[CIG-SHORT] Fault implementation

[Brad Aagaard]

On 06/26/2012 07:11 AM, Birendra jha wrote:
> I am looking at FaultCohesiveDyn.cc
>
> In the integrateResidual function, what is the meaning of Line 338:
>
> residualVertexN = areaVertex * (dispTpdtVertexL - initialTractionsVertex);

The solution field is made up of displacements and Lagrange multipliers. 
dispTpdtVertexL is the fault traction at time t+dt associated with the 
Lagrange multiplier vertex. This is the term C^T l in equation 6.53.

> Also Line 329:
>      tractionNormal +=
> 	orientationVertex[indexN*spaceDim+jDim] * dispTpdtVertexL[jDim];

This resolves the traction vector in the xyz coordinate frame to the 
fault normal traction.

> In the integrateResidual are we adding the additional terms due to lagrange multiplier to the residual i.e. Eq.(6.27) (6.28) in the manual?

Using equation 6.53, the residual is

r = [ b ] - [ A C^T ][ u ]
     [ d ]   [ C  0  ][ l ]

In FaultCohesiveDyn, we are adding the term C^T l to the residual.

Regards,
Brad