3.2.4.3. Energy Increment¶

This command is used to construct a convergence test which uses the energy increment, $0.5 (x^T b)$, where the two vector come from the matrix equation $Ax=b$, to determine if convergence has been reached. What the right-hand-side of the matrix equation is depends on integrator and constraint handler chosen. Usually, though not always, $x$ is equal to the incremental displacement and $b$ the unbalanced force. The command to create a NormEnergyIncr test is the following:

test EnergyIncr $tol $iter <$pFlag>

Argument	Type	Description
$tol	float	the tolerance criteria used to check for convergence
$iter	integer	the max number of iterations to check before returning failure condition
$pFlag	integer	print flag (optional: default is 0) valid options: 0 print nothing 1 print information on norms each time test() is invoked 2 print information on norms and number of iterations at end of successful test 4 at each step it will print the norms and also the <math>Delta U</math> and <math>R(U)</math> vectors. 5 if it fails to converge at end of $numIter it will print an error message BUT RETURN A SUCCESSFUL test.

Note

When using a penalty constraint handler, large forces (those necessary to enforce the constraint) are included in the $x$ vector. Even for very small changes in the displacement, if user has selected overly large penalty factor, large forces can appear in the $x$ vector.

Example:

The following examples demonstrate the command to create a NormEnergyIncr test which allows 10 iterations till failure with an energy increment $0.5 (x^T b)$ of 1.0e-2.

Tcl Code

test EnergyIncr 1.0e-2  10 2

Python Code

test('EnergyIncr', 1.0e-2, 10, 2)

Code Developed by: fmk