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Make PCLSC scalable

Alexander requested to merge lindad/petsc:more-lsc-scaling into main

Running a lid driven cavity problem with stable Q2-Q1 elements in MOOSE with Re of 1 for now, this is the Schur solve for the last nonlinear iteration

4x4 grid

      Residual norms for fieldsplit_p_ solve.
      0 KSP Residual norm 1.264317955512e-01 
      1 KSP Residual norm 5.353171872963e-02 
      2 KSP Residual norm 1.320145433260e-02 
      3 KSP Residual norm 9.527418518619e-03 
      4 KSP Residual norm 2.467312754883e-03 
      5 KSP Residual norm 1.025942620036e-03 
      6 KSP Residual norm 3.949588141702e-04 
      7 KSP Residual norm 6.508950968319e-05 
      8 KSP Residual norm 3.872489716724e-05 
      9 KSP Residual norm 1.742680450565e-05 
     10 KSP Residual norm 4.898127115304e-06 
     11 KSP Residual norm 1.911392437388e-06 
     12 KSP Residual norm 7.469172695319e-07

16x16 grid

      Residual norms for fieldsplit_p_ solve.
      0 KSP Residual norm 1.347318898775e-01 
      1 KSP Residual norm 4.639139139661e-02 
      2 KSP Residual norm 2.677855300982e-02 
      3 KSP Residual norm 1.556054595618e-02 
      4 KSP Residual norm 6.648612762279e-03 
      5 KSP Residual norm 2.340317979227e-03 
      6 KSP Residual norm 7.637512953759e-04 
      7 KSP Residual norm 3.129086418093e-04 
      8 KSP Residual norm 1.340851724753e-04 
      9 KSP Residual norm 5.838390574194e-05 
     10 KSP Residual norm 3.388639556529e-05 
     11 KSP Residual norm 1.072913525381e-05 
     12 KSP Residual norm 4.348611864699e-06 
     13 KSP Residual norm 2.101322471530e-06 
     14 KSP Residual norm 4.716187231465e-07

64x64 grid

      Residual norms for fieldsplit_p_ solve.
      0 KSP Residual norm 1.366046287802e-01 
      1 KSP Residual norm 3.285347668767e-02 
      2 KSP Residual norm 9.069925923552e-03 
      3 KSP Residual norm 4.352838575961e-03 
      4 KSP Residual norm 2.321448818500e-03 
      5 KSP Residual norm 1.376144461763e-03 
      6 KSP Residual norm 7.417347301474e-04 
      7 KSP Residual norm 3.686330102261e-04 
      8 KSP Residual norm 1.388093252520e-04 
      9 KSP Residual norm 4.157103751309e-05 
     10 KSP Residual norm 1.369625982313e-05 
     11 KSP Residual norm 4.918937417168e-06 
     12 KSP Residual norm 1.878039180136e-06 
     13 KSP Residual norm 9.262813634624e-07
Edited by Alexander

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