3.2.4.1. Norm Unbalance

This command is used to construct a convergence test which uses the norm of the right hand side of the matrix equation, i.e. $b$ vector in $Ax=b$, 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, it is equal to the unbalanced forces in the system. The command to create a NormUnbalance test is the following:

test NormUnbalance $tol $iter <$pFlag> <$nType>

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.
$nType	integer	type of norm (optional: default is 2 (0 = max-norm 1 = 1-norm 2 = 2-norm …))

Note

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

Example:

The following examples demonstrate the command to create a NormUnbalance test which allows 10 iterations till failure with a 2-norm in the $b$ vector, i.e. $\sqrt(b^T b)$ of 1.0e-2.

Tcl Code

test NormUnbalance 1.0e-2  10 2

Python Code

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

Code Developed by: fmk