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 penalty constraint handler:




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


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{|
|  style="width:150px" | '''$alphaS ''' || penalty <math>\alpha_S</math> factor on single point constraints
|-
|  '''$alphaM''' || penalty <math>\alpha_M</math> factor on multi-point constraints
|}
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NOTES:
NOTES:
* As mentioned, this constraint handler can only enforce homogeneous single point constraints (fix command) and multi-pont constraints where the constraint matrix is equal to the identity (equalDOF command).
* 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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THEORY:




Latest revision as of 17:44, 12 October 2011



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 penalty 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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