Modifying the Default Convergence Checks

Warning: The information in this section is provided for users who might want to adjust the default convergence criteria for the solution of nonlinear systems. In most cases these criteria need not be adjusted. The use of this set of features requires some experience and testing to ensure that the alternative convergence measures produce results with an acceptable level of accuracy.
You can use solution convergence checks to control the nonlinear equation solution accuracy, time incrementation, and overall solution time in Abaqus/Standard. For most analyses, the solution convergence check parameters need not be changed . However, in certain simulations that involve strong coupling between multiple physical fields, alternative convergence checks might reduce the solution time with minimal change in solution accuracy.

This section summarizes the more important solution convergence parameters and describes the circumstances in which they can be used effectively.

Values given for the solution convergence parameters remain in effect for the remainder of the analysis or until they are reset. You can restore all solution control parameters to their default values (see About Convergence and Time Integration Criteria).

This page discusses:

See Also
About Convergence and Time Integration Criteria
In Other Guides
*CONTROLS
Customizing general solution controls

Products Abaqus/Standard Abaqus/CAE

Convergence Checks

By default, Abaqus/Standard uses a combination of factors to determine whether the solution during a given increment has converged or not. The convergence checking algorithms are based upon the following:

  • comparing the largest residual for a given field to the corresponding time-averaged flux, and
  • comparing the largest correction for a field to the largest increment for the same field.
However, there are some subtleties within that basic framework (for example, to determine if the flux during a given increment is zero and/or whether the response within an increment is linear). For additional details, see Analysis Convergence Controls.

The default convergence checks tend to work quite well in most applications, especially in the structural mechanics domain. However, in problems involving strong coupling between two or more physical fields (that is, multiphysics applications), the default criteria can be somewhat strict and conservative, possibly leading to a large number of iterations, cutbacks, and increments. For such problems, Abaqus/Standard also offers a set of alternative and relaxed convergence measures. Within a given step, these alternative convergence measures can be used globally such that a specified convergence measure is applied to all the active fields in the model or they can be applied on an individual field basis. In the latter case, Abaqus/Standard continues to use the default convergence criteria for all the other fields. Within such a framework, Abaqus/Standard also provides the additional flexibility of changing the convergence criteria for the various active fields from one step to another.

Strict (Default) Convergence Measure

Abaqus/Standard provides default convergence measures applicable for all fields in a multiphysics simulation. However, you can optionally choose to apply the strict criteria to one or more specific fields only and to augment this strict criteria with alternative (and potentially different) criteria for each of the other fields. The strict convergence measure requires the following conditions to be satisfied before Abaqus/Standard accepts the incremental solution as converged:

  • Ratio of the largest residual flux to the time averaged flux is less than a tolerance, and
  • Ratio of the largest correction to the largest increment is less than a tolerance.

Input File Usage

CONTROLS, PARAMETERS=FIELD, FIELD=field, CONVERGENCE CHECK=STRICT

Moderate Convergence Measure

The moderate convergence measure requires the following conditions to be satisfied for the specified field for Abaqus/Standard to accept the incremental solution as converged:

  • Ratio of the largest residual to the largest flux is less than a tolerance, and
  • Ratio of the largest correction to the largest increment is less than a tolerance.

Compared to the strict convergence criterion, the moderate convergence criterion uses a different metric for the residual convergence. It compares the largest residual to the largest flux (instead of to the time-averaged flux, as in the strict measure) anywhere in the domain. This criterion is useful for applications when it is important to model the region with the largest flux for a particular field accurately. Relatively smaller changes in flux in other regions of the model do not affect the convergence in this approach. This measure might be a useful alternative in models for which the time-average flux is small, making it difficult for the strict measure to be satisfied.

Input File Usage

CONTROLS, PARAMETERS=FIELD, FIELD=field, CONVERGENCE CHECK=MODERATE

Relaxed Convergence Measure

The relaxed convergence measure is based only upon the largest correction to the specified field. The residual tolerances do not play any role for this criterion. Therefore, the relaxed measure accepts an incremental solution as converged when only the following criterion is satisfied:

  • The ratio of the largest correction to the largest increment is less than a tolerance.

The relaxed convergence measure ignores the residual checks. For well-posed nonlinear incremental boundary value problems with a nonsingular “stiffness matrix” (left-hand side of the linear system of equations), it is reasonable to assume that in most cases a small correction is the result of a small residual (right-hand side of the linear system of equations). For such well-posed problems, a relaxed convergence measure might prove more effective, especially when the time-averaged residual for a particular field is quite “small,” and does not decrease with further iterations.

Input File Usage

CONTROLS, PARAMETERS=FIELD, FIELD=field, CONVERGENCE CHECK=RELAXED

Concept Design Convergence Measure

The concept design convergence measure treats an increment as converged if either the residual check or the correction check of the strict convergence measure is satisfied. In other words, the incremental solution is accepted if either one of the following conditions is satisfied:

  • Ratio of the largest residual to the time-average flux is less than a tolerance, or
  • Ratio of the largest correction to the largest increment is less than a tolerance.

Input File Usage

CONTROLS, PARAMETERS=FIELD, FIELD=field, CONVERGENCE CHECK=CONCEPT DESIGN

Suggested Usage

In situations where the response of certain fields is mostly linear over the range of interest, you might get faster solutions using either the relaxed or the concept design measures, with minimal differences in results compared to the default (strict) approach. In situations where the flux might be relatively large in the regions of interest in a model (compared to the flux in other regions), you can use the moderate convergence approach to reach a converged solution faster.

In many cases, the relaxed convergence measure gives a sufficiently accurate solution with a reduced computation time. The concept design convergence measure is useful to arrive at quick solutions when evaluating multiple designs in the early stages of a design process. Once the initial design is refined, you can modify the convergence checks to use the default strict measure to validate the results obtained with the relaxed or the concept design approach.

Input File Template

The following multiphysics example consists of two fully coupled thermal-electrochemical-structural analysis steps. In this analysis the active fields are ion concentration, solid electric potential, fluid electric potential, displacement, and temperature. In the first step, the moderate convergence measure is applied for all five fields. In the second step, the ion concentration and the fluid electric potential fields use the relaxed convergence measure, while the other fields use the default (strict) convergence measure.

HEADING
*NODE
*ELEMENT
*MATERIAL
...

*STEP,NAME=step1
*COUPLED TEMPERATURE-DISPLACEMENT, ELECTROCHEMICAL
CONTROLS, PARAMETERS=FIELD, CONVERGENCE CHECK=MODERATE
...
*END STEP
***
*STEP,NAME=step2
*COUPLED TEMPERATURE-DISPLACEMENT, ELECTROCHEMICAL
CONTROLS, PARAMETERS=FIELD,  FIELD=ION CONCENTRATION, CONVERGENCE CHECK=RELAXED
CONTROLS, PARAMETERS=FIELD,  FIELD=FLUID ELECTRIC POTENTIAL, CONVERGENCE CHECK=RELAXED
...
*END STEP