ISSUE 3763: Fix default solver options in documentation

CITATION.rst

@@ -12,7 +12,7 @@ If you publish results using Firedrake, we would be grateful if you would cite t
 
   @manual{FiredrakeUserManual,
     title        = {Firedrake User Manual},
-    author       = {David A. Ham and Paul H. J. Kelly and Lawrence Mitchell and Colin J. Cotter and Robert C. Kirby and Koki Sagiyama and Nacime Bouziani and Thomas J. Gregory and Jack Betteridge and Daniel R. Shapero and Reuben W. Nixon-Hill and Connor J. Ward and Patrick E. Farrell and Pablo D. Brubeck and India Marsden and Daiane I. Dolci and Joshua Hope-Collins and Sophia Vorderwuelbecke and Thomas H. Gibson and Miklós Homolya and Tianjiao Sun and Andrew T. T. McRae and Fabio Luporini and Alastair Gregory and Michael Lange and Simon W. Funke and Florian Rathgeber and Gheorghe-Teodor Bercea and Graham R. Markall},
+    author       = {David A. Ham and Paul H. J. Kelly and Lawrence Mitchell and Colin J. Cotter and Robert C. Kirby and Koki Sagiyama and Nacime Bouziani and Thomas J. Gregory and Jack Betteridge and Daniel R. Shapero and Reuben W. Nixon-Hill and Connor J. Ward and Patrick E. Farrell and Pablo D. Brubeck and India Marsden and Daiane I. Dolci and Joshua Hope-Collins and Umberto Zerbinati and Sophia Vorderwuelbecke and Thomas H. Gibson and Miklós Homolya and Tianjiao Sun and Andrew T. T. McRae and Fabio Luporini and Alastair Gregory and Michael Lange and Simon W. Funke and Florian Rathgeber and Gheorghe-Teodor Bercea and Graham R. Markall},
     organization = {Imperial College London and University of Oxford and Baylor University and University of Washington},
     edition      = {First edition},
     year         = {2023},

docs/source/solving-interface.rst

@@ -257,7 +257,7 @@ definite, and therefore can choose the conjugate gradient method,
 rather than GMRES.
 
 .. code-block:: python3
-
+   
    solve(a == L, solver_parameters={'ksp_type': 'cg'})
 
 To change the preconditioner used, we set the ``'pc_type'`` option.
@@ -271,17 +271,21 @@ precondition the system with:
          solver_parameters={'pc_type': 'hypre',
                             'pc_hypre_type': 'boomeramg'})
 
-Although the `KSP` name suggests that only Krylov methods are
-supported, this is not the case.  We may, for example, solve the
-system directly by computing an LU factorisation of the problem.  To
+Although the ``KSP`` name suggests that only Krylov methods are
+supported, this is not the case. We may, for example, solve the
+system directly by computing an LU factorisation of the problem. To
 do this, we set the ``pc_type`` to ``'lu'`` and tell PETSc to use a
 "preconditioner only" Krylov method:
 
 .. code-block:: python3
 
-   solve(a == L,
-         solver_parameters={'ksp_type': 'preonly',
-                            'pc_type': 'lu'})
+    solve(a == L,
+          solver_parameters={
+              'mat_type': 'aij',
+              'ksp_type': 'preonly',
+              'ksp_rtol': 1e-7,
+              'pc_type': 'lu'
+          })
 
 In a similar manner, we can use Jacobi preconditioned Richardson
 iterations with:
@@ -290,7 +294,7 @@ iterations with:
 
    solve(a == L,
          solver_parameters={'ksp_type': 'richardson',
-                            'pc_type': 'jacobi'}
+                            'pc_type': 'jacobi'})
 
 .. note::
 
@@ -728,32 +732,40 @@ solving with.
 Default solver options
 ~~~~~~~~~~~~~~~~~~~~~~
 
-If no parameters are passed to a solve call, we use, in most cases,
+
+If no parameters are passed to a ``solve`` call, we use, in most cases,
 the defaults that PETSc supplies for solving the linear or nonlinear
-system.  We describe the most commonly modified options (along with
-their defaults in Firedrake) here.  For linear variational solves we
+system. We describe the most commonly modified options (along with
+their defaults in Firedrake) here. For linear variational solves we
 use:
 
-* ``ksp_type``: GMRES, with a restart (``ksp_gmres_restart``) of 30
-* ``ksp_rtol``: 1e-7
-* ``ksp_atol``: 1e-50
-* ``ksp_divtol`` 1e4
-* ``ksp_max_it``: 10000
-* ``pc_type``: ILU (Jacobi preconditioning for mixed problems)
+* ``mat_type``: ``aij``
+* ``ksp_type``: ``preonly``
+* ``ksp_rtol``: ``1e-7``
+* ``ksp_atol``: ``1e-50``
+* ``ksp_divtol``: ``1e4``
+* ``ksp_max_it``: ``10000``
+* ``pc_type``: ``lu``
+
 
 For nonlinear variational solves we have:
 
 * ``snes_type``: Newton linesearch
-* ``ksp_type``: GMRES, with a restart (``ksp_gmres_restart``) of 30
+* ``ksp_type``: ``preonly``
+* ``mat_type``: ``aij``
 * ``snes_rtol``: 1e-8
 * ``snes_atol``: 1e-50
 * ``snes_stol``: 1e-8
 * ``snes_max_it``: 50
+* ``snes_type`` : ``newtonls``
+* ``snes_linesearch_type`` : `basic`
 * ``ksp_rtol``: 1e-5
 * ``ksp_atol``: 1e-50
 * ``ksp_divtol``: 1e4
 * ``ksp_max_it``: 10000
-* ``pc_type``: ILU (Jacobi preconditioning for mixed problems)
+* ``pc_type``: ``lu``
+* ``pc_factor_mat_solver_type`` : ``mumps``
+* ``pc_factor_mat_mumps_icntl_14``: 200
 
 To see the full view that PETSc has of solver objects, you can pass a
 view flag to the solve call.  For linear solves pass: