use Jacobi to speed up test

Author: pbrubeck

demos/adaptive_multigrid/adaptive_multigrid.py.rst

@@ -64,7 +64,7 @@ Our approach strongly follows the similar problem in this `lecture course <https
       return uh
 
 Note the code after the construction of the :class:`.NonlinearVariationalProblem`. To use the :class:`.AdaptiveMeshHierarchy` with the existing Firedrake solver, we have to set the :class:`.AdaptiveTransferManager` as the transfer manager of the multigrid solver.
-For the parameters of the multigrid solver, we will be using patch relaxation, which we define with ::
+Since we are using linear CG elements, we will employ Jacobi as the multigrid relaxation, which we define with ::
 
    solver_params = {
       "mat_type": "matfree",
@@ -73,30 +73,17 @@ For the parameters of the multigrid solver, we will be using patch relaxation, w
       "mg_levels": {
           "ksp_type": "chebyshev",
           "ksp_max_it": 1,
-          "pc_type": "python",
-          "pc_python_type": "firedrake.PatchPC",
-          "patch": {
-              "pc_patch": {
-                  "construct_type": "star",
-                  "construct_dim": 0,
-                  "sub_mat_type": "seqdense",
-                  "dense_inverse": True,
-                  "save_operators": True,
-                  "precompute_element_tensors": True,
-              },
-              "sub_ksp_type": "preonly",
-              "sub_pc_type": "lu",
-          },
+          "pc_type": "jacobi",
       },
       "mg_coarse": {
-          "ksp_type": "preonly",
-          "pc_type": "python",
-          "pc_python_type": "firedrake.AssembledPC",
-          "assembled": {"ksp_type": "preonly", "pc_type": "lu"},
+          "mat_type": "aij",
+          "pc_type": "lu",
       },
    }
 
-For more information about patch relaxation, 
+Alternatively for high-order CG elements, it is recommended to use patch relaxation
+to achieve degree-independent multigrid convergence.
+For more information
 see :doc:`Using patch relaxation for multigrid <poisson_mg_patches.py>`. 
 The initial solution is shown below.