Penalty Method: Difference between revisions

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{{CommandManualMenu}}
{{CommandManualMenu}}


This command is used to construct a LagrangeMultiplier constraint handler, which enforces the constraints by introducing lagrange multiplies to the system of equation. The following is the command to construct a plain constraint handler:
This command is used to construct a Penalty constraint handler, which enforces the constraints using the penalty method. The following is the command to construct a plain constraint handler:




{|  
{|  
| style="background:yellow; color:black; width:800px" | '''constraints Lagrange <$alphaS $alphaM >'''
| style="background:yellow; color:black; width:800px" | '''constraints Penalty $alphaS $alphaM '''
|}
|}


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{|
{|
|  style="width:150px" | '''$alphaS ''' || <math>\alpha_S</math> factor on singe points. optional, default = 1.0
|  style="width:150px" | '''$alphaS ''' || penalty <math>\alpha_S</math> factor on single point constraints
|-
|-
|  '''$alphaM''' || <math>\alpha_M</math> factor on multi-points, optional default = 1.0;
|  '''$alphaM''' || penalty <math>\alpha_M</math> factor on multi-point constraints
 
|}
|}


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NOTES:
NOTES:
* The lagrange multiplier method introduces new unknowns to the system of equations. The diagonal part of the system corresponding to these new unknowns is 0.0. This ensure that the system IS NOT symmetric positive definite.
* The degree to which the constraints are enforced is dependent on the penalty values chosen. Problems can arise if these values are too small (constraint not enforced strongly enough) or too large (problems associated with conditioning of the system of equations).
 


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Revision as of 17:08, 15 October 2010



This command is used to construct a Penalty constraint handler, which enforces the constraints using the penalty method. The following is the command to construct a plain constraint handler:


constraints Penalty $alphaS $alphaM


$alphaS penalty <math>\alpha_S</math> factor on single point constraints
$alphaM penalty <math>\alpha_M</math> factor on multi-point constraints

NOTES:

  • The degree to which the constraints are enforced is dependent on the penalty values chosen. Problems can arise if these values are too small (constraint not enforced strongly enough) or too large (problems associated with conditioning of the system of equations).


THEORY:


Code Developed by: fmk

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