Relative Norm Unbalance Test

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This command is used to construct a convergence test which uses the relative norm of the right hand side of the matrix equation 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 RelativeNormUnbalance test is the following:

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

$tol	the tolerance criteria used to check for convergence
$iter	the max number of iterations to check before returning failure condition
$pFlag	optional print flag, 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	optional type of norm, default is 2. (0 = max-norm, 1 = 1-norm, 2 = 2-norm, ...)

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NOTES:

1. When using the Penalty method additional large forces to enforce the penalty functions exist on the right hand side, making

convergence using this test usually impossible (even though solution might have converged).

1. <math> \parallel R(U^0) \parallel \!</math> is the initial unbalance seen by the system when solveCurrentStep() is invoked on the algorithm.
2. Sometimes there may be problems converging if <math> \parallel R(U^0) \parallel \!</math> is very small to being with.

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THEORY:

If the system of equations formed by the integrator is:

<math>K \Delta U^i = R(U^i)\,\!</math>

This integrator is testing:

<math>\frac{\parallel R(U^i) \parallel}{\parallel R(U^0) \parallel} < \text{tol} \!</math>

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Code Developed by: fmk