Stokes example

Signed-off-by: Umberto Zerbinati <[email protected]>
NGSolve · Jun 4, 2024 · f90d700 · f90d700
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diff --git a/docs/src/PETScPC/stokes.py.rst b/docs/src/PETScPC/stokes.py.rst
@@ -142,7 +142,7 @@ We can also construct a multi-grid preconditioner for the top left block of the
    C = BlockMatrix( [ [twolvpre, None], [None, mpre] ] )
    gfu.vec.data[:] = 0; gfp.vec.data[:] = 0;
    gfu.Set(uin, definedon=mesh.Boundaries("inlet"))
-   print("-----------|Mass & Two Level Additivew Schwarz|-----------")
+   print("-----------|Mass & Two Level Additive Schwarz|-----------")
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-8,
                    maxsteps=100, printrates=True, initialize=False)
    
@@ -156,7 +156,7 @@ We can also construct a multi-grid preconditioner for the top left block of the
      - 4 (9.15e-14)
    * - Mass & LU
      - 66 (2.45e-08)
-   * - Mass & Two Level Additivew Schwarz
+   * - Mass & Two Level Additive Schwarz
      - 100 (4.68e-06)
 
 The mass matrix as a preconditioner doesn't seem to be ideal, in fact, our Krylov solver took many iterations to converge with a direct LU factorization of the velocity block and did not converge at all with `HYPRE`.
@@ -188,21 +188,53 @@ This formulation can easily be constructed by adding a new velocity block in the
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-10,
                    printrates=True, initialize=False)
    Draw(gfu)
+ 
+.. list-table:: Preconditioners performance
+   :widths: auto
+   :header-rows: 1
+
+   * - Preconditioner
+     - Iterations
+   * - Schur complement
+     - 4 (9.15e-14)
+   * - Mass & LU
+     - 66 (2.45e-08)
+   * - Mass & Two Level Additive Schwarz
+     - 100 (4.68e-06)
+   * - Augmented Lagrangian LU
+     - 2 (9.24e-8)
 
 Notice that so far we have been inverting the matrix corresponding to the Laplacian block using a direct LU factorization.
 This is not ideal for large problems, and we can use a `Hypre` preconditioner for the Laplacian block. ::
 
    smoother = aG.mat.CreateBlockSmoother(blocks)
-   preHG = PETScPreconditioner(aG.mat, vertexdofs, solverParameters={"pc_type":"gamg"})
+   preHG = PETScPreconditioner(aG.mat, vertexdofs, solverParameters={"pc_type":"hypre"})
    twolvpre = preHG + smoother
    C = BlockMatrix( [ [twolvpre, None], [None, mGpre] ] )
    gfu.vec.data[:] = 0; gfp.vec.data[:] = 0;
    gfu.Set(uin, definedon=mesh.Boundaries("inlet"))
-   print("-----------|Augmented Two Level Additivew Schwarz|-----------")
+   print("-----------|Augmented Two Level Additive Schwarz|-----------")
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-10,
                    printrates=True, initialize=False)
    Draw(gfu)
 
+.. list-table:: Preconditioners performance
+   :widths: auto
+   :header-rows: 1
+
+   * - Preconditioner
+     - Iterations
+   * - Schur complement
+     - 4 (9.15e-14)
+   * - Mass & LU
+     - 66 (2.45e-08)
+   * - Mass & Two Level Additive Schwarz
+     - 100 (4.68e-06)
+   * - Augmented Lagrangian LU
+     - 2 (9.24e-08)
+   * - Augmented Two Level Additive Schwarz
+     - 100 (1.06e-03)
+
 Our first attempt at using a `HYPRE` preconditioner for the Laplacian block did not converge. This is because the top left block of the saddle point problem now contains the augmentation term, which has a very large kernel.
 It is well known that algebraic multi-grid methods do not work well with indefinite problems, and this is what we are observing here. ::
 
@@ -264,4 +296,23 @@ In fact, since we know that the augmentation block has a lower rank than the Lap
    print("-----------|Boffi--Lovadina Augmentation Sherman-Morrisson-Woodbory|-----------")
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-13,
                    printrates=True, initialize=False)
-   Draw(gfu)
+   Draw(gfu)
+
+.. list-table:: Preconditioners performance
+   :widths: auto
+   :header-rows: 1
+
+   * - Preconditioner
+     - Iterations
+   * - Schur complement
+     - 4 (9.15e-14)
+   * - Mass & LU
+     - 66 (2.45e-08)
+   * - Mass & Two Level Additive Schwarz
+     - 100 (4.68e-06)
+   * - Augmented Lagrangian LU
+     - 2 (9.24e-08)
+   * - Augmented Two Level Additive Schwarz
+     - 100 (1.06e-03)
+   * - Augmentation Schermon-Morrisson-Woodbory
+     - 84 (1.16e-07)
diff --git a/docs/src/index.rst b/docs/src/index.rst
@@ -17,6 +17,7 @@ Welcome to ngsPETSc's documentation!
    :caption: PETSc PC
 
    PETScPC/poisson.py
+   PETScPC/stokes.py
 
 .. toctree::
    :maxdepth: 1