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~~NOTOC~~
===== Solver ComputeStrainRate =====

==== General Informations ====
  * **Solver Fortran File:** ''ComputeStrainRate.f90''
  * **Solver Name:** ''ComputeStrainRate''
  * **Required Output Variable(s):** default is ''StrainRate'' (else in ''StrainRate Variable Name'')  
  * **Required Input Variable(s):** A ''Flow Solution'' (in ''Flow Solution Name'')
  * **Optional Output Variable(s):** None  
  * **Optional Input Variable(s):** None


==== General Description ====
The aim of this solver is to compute the strain-rate tensor from the flow solution. For a 2D simulation there are 5 DOFs ''(E11, E22, E33, E12, Eii)'' and for a 3D simulation, 2 additional (7 DOFs) are being solved for ''(E11, E22, E33, E12, E23, E31, Eii)''. This solver uses a dummy variable and solves 5 (7 in 3D) times a 1 DOF system for each strain-rate components and the trace of the strain-rate tensor ''(Eii)''. 

The Strain-rate tensor is computed using:\\
<m> epsilon_{ij}  =  {1/2} ({u_{i,j} + u_{j,i}}) </m> \\
where <m> u </m> is the velocity vector solution of the Stokes problem.

==== SIF contents ====
The required keywords in the SIF file for this solver are:

<code>
Solver 1
  Equation = "Strain Rate"
  Procedure = "ElmerIceSolvers" "ComputeStrainRate"
! this is just a dummy, hence no output is needed
!-----------------------------------------------------------------------  
  Variable = -nooutput "Eij"
  Variable DOFs = 1

  Exported Variable 1 = "StrainRate"
  Exported Variable 1 DOFs = 5 !in 2D, 7 in 3D

! the name of the variable containing the flow solution (U,V,W,Pressure)
!-----------------------------------------------------------------------
  Flow Solver Name = String "Flow Solution"
! the name of the strain-rate solution (default is 'StrainRate')
  StrainRate Variable Name = String "StrainRate"
  
  Linear System Solver = Direct
  Linear System Direct Method = umfpack
End
</code>

==== Examples ====
An example using this solver can be found in ''[ELMER_TRUNK]/elmerice/examples/Test_StrainRate''.