executive_control set integrator_parameters dstiff
The DSTIFF command specifies the integration error tolerance and other parameters for a dynamic analysis using the DASSL computer code.
The principal distinctions among the various ways that the backward differentiation formulas can be implemented in an integration code involve the method of incorporating the variable step size in prediction scheme. The DASSL integrator uses a fixed leading coefficient formulation for the finite difference approximations to the derivatives.
While not as computationally efficient, the approach used by DASSL should be more stable numerically than the fixed-coefficient method in GSTIFF. The trade-off works in reverse order in comparison to the variable coefficients computed for the WSTIFF integrator in Adams. In general, for problems with behavior that do not exhibit severe gradients in the solution, the savings in CPU time need not be sacrificed for the more stable methods.
A second distinguishing feature of DSTIFF is that it is able to interpolate output data between integration steps. By default, DSTIFF also corrects the interpolated output data to be consistent with the system constraints (see the RECONCILE_VEL_AND_ACC parameter). While GSTIFF and WSTIFF must integrate exactly to an output step in order to generate output data, DSTIFF may take an integration step past an output time and interpolate the output data. This allows DSTIFF to adjust the integration step based solely on the error criteria, and take larger integration step than output step when possible. As a result, DSTIFF may be able to complete a simulation with fewer integration steps than would GSTIFF or WSTIFF. This may result in speed improvement (although the interpolation and correction require some computation as well).
As described in the various sections covering the ERROR_TOLERANCE parameter for the GSTIFF, DSTIFF, and WSTIFF commands, the only other significant differences between the integrators in Adams involve the error control algorithms.
For an analysis with the EQUILIBRIUM, IC, or KINEMATICS commands, the ALIMIT parameter controls the maximum angular increment per iteration and the TLIMIT parameter controls the maximum translational increment per iteration. The DSTIFF, GSTIFF, and WSTIFF commands do not allow you to control either the maximum angular increment per iteration or the maximum translational increment per iteration. Because large rotational displacements often cause problems for dynamic simulations, Adams limits the maximum angular increment per iteration to 0.5 rads (~ 29 deg.). However, because large translational displacements do not generally cause problems during dynamic simulations, Adams imposes no limit on the maximum translational increment per iteration. Format:
Description:
Parameter | Value Type | Description |
|---|
model_name | An existing model | Specifies the model to be modified. You use this parameter to identify the existing model to be affected with this command. |
error_tolerance | Real | Specifies the integration error tolerance. The ERROR_TOLERANCE parameter is also used to determine the convergence criterion for the corrector. The convergence tolerance is the value of ERROR_TOLERANCE parameter divided by 1000. |
hinit_time_step | Real number | Specifies the initial time step to be attempted in the integrator. |
hmax_time_step | Real number | Specifies the maximum integration step size Adams is to allow. |
kmax_integrator_order | Integer | Specifies the maximum order of the integrator. Reducing KMAX may speed integration when damping is light and the equations are numerically stiff. |
maxit_corrector_iterations | Integer | Specifies the maximum number of iterations that the corrector will take before the integrator backs off on the current value of the time step and tries a smaller value to achieve further progress. |
pattern_for_jacobian | Yes/No | Specifies as many as ten character strings that together establish the pattern for evaluating the Jacobian matrix during Newton-Raphson iteration. |
watch_integrator_perf | MONITOR, NO_MONITOR, INTERR, NO_INTERR, CORERR, NO_CORERR, INTFAIL, NO_INTFAIL, CORFAIL, NO_CORFAIL, MATRIX, NO_MATRIX, STEPSIZE, NO_STEPSIZE, NEWSTEP, NO_NEWSTEP, OUTPUT, NO_OUTPUT, ALL, NONE | Specifies as many as nine character strings that together establish the aspects of integrator performance you want to watch. |
reconcile_vel_and_acc | YES/NO | Reconciles the values of the displacements with the constraint equations in the problem. |
Extended Definition:
1. You may identify a model by typing its name or by picking it from the screen.
If the model is not visible on the screen, you must type the name. You may also find it convenient to type the name even if the model is displayed.
You must separate multiple model names by commas.
If the model is visible in one of your views, you may identify it by picking on any of the graphics associated with it.
You need not separate multiple model picks by commas.
2. A predictor-corrector scheme is implemented in DASSL to integrate the system of differential and algebraic equations. The predictor algorithm uses a polynomial fit to the previous values of each component of state vector to estimate its value at the next time step. The corrector algorithm begins with the set of predicted values and uses a modified Newton-Raphson iteration scheme to find a solution that satisfies the equations to within the convergence tolerance.
The convergence criterion imposed on the DASSL integrator in Adams uses the maximum norm over the relative errors in all of the components of the state vector. The result must be bounded by .001r, i.e. by thousandth of the specified integration error tolerance r.
3. HINIT_TIME_STEP is not specified or if it is set equal to 0, then the integrator will attempt to get started with the default value. The initial step actually used by the integrator is determined by the error tolerance.
4. For the pattern_for_jacobian for each iteration, T or TRUE indicates that Adams is to evaluate the Jacobian, or F or FALSE indicates that Adams is not to evaluate the Jacobian. Thus cj determines whether or not Adams is to evaluate the Jacobian at the jth iteration. If necessary, Adams repeats the pattern of evaluation until it reaches the maximum number of iterations (MAXIT). The number of Y's or Yes’s and N's or No's, together, must be at least one and no more than ten. PATTERN defaults to Y:N:N:N:Y:N:N:N:Y:N, i.e. to evaluating the Jacobian at every fourth iteration.
5. For the watch_integrator_perf parameter, the items you can watch and the defaults are as follows:
(NO) CORERR - (Do Not) Print the maximum corrector error and the equation in which it occurs, and the largest variable change and the equation in which it occurs. The default is no CORERR.
(NO) CORFAIL - (Do Not) Print every time the corrector does not converge within the number of iterations set by MAXIT. The default is no CORFAIL
(NO) INTERR - (Do Not) Print the maximum integration error at each integration step and the variable in which it occurs. The default is no INTERR.
(NO) INTFAIL - (Do Not) Print every time Adams tries a step that exceeds the integration error tolerance. The default is no INTFAIL.
(NO) MATRIX - (Do Not) Print the inverse condition number of the Jacobian matrix for teach factorization. The default is no MATRIX.
(NO) MONITOR - (Do Not) Print the general statistics ten times during the simulation period. The default is no MONITOR.
(NO) OUTPUT - (Do Not) Print each time Adams sends results to the output files. The default is no OUTPUT.
(NO) NEWSTEP - (Do Not) Print the new step size and order at the beginning of each trial step. The default is no NEWSTEP.
(NO) STEPSIZE - (Do Not) Print the statistics when changing the integration step size. The default is no STEPSIZE.
In addition, the following items affect all aspects:
ALL - Print all of the aspects of the integration process.
NONE - Print none of the aspects of the integration process.
Watch defaults to : NO_CORERR, NO_CORFAIL, NO_INTERR, NO_INTFAIL, NO_MATRIX, MONITOR, NO_OUTPUT, NO_NEWSTEP, NO_STEPSIZE.
6. The interpolated values of the velocities and accelerations are also corrected to satisfy the derivatives of the constraint equations only when RECONCILE_VEL_AND_ACC is turned on. Otherwise, the output values for the velocities and accelerations are the interpolated results. Since the integration step is determined solely by the error tolerance, the DASSL integrator generally does not compute the solution at the output points. Therefore, the output values of the solution are interpolated from the computed values at the integration steps. Thus, Adams must correct the displacements for the output values to satisfy the constraints.