Fix after Patrick comments

NGSolve · Jun 28, 2024 · b27f3a8 · b27f3a8
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diff --git a/docs/src/PETScKSP/poisson.py.rst b/docs/src/PETScKSP/poisson.py.rst
@@ -101,15 +101,13 @@ We do this changing the flag :code:`"pc_type"` to :code:`"gamg"` ::
      - 35
 
 We can also use the PETSc `BDDC` preconditioner.
-Once again we will select this option via the flag :code:`"pc_type"` flag.
-We will also use the flag :code:`"ksp_rtol"` to obtain a more accurate solution of the linear system. ::
+Once again we will select this option via the flag :code:`"pc_type"` flag. ::
 
     solver = KrylovSolver(a, fes.FreeDofs(), 
                           solverParameters={"ksp_type": "cg", 
                                             "ksp_monitor": "",
                                             "pc_type": "bddc",
-                                            "ngs_mat_type": "is",
-                                            "ksp_rtol": 1e-10})
+                                            "ngs_mat_type": "is"})
     gfu = GridFunction(fes)
     solver.solve(f.vec, gfu.vec)
     print ("BDDC L2-error:", sqrt (Integrate ( (gfu-exact)*(gfu-exact), mesh)))
@@ -126,11 +124,11 @@ We will also use the flag :code:`"ksp_rtol"` to obtain a more accurate solution
    * - PETSc GAMG
      - 35
    * - PETSc BDDC (N=2)
-     - 10
+     - 5
    * - PETSc BDDC (N=4)
-     - 12
+     - 7
    * - PETSc BDDC (N=6)
-     - 14
+     - 9
 
 We can see that for an increasing number of subdomains :math:`N` the number of iterations also increases.
 Notice that in all the cases we have considered, the :code:`KrylovSolver` class creates a PETSc matrix from the NGSolve matrix in order to assemble the required preconditioners.
@@ -163,11 +161,11 @@ We will now use the :code:`KrylovSolver` class in a matrix-free fashion with the
    * - PETSc GAMG
      - 35
    * - PETSc BDDC (N=2)
-     - 10
+     - 5
    * - PETSc BDDC (N=4)
-     - 12
+     - 7
    * - PETSc BDDC (N=6)
-     - 14
+     - 9
    * - Element-wise BDDC
      - 14
 

diff --git a/docs/src/PETScPC/stokes.py.rst b/docs/src/PETScPC/stokes.py.rst
@@ -1,8 +1,8 @@
-Boffi-Lovadina Augmentation for Bernardi-Raugel discretisation of the Stokes problem
+Augmented Lagrangian preconditioning for P2-P0 discretisation of the Stokes problem
 ======================================================================================
 
-In this tutorial, we explore constructing preconditioners for Bernardi-Raugel discretisations of the Stokes problem with Boffi-Lovadina augmentation.
-In particular, we will consider a Bernardi-Raugel inf-sup stable discretisation of the Stokes problem, i.e.
+In this tutorial, we explore constructing preconditioners for discretisations of the Stokes problem with Boffi-Lovadina augmentation.
+In particular, we will consider a P2-P0 inf-sup stable discretisation of the Stokes problem, i.e.
 
 .. math::       
    

diff --git a/docs/src/SLEPcEPS/poisson.py.rst b/docs/src/SLEPcEPS/poisson.py.rst
@@ -71,7 +71,7 @@ We can discretise this problem using NGSolve as follows: ::
    m.Assemble()
 
 We can again solve the eigenvalue problem using ngsPETSc's `EigenSolver` class.
-The mass matrix now has a large kernel, hence is no longer symmetric positive definite, therefore we can not use LOBPCG as a solver.
+The matrix on the right-hand side of the generalised eigenvalue problem now has a large kernel, hence is no longer symmetric positive definite, therefore we can not use LOBPCG as a solver.
 Instead, we will use a Krylov-Schur solver with a shift-and-invert spectral transformation to target the smallest eigenvalues.
 Notice that because we are using a shift-and-invert spectral transformation we only need to invert the stiffness matrix which has a trivial kernel since we are using an inf-sup stable discretisation.
 If we tried to use a simple shift transformation to target the largest eigenvalues we would have run into the error of trying to invert a singular matrix.::