Relative Norm Displacement Increment Test

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This command is used to construct a convergence test which uses the relative

. The command to create a RelativeNormDispIncr test is the following:

test RelativeNormDispIncr $tol $iter <$pFlag>

$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 successfull 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 SUCEESSFULL test

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NOTES:

1. When using the Lagrange Multipliers method additional unknows, the lagrange multipliers, exist in the solution vector, making

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

1. <math> \parallel \Delta(U^0) \parallel \!</math> is the initial solution when solveCurrentStep() is invoked on the algorithm.
2. Sometimes there may be problems converging if <math> \parallel \Delta (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 \Delta(U^i) \parallel}{\parallel \Delta(U^0) \parallel} < \text{tol} \!</math>