Datatype DAEMesh for DAEs (#384)

* Added DAE mesh

* Updated all DAE problems and the SDC-DAE sweeper

* Updated playgrounds with new DAE datatype

* Adapted tests

* Minor changes

* Black.. :o

* Added DAEMesh only to semi-explicit DAEs + update for FI-SDC and ProblemDAE.py

* Black :D

* Removed unnecessary approx_solution hook + replaced by LogSolution hook

* Update WSCC9 problem class

* Removed unnecessary comments

* Removed test_misc.py

* Removed registering of newton_tol from child classes

* Update test_problems.py

* Rename error hook class for logging global error in differential variable(s)

* Added MultiComponentMesh - @brownbaerchen + @tlunet + @pancetta Thank ugit add pySDC/implementations/datatype_classes/MultiComponentMesh.py

* Updated stuff with new version of DAE data type

* (Hopefully) faster test for WSCC9

* Test for DAEMesh

* Renaming

* ..for DAEMesh.py

* Bug fix

* Another bug fix..

* Preparation for PDAE stuff (?)

* Changes + adapted first test for PDAE stuff

* Commented out test_WSCC9_SDC_detection() - too long runtime

* Minor changes for test_DAEMesh.py

* Extended test for DAEMesh - credits for @brownbaerchen

* Test for HookClass_DAE.py

* Update for DAEMesh + tests

* 🎉 - speed up test a bit (at least locally..)

* Forgot to enable other tests again

* Removed if-else-statements for mesh type

* View for unknowns in implSysFlatten

pySDC/projects/DAE/misc/DAEMesh.py

@@ -0,0 +1,12 @@
+from pySDC.implementations.datatype_classes.mesh import MultiComponentMesh
+
+
+class DAEMesh(MultiComponentMesh):
+    r"""
+    Datatype for DAE problems. The solution of the problem can be splitted in the differential part
+    and in an algebraic part.
+
+    This data type can be used for the solution of the problem itself as well as for its derivative.
+    """
+
+    components = ['diff', 'alg']

pySDC/projects/DAE/misc/HookClass_DAE.py

@@ -1,84 +1,82 @@
 from pySDC.core.Hooks import hooks
 
 
-class approx_solution_hook(hooks):
+class LogGlobalErrorPostStepDifferentialVariable(hooks):
     """
-    Hook class to add the approximate solution to the output generated by the sweeper after each time step
+    Hook class to log the error to the output generated by the sweeper after
+    each time step.
     """
 
-    def __init__(self):
-        """
-        Initialization routine for the custom hook
-        """
-        super(approx_solution_hook, self).__init__()
-
     def post_step(self, step, level_number):
-        """
-        Default routine called after each step
-        Args:
-            step: the current step
-            level_number: the current level number
+        r"""
+        Default routine called after each step.
+
+        Parameters
+        ----------
+        step : pySDC.core.Step
+            Current step.
+        level_number : pySDC.core.level
+            Current level number.
         """
 
-        super(approx_solution_hook, self).post_step(step, level_number)
+        super().post_step(step, level_number)
 
         # some abbreviations
         L = step.levels[level_number]
+        P = L.prob
 
         # TODO: is it really necessary to recompute the end point? Hasn't this been done already?
         L.sweep.compute_end_point()
 
+        # compute and save errors
+        # Note that the component from which the error is measured is specified here
+        upde = P.u_exact(step.time + step.dt)
+        e_global_differential = abs(upde.diff - L.uend.diff)
+
         self.add_to_stats(
             process=step.status.slot,
             time=L.time + L.dt,
             level=L.level_index,
             iter=step.status.iter,
             sweep=L.status.sweep,
-            type='approx_solution',
-            value=L.uend,
+            type='e_global_differential_post_step',
+            value=e_global_differential,
         )
 
 
-class error_hook(hooks):
+class LogGlobalErrorPostStepAlgebraicVariable(hooks):
     """
-    Hook class to add the approximate solution to the output generated by the sweeper after each time step
+    Logs the global error in the algebraic variable
     """
 
-    def __init__(self):
-        """
-        Initialization routine for the custom hook
-        """
-        super(error_hook, self).__init__()
-
     def post_step(self, step, level_number):
-        """
-        Default routine called after each step
-        Args:
-            step: the current step
-            level_number: the current level number
+        r"""
+        Default routine called after each step.
+
+        Parameters
+        ----------
+        step : pySDC.core.Step
+            Current step.
+        level_number : pySDC.core.level
+            Current level number.
         """
 
-        super(error_hook, self).post_step(step, level_number)
+        super().post_step(step, level_number)
 
-        # some abbreviations
         L = step.levels[level_number]
         P = L.prob
 
-        # TODO: is it really necessary to recompute the end point? Hasn't this been done already?
         L.sweep.compute_end_point()
 
