# Integrator

Model ElementIntegrator defines the simulation control parameters for a time-domain-based nonlinear dynamic analysis.

Integrator

## Description

These parameters control:
• 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.

Integrator supports two different categories of equation formulations:
• The Ordinary Differential Equations (ODE) form of the equations.
• The Differential Algebraic Equations (DAE) form of the equations.

## Attribute Summary

Name Property Modifiable by command?
type Enum ("GSTIFF DSTIFF HSTIFF MSTIFF VSTIFF ABAM", default="DSTIFF") Yes
error Double (default=None) Yes
hinit Double (default=None) Yes
hmax Double (default=None) Yes
hmin Double (default=None) Yes
kmax Int (default=None) Yes
interpolate Bool (False) Yes
maxit Int (default=None) Yes
pattern Pattern (default=None) Yes
alpha Double ()
beta Double ()
gamma Double ()
vel_tol_factor Double () Yes
minit
dae_index   Yes
dae_eval_expiry   Yes
dae_constr_tol Double () Yes
dae_vc_error_ctrl Bool () Yes
dae_vc_tol_factor Double () Yes

## Usage

# Integrator using "DSTIFF"
Integrator (type="DSTIFF", optional_attributes)

# Integrator using "VSTIFF", "MSTIFF" or "ABAM"
Integrator (type="VSTIFF", optional_attributes)
Integrator (type="MSTIFF", optional_attributes)
Integrator (type="ABAM",   optional_attributes)

## Attributes

Integrator using "DSTIFF" or "GSTIFF"
type
String
Defines the integrator to be used.
Select "DSTIFF".
hmin
Double
Defines the minimum step size the integrator is allowed to take.
The hmin attribute is optional.
When not specified, the default value for hmin is 1.0E-6.
interpolate
Boolean
Specifies whether the integrator uses interpolation for the results at the output steps.
• True means that MotionSolve interpolates (as needed) to obtain the results at the output points requested by the user.
• False means that MotionSolve forces the DASPK integrator to step exactly to the output points requested by the user.
The interpolate attribute is optional.
When not specified, interpolate = True
maxit
Integer
The maximum number of iterations that the corrector is allowed to take to achieve convergence.
The default value for maxit is 4. Under no circumstances should this be increased beyond 8. If the results don't converge for a particular time step, it may be better to let the integrator fail and try to solve with a smaller time step.
vel_tol_factor
Double
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.
minit
Int
The minimum number of iterations that the corrector is allowed to take before it checks for corrector divergence.
The default value for minit is 1. Under no circumstances should this be increased beyond 3.
dae_index
Int
The index of the DAE formulation.
Index 3 indicates that position constraints are added to the equations of motion.
Index 1 indicates that position, velocity, and acceleration constraints are added (Stabilized Index 1).
The default value for index is 3.
dae_eval_expiry
Int
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.
dae_constr_tol
Double
The tolerance on all algebraic constraint equations that the corrector must satisfy at convergence.
The default value for dae_constr_tol is 1.0E-5. Decrease this value only if you see a lot of "noise" in the joint or motion reaction forces. Smaller values for this attribute will decrease the speed of the solution.
pattern
String
This attribute controls the frequency of evaluation of the Jacobian matrix during corrector iterations. The "Kth" entry in the string tell MotionSolve whether to evaluate the Jacobian or not for the "Kth" iteration.
• A value of "T" implies that a new Jacobian is to be calculated at the "Kth" iteration.
• A value of "F" implies that a new Jacobian is not to be calculated at the "Kth" iteration.
Specify pattern only when the default setting does not work well. Frequent Jacobian iterations can slow down the simulations dramatically.
When not specified, the integrator examines the rate of convergence of the corrector to automatically determine if a new Jacobian is needed.
Integrator using "VSTIFF", "ABAM" or "MSTIFF:
type
String
Defines the integrator to be used.
Select "VSTIFF", "ABAM" or "MSTIFF"
Optional attributes - Available to all variants
error
Double
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 DIFF, TFSISO, and the GSE modeling entities. Since displacement and velocity have different units, they are subject to different error tolerances.
The error attribute is optional.
When not specified, the default value for error is 1.0E-3.
hmax
Double
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 hmax should be specified.
The hmax attribute is optional.
When not specified, the default value for hmax is 0.01.
hinit
Double
Specifies the maximum initial step size.
The hinit attribute is optional.
When not specified, the default value for hinit is 1.0E-8.
kmax
Integer
Specifies the maximum order that the integrator is to take. Higher orders lead to higher accuracy, but lower stability in the numerical method.
For models that contain contact or other discontinuous events, it may beneficial to set kmax = 2, which prevents the integrator from trying to use a higher order that will normally not succeed.
The kmax attribute is optional.
The table below specifies the maximum order for each integrator.
Integrator
KMAX
DSTIFF
5
VSTIFF
5
ABAM
12
MSTIFF
9
When not specified, kmax is given the maximum value the integrator can have.
Note: kmax ≥ 1

## Example

This example shows the default settings for the Integrator element that uses DSTIFF method.
DSTIFF = Integrator (type="DSTIFF", error=0.001, hinit=
1e-008, hmax=0.01, hmin=1e-006, kmax=5)