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docs/source/projects/doc_parallelSDC_nonlinear.rst

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.. image:: ../../../data/parallelSDC_fisher.png
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:scale: 50 %
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Full code: `projects/parallelSDC/newton_vs_sdc.py <https://github.com/Parallel-in-Time/pySDC/blob/master/projects/parallelSDC/newton_vs_sdc.py>`_
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.. literalinclude:: ../../../projects/parallelSDC/newton_vs_sdc.py
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Results:
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.. image:: ../../../data/parallelSDC_fisher_newton.png
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projects/parallelSDC/README.rst

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- ``IEpar``: one Euler step from t0 to the current node
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- ``Qpar``: Jacobi-like diagonal part of Q
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This part also contains ``minimization.py``, producing the heat maps for the spectral radius of the stiff limit matrix.
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.. include:: doc_parallelSDC_preconditioner.rst
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Simplified Newton for nonlinear problems
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Yet, the naive implementation still does not decouple space and time, so that we need to fix the Jacobian at e.g. node 0.
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This example compares the iteration counts and errors for this idea (incl. a modified Newton where the Jacobian is not fixed but the approach is applied nonetheless).
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Three new sweepers are used here: ``linearized_implicit_parallel``, ``linearized_implicit_fixed_parallel`` and ``linearized_implicit_fixed_parallel_prec``.
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This part also contains the code ``newton_vs_sdc.py`` where simplified and inexact Newton are compared to standard SDC for the generalized Fisher's equation.
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.. include:: doc_parallelSDC_nonlinear.rst
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