:py:mod:`femo_alpha.dynamic_rm_shell.nonlinear_utils`
=====================================================

.. py:module:: femo_alpha.dynamic_rm_shell.nonlinear_utils


Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   femo_alpha.dynamic_rm_shell.nonlinear_utils.NewtonSolver
   femo_alpha.dynamic_rm_shell.nonlinear_utils.NonlinearProblem_mod



Functions
~~~~~~~~~

.. autoapisummary::

   femo_alpha.dynamic_rm_shell.nonlinear_utils.solveNonlinear_mod



.. py:class:: NewtonSolver(comm: mpi4py.MPI.Intracomm, problem: NonlinearProblem)

   Bases: :py:obj:`dolfinx.cpp.nls.petsc.NewtonSolver`

   
   This class was copied from dolfinx.nls.petsc.NewtonSolver, for reference and for future modifications
















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   .. py:property:: A
      :type: petsc4py.PETSc.Mat

      
      Jacobian matrix
















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   .. py:property:: b
      :type: petsc4py.PETSc.Vec

      
      Residual vector
















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   .. py:method:: setP(P: types.FunctionType, Pmat: petsc4py.PETSc.Mat)

      
      Set the function for computing the preconditioner matrix

      Args:
          P: Function to compute the preconditioner matrix
          Pmat: Matrix to assemble the preconditioner into















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   .. py:method:: solve(u: fem.Function)

      
      Solve non-linear problem into function u. Returns the number
      of iterations and if the solver converged.
















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.. py:class:: NonlinearProblem_mod(F: ufl.form.Form, u: dolfinx.fem.function.Function, bcs: List[dolfinx.fem.bcs.DirichletBCMetaClass] = [], J: ufl.form.Form = None, form_compiler_options={}, jit_options={})

   
   Nonlinear problem class for solving the non-linear problem
   :math:`F(u, v) = 0 \ \forall v \in V` using PETSc as the linear algebra
   backend. This class was copied from the `NonlinearProblem` class that is built-in in DOLFINx
















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   .. py:property:: L
      :type: dolfinx.fem.forms.FormMetaClass

      
      Compiled linear form (the residual form)
















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   .. py:property:: a
      :type: dolfinx.fem.forms.FormMetaClass

      
      Compiled bilinear form (the Jacobian form)
















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   .. py:method:: F(x: petsc4py.PETSc.Vec, b: petsc4py.PETSc.Vec)

      
      Assemble the residual F into the vector b.

      Args:
          x: The vector containing the latest solution
          b: Vector to assemble the residual into















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   .. py:method:: J(x: petsc4py.PETSc.Vec, A: petsc4py.PETSc.Mat)

      
      Assemble the Jacobian matrix.

      Args:
          x: The vector containing the latest solution















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   .. py:method:: form(x: petsc4py.PETSc.Vec)

      
      This function is called before the residual or Jacobian is
      computed. This is usually used to update ghost values.

      Args:
         x: The vector containing the latest solution















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.. py:function:: solveNonlinear_mod(F, w, bcs, abs_tol=1e-50, max_it=1, log=False)

   
   Wrap up the nonlinear solver for the problem F(w)=0 and
   returns the solution
















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