Relative Energy Increment Test

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This command is used to construct a convergence test which uses the dot product of the solution vector and norm of the right hand side of the matrix equation to determine if convergence has been reached. The physical meaning of this quantity depends on the integrator and constraint handler chosen. Usually, though not always, it is equal to the energy unbalance in the system. The test is relatively to the first dot product computed for each step. The command to create a EnergyIncr test is the following:

test RelativeEnergyIncr $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 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
$nType	optional type of norm, default is 2. (0 = max-norm, 1 = 1-norm, 2 = 2-norm, ...)

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NOTES:

• When using the Penalty method additional large forces to enforce the penalty functions exist on the right had side, making

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

• When Lagrange multipliers are used, the solution vector contains the Lagrange multiplies.

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

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Code Developed by: fmk