default value for
`h0_max`is 1.0E-8. `vel_tol_factor`- A factor that multiplies
`integr_tol`to yield the error tolerance for velocity states. `rel_abs_tol_ratio`- The factor that multiplies
`integr_tol`to yield the relative error tolerance for the integrator. `max_order`- Specifies the maximum order that the integrator is to take. Each integrator
has its own built-in maximum order. Higher orders lead to higher accuracy,
but lower stability in the numerical method. The table below shows the
maximum order for the various integrators in MotionSolve that work with the ODE form of the
equations.
**Integrator****Maximum Order**- ABAM
- 12
- VSTIFF
- 05
- MSTIFF
- 09

## Attributes (DAE)

`integrator_type`- Defines the integrator to be used with the DAE form of the equations of motion. Currently, only one DAE integrator is supported - DSTIFF.
`integr_tol`- Represents the maximum absolute error per step the integrator is allowed in computing the displacement, velocity, and differential equations states. Differential equation states include those found in <Control_Diff>, <Control_SISO>, and the <Control_StateEqn> modeling entities.
`h_max`- Defines the maximum step size the integrator is allowed to take. You can
also use this parameter to control the accuracy of the results. Generally, a
smaller time step leads to more accurate results. For models with
discontinuities, such as contact, a smaller value of
`h_max`should be specified. `h_min`- Defines the minimum step size the integrator is allowed to take.
`h0_max`- The maximum initial step size.
`vel_tol_factor`- The factor that multiplies
`integr_tol`to yield the error tolerance for velocity states.The default value for`vel_tol_factor`is 1000. A good value for`vel_tol_factor`is the highest frequency in the system that you want to track. `max_order`- Specifies the maximum order that the integrator is to take. Higher orders lead to higher accuracy, but lower stability in the numerical method. The default maximum order for DSTIFF is 5.
`dae_alg_tol_factor`- The factor that multiplies
`integr_tol`to yield the error tolerance for algebraic states like Lagrange Multipliers. `dae_index`- The index of the DAE formulation.
`dae_constr_tol`- The tolerance on all algebraic constraint equations that the corrector must satisfy at convergence.
`dae_corrector_maxit`- The maximum number of iterations that the corrector is allowed to take to achieve convergence.
`dae_corrector_minit`- The minimum number of iterations that the corrector is allowed to take before it checks for corrector divergence.
`dae_vel_ctrl`- The logical flag that controls whether the velocity states are checked for
local integration error at each step. This is only valid for the SI1
integrator (see
`dae_index`).- "TRUE" indicates that the integrator is to include velocity states in its check for local integration at the end of each step.
- "FALSE" indicates that the integrator is to exclude velocity states in its check for local integration at the end of each step.

When not specified, this defaults to "TRUE" for the SI1 formulation and "FALSE" for the I3 formulation. For more information on formulations, refer to comments 4-6.**Integrator****DAE_VEL_CTRL**- I3 Formulation
- "FALSE"
- SI1 Formulation
- "TRUE"

The I3 formulation is not designed to track velocity errors. Hence, even when

`DAE_VEL_CTRL`is TRUE for I3, velocity errors will not be tracked. `dae_jacob_eval`- This attribute controls the frequency of evaluation of the Jacobian matrix
during corrector iterations.
- A value of "0" implies that the integrator automatically determines when a new Jacobian is needed by examining the rate of convergence.
- A value of "1" implies that a new Jacobian is to be calculated at every iteration.
- A value of "2" implies that a new Jacobian is to be calculated at every other iteration, for example at iteration 1-3-5, and so on.
- A value of "3" implies that a new Jacobian is to be calculated at every third iteration, for example at iterations 1-4-7, and so on.

Specify

`dae_jacob_eval`only when the default setting does not work well. Frequent Jacobian iterations can slow down the simulations dramatically.When not specified, the integrator automatically determines when a new Jacobian is needed by examining the rate of convergence.

`dae_eval_expiry`- This is an optional attribute. It defines the number of integration steps
after which the evaluation pattern defined by
`dae_jacob_eval`is ignored, and the default evaluation pattern is to be used. The default evaluation pattern is automatically determined when a new Jacobian is needed by examining the convergence rate of the corrector.For example,

`dae_eval_expiry`= "10" indicates that after 10 successful integration steps, the pattern specified by`dae_jacob_eval`is to be ignored.The default value of

`dae_eval_expiry`is 0, which means that the pattern specified by`dae_jacob_eval`is obeyed throughout the simulation.Use this flag when you want

`dae_jacob_eval`to be in effect only to overcome an initial transience in the system. `dae_jacob_init`- This attribute controls the Jacobian matrix evaluation during corrector
iterations.
- A value of "0" implies that the integrator automatically determines when a new Jacobian is needed by examining the rate of convergence.
- A value of "1" implies that a new Jacobian is to be calculated at the first iteration.
- A value of "2" implies that a new Jacobian is to be calculated at the second iteration.

Default = 0

`dae_interpolation`- Specifies whether the integrator uses interpolation for the results at the
output steps.
- TRUE implies that MotionSolve forces the integrator to
integrate the states from
`start_time`to`end_time`as specified in the <Simulate> block. MotionSolve then interpolates the results at the output points requested by the user. - FALSE implies that MotionSolve does not place any restrictions
on the integrator. Note: The integrator (DASPK) itself may use interpolation to obtain states at the exact output points if needed.

Default = TRUE

- TRUE implies that MotionSolve forces the integrator to
integrate the states from