-        # compute and save errors
-        # Note that the component from which the error is measured is specified here
         upde = P.u_exact(step.time + step.dt)
-        err = abs(upde[0] - L.uend[0])
-        # err = abs(upde[4] - L.uend[4])
+        e_global_algebraic = abs(upde.alg - L.uend.alg)
 
         self.add_to_stats(
             process=step.status.slot,
             time=L.time + L.dt,
             level=L.level_index,
             iter=step.status.iter,
             sweep=L.status.sweep,
-            type='error_post_step',
-            value=err,
+            type='e_global_algebraic_post_step',
+            value=e_global_algebraic,
         )

pySDC/projects/DAE/misc/ProblemDAE.py

@@ -2,7 +2,7 @@
 from scipy.optimize import root
 
 from pySDC.core.Problem import ptype, WorkCounter
-from pySDC.implementations.datatype_classes.mesh import mesh
+from pySDC.projects.DAE.misc.DAEMesh import DAEMesh
 
 
 class ptype_dae(ptype):
@@ -25,8 +25,8 @@ class ptype_dae(ptype):
         in work_counters['rhs']
     """
 
-    dtype_u = mesh
-    dtype_f = mesh
+    dtype_u = DAEMesh
+    dtype_f = DAEMesh
 
     def __init__(self, nvars, newton_tol):
         """Initialization routine"""
@@ -54,14 +54,18 @@ def solve_system(self, impl_sys, u0, t):
         me : dtype_u
             Numerical solution.
         """
-
         me = self.dtype_u(self.init)
+
+        def implSysFlatten(unknowns, **kwargs):
+            sys = impl_sys(unknowns.reshape(me.shape).view(type(u0)), **kwargs)
+            return sys.flatten()
+
         opt = root(
-            impl_sys,
+            implSysFlatten,
             u0,
             method='hybr',
             tol=self.newton_tol,
         )
-        me[:] = opt.x
+        me[:] = opt.x.reshape(me.shape)
         self.work_counters['newton'].niter += opt.nfev
         return me

pySDC/projects/DAE/problems/DiscontinuousTestDAE.py

@@ -1,5 +1,6 @@
 import numpy as np
 
+from pySDC.core.Problem import WorkCounter
 from pySDC.projects.DAE.misc.ProblemDAE import ptype_dae
 
 
@@ -57,14 +58,12 @@ class DiscontinuousTestDAE(ptype_dae):
 
     def __init__(self, newton_tol=1e-12):
         """Initialization routine"""
-        nvars = 2
-        super().__init__(nvars, newton_tol)
-        self._makeAttributeAndRegister('nvars', localVars=locals(), readOnly=True)
-        self._makeAttributeAndRegister('newton_tol', localVars=locals())
+        super().__init__(nvars=2, newton_tol=newton_tol)
 
         self.t_switch_exact = np.arccosh(50)
         self.t_switch = None
         self.nswitches = 0
+        self.work_counters['rhs'] = WorkCounter()
 
     def eval_f(self, u, du, t):
         r"""
@@ -85,24 +84,21 @@ def eval_f(self, u, du, t):
             The right-hand side of f (contains two components).
         """
 
-        y, z = u[0], u[1]
-        dy = du[0]
+        y, z = u.diff[0], u.alg[0]
+        dy = du.diff[0]
 
         t_switch = np.inf if self.t_switch is None else self.t_switch
 
         h = 2 * y - 100
         f = self.dtype_f(self.init)
 
         if h >= 0 or t >= t_switch:
-            f[:] = (
-                dy,
-                y**2 - z**2 - 1,
-            )
+            f.diff[0] = dy
+            f.alg[0] = y**2 - z**2 - 1
         else:
-            f[:] = (
-                dy - z,
-                y**2 - z**2 - 1,
-            )
+            f.diff[0] = dy - z
+            f.alg[0] = y**2 - z**2 - 1
+        self.work_counters['rhs']()
         return f
 
     def u_exact(self, t, **kwargs):
@@ -125,9 +121,11 @@ def u_exact(self, t, **kwargs):
 
         me = self.dtype_u(self.init)
         if t <= self.t_switch_exact:
-            me[:] = (np.cosh(t), np.sinh(t))
+            me.diff[0] = np.cosh(t)
+            me.alg[0] = np.sinh(t)
         else:
-            me[:] = (np.cosh(self.t_switch_exact), np.sinh(self.t_switch_exact))
+            me.diff[0] = np.cosh(self.t_switch_exact)
+            me.alg[0] = np.sinh(self.t_switch_exact)
         return me
 
     def get_switching_info(self, u, t):
@@ -162,14 +160,14 @@ def get_switching_info(self, u, t):
         m_guess = -100
 
         for m in range(1, len(u)):
-            h_prev_node = 2 * u[m - 1][0] - 100
-            h_curr_node = 2 * u[m][0] - 100
+            h_prev_node = 2 * u[m - 1].diff[0] - 100
+            h_curr_node = 2 * u[m].diff[0] - 100
             if h_prev_node < 0 and h_curr_node >= 0:
                 switch_detected = True
                 m_guess = m - 1
                 break
 
-        state_function = [2 * u[m][0] - 100 for m in range(len(u))]
+        state_function = [2 * u[m].diff[0] - 100 for m in range(len(u))]
         return switch_detected, m_guess, state_function
 
     def count_switches(self):