bugfixes and documentation

Author: pancetta

docs/source/projects/doc_matrixPFASST_matrix.rst

@@ -0,0 +1,7 @@
+Full code: `pySDC/projects/matrixPFASST/compare_to_matrixbased.py <https://github.com/Parallel-in-Time/pySDC/blob/master/pySDC/projects/matrixPFASST/compare_to_matrixbased.py>`_
+
+.. literalinclude:: ../../../pySDC/projects/matrixPFASST/compare_to_matrixbased.py
+
+Results:
+
+.. literalinclude:: ../../../comparison_matrix_vs_nomat_detail.txt

docs/source/projects/doc_matrixPFASST_propagator.rst

@@ -0,0 +1,7 @@
+Full code: `pySDC/projects/matrixPFASST/compare_to_propagator.py <https://github.com/Parallel-in-Time/pySDC/blob/master/pySDC/projects/matrixPFASST/compare_to_propagator.py>`_
+
+.. literalinclude:: ../../../pySDC/projects/matrixPFASST/compare_to_propagator.py
+
+Results:
+
+.. literalinclude:: ../../../comparison_matrix_vs_propagator_detail.txt

docs/source/projects/matrixPFASST.rst

@@ -0,0 +1 @@
+.. include:: /../../pySDC/projects/matrixPFASST/README.rst

pySDC/implementations/controller_classes/allinclusive_multigrid_MPI.py

@@ -291,7 +291,6 @@ def pfasst(self, comm, num_procs):
                 else:  # SDC
                     self.S.status.stage = 'IT_FINE'
 
-
             else:
                 self.S.levels[0].sweep.compute_end_point()
                 self.hooks.post_step(step=self.S, level_number=0)
@@ -334,8 +333,6 @@ def pfasst(self, comm, num_procs):
 
             # go up the hierarchy from finest to coarsest level (parallel)
 
-
-
             self.S.transfer(source=self.S.levels[0], target=self.S.levels[1])
 
             # sweep and send on middle levels (not on finest, not on coarsest, though)
@@ -451,7 +448,8 @@ def pfasst(self, comm, num_procs):
                             self.logger.debug('recv data: process %s, stage %s, time %s, source %s, tag %s, iter %s' %
                                               (self.S.status.slot, self.S.status.stage, self.S.time, self.S.prev,
                                                l - 1, self.S.status.iter))
-                            self.recv(target=self.S.levels[l - 1], source=self.S.prev, tag=self.S.status.iter, comm=comm)
+                            self.recv(target=self.S.levels[l - 1], source=self.S.prev, tag=self.S.status.iter,
+                                      comm=comm)
 
                         if not self.S.status.last and self.params.fine_comm:
                             req_send.wait()

pySDC/implementations/problem_classes/Van_der_Pol_implicit.py

@@ -27,9 +27,9 @@ def __init__(self, problem_params, dtype_u, dtype_f):
             if key not in problem_params:
                 msg = 'need %s to instantiate problem, only got %s' % (key, str(problem_params.keys()))
                 raise ParameterError(msg)
-
+        problem_params['nvars'] = 2
         # invoke super init, passing dtype_u and dtype_f, plus setting number of elements to 2
-        super(vanderpol, self).__init__(2, dtype_u, dtype_f, problem_params)
+        super(vanderpol, self).__init__(problem_params['nvars'], dtype_u, dtype_f, problem_params)
 
     def u_exact(self, t):
         """

pySDC/projects/matrixPFASST/README.rst

@@ -0,0 +1,28 @@
+Matrix-based versions of PFASST
+===============================
+
+In this project, we use and test two matrix-based version of PFASST for linear problems:
+we write PFASST as a standard twogrid method and we derive the propagaton matrix of PFASST.
+Both approaches are compared to the standard multigrid controller of PFASST and with each other.
+This includes tests with the heat, the advection as well as the test equation.
+
+Matrix-based PFASST
+-------------------
+
+When written as a multigrid method for a linear composite collocation problem, PFASST can be compactly defined via a
+smoothing and a coarse-grid correction step, just as a standard two-grid method. In the new (and very specialized)
+controller ``allinclusive_matrix_nonMPI.py``, this concept is exploited to obtain a PFASST (and MLSDC and SDC)
+controller closely resembling this idea and notation. In ``compare_to_matrixbased.py``, this controller is tested
+against the standard PFASST implementation.
+
+.. include:: doc_matrixPFASST_matrix.rst
+
+Propagator-based PFASST
+-----------------------
+
+The second approach follows directly from the matrix formulation: instead of writing PFASST as an iterative scheme,
+we now derive the full propagation matrix, which takes the initial value u0 and produces the final value uend,
+over all steps, iterations and sweeps. This matrix can be used to analyze PFASST in yet another exciting way.
+
+.. include:: doc_matrixPFASST_propagator.rst
+