docs: Add a section on adding a custom backend.

Author: Sbte

docs/custom-backend.rst

@@ -0,0 +1,36 @@
+Adding a custom backend
+=======================
+Adding a custom backend can be useful when using an external package for providing a model, or when using a custom solver.
+As mentioned in :ref:`choosing a backend`, we provide some basic parallel backends (:mod:`Epetra <.interface.Epetra>` and :mod:`PETSc <.interface.PETSc>`) that can be used as base classes.
+
+There are only a few methods that should be implemented when adding a custom backend.
+These methods are the ones that raise a ``NotImplementedError`` in :mod:`BaseInterface <.interface.BaseInterface>`.
+Of course all other methods in :mod:`BaseInterface <.interface.BaseInterface>` can also be overloaded, but they are all just convenience methods and are not required by this package.
+
+``solve(self, jac, rhs)`` or optionally ``solve(self, jac, rhs, rhs2=None, V=None, W=None, C=None)``
+  Should solve a linear system with matrix ``jac`` and right-hand side ``rhs`` and then return the solution.
+
+``jacobian(self, state)``
+  Should return a matrix object for the current state that can be used by the linear solver.
+
+``rhs(self, state)``
+  Should return the right-hand side for the current state.
+
+``vector(self)``
+  Should return a new vector that can interact with the linear solver.
+
+``mass_matrix(self)``
+  Should return a mass matrix object as used for time integration and eigenvalue computation.
+  This is optional if neither of those is used.
+
+``eigs(self, state, return_eigenvectors=False, enable_recycling=False)``
+  Used for eigenvalue computation during the continuation.
+  This is optional and only used when automatically detecting bifurcations.
+
+``set_parameter(self, name, value)``
+  Used during the continuation to set the continuation parameter.
+  This already has a default implementation that can be used if no custom discretization is being provided.
+
+..
+    Explicitly enable math mode
+.. math::

docs/index.rst

@@ -19,6 +19,7 @@ The package is fully agnostic of the computational backend, which allows for eas
    examples
    custom-bc
    custom-model
+   custom-backend
 
 .. _problem definitions:
 .. toctree::