From 16ea3a3e40f9aefd34ce13f6cbbf3f9e65d37807 Mon Sep 17 00:00:00 2001
From: David <forenkram@gmx.de>
Date: Sun, 28 Jun 2020 18:31:01 +0200
Subject: [PATCH] clean up multi-patch with inner patch by helpers and
 substructuring

---
 LDDsimulation/domainSubstructuring.py         | 163 ++++++
 .../TP-R-multi-patch-with-inner-patch.py      | 512 ++++++++----------
 2 files changed, 398 insertions(+), 277 deletions(-)

diff --git a/LDDsimulation/domainSubstructuring.py b/LDDsimulation/domainSubstructuring.py
index 9c127c9..43a78d5 100644
--- a/LDDsimulation/domainSubstructuring.py
+++ b/LDDsimulation/domainSubstructuring.py
@@ -529,3 +529,166 @@ class layeredSoilInnerPatch(domainSubstructuring):
             5: self.__subdomain5_outer_boundary_verts,
             6: self.__subdomain6_outer_boundary_verts
         }
+
+
+class chessBoardInnerPatch(domainSubstructuring):
+    """layered soil substructuring with inner patch."""
+
+    def __init__(self):
+        """Layered soil case with inner patch."""
+        super().__init__()
+        hlp.print_once("\n Layered Soil with inner Patch:\n")
+        # global domain
+        self.__subdomain0_vertices = [
+            df.Point(-1.0, -1.0),
+            df.Point(1.0, -1.0),
+            df.Point(1.0, 1.0),
+            df.Point(-1.0, 1.0)
+            ]
+
+        self.__interface_def_points()
+        self.__adjacent_subdomains()
+        self.__subdomain_def_points()
+        self.__outer_boundary_def_points()
+
+    def __interface_def_points(self):
+        """Set self._interface_def_points."""
+        self.__interface23_vertices = [
+            df.Point(0.0, -0.6),
+            df.Point(0.7, 0.0)]
+
+        self.__interface12_vertices = [
+            self.__interface23_vertices[1],
+            df.Point(1.0, 0.0)]
+
+        self.__interface13_vertices = [
+            df.Point(0.0, 0.0),
+            self.__interface23_vertices[1]]
+
+        self.__interface15_vertices = [
+            df.Point(0.0, 0.0),
+            df.Point(0.0, 1.0)]
+
+        self.__interface34_vertices = [
+            df.Point(0.0, 0.0),
+            self.__interface23_vertices[0]]
+
+        self.__interface24_vertices = [
+            self.__interface23_vertices[0],
+            df.Point(0.0, -1.0)]
+
+        self.__interface45_vertices = [
+            df.Point(-1.0, 0.0),
+            df.Point(0.0, 0.0)]
+
+        # interface_vertices introduces a global numbering of interfaces.
+        self.interface_def_points = [
+            self.__interface13_vertices,
+            self.__interface12_vertices,
+            self.__interface23_vertices,
+            self.__interface24_vertices,
+            self.__interface34_vertices,
+            self.__interface45_vertices,
+            self.__interface15_vertices,
+            ]
+
+    def __adjacent_subdomains(self):
+        """Set self._adjacent_subdomains."""
+        self.adjacent_subdomains = [
+                [1, 3],
+                [1, 2],
+                [2, 3],
+                [2, 4],
+                [3, 4],
+                [4, 5],
+                [1, 5]
+            ]
+
+    def __subdomain_def_points(self):
+        """Set self._subdomain_def_points."""
+        # subdomain1.
+        self.__subdomain1_vertices = [
+            self.__interface23_vertices[0],
+            self.__interface23_vertices[1],
+            self.__interface12_vertices[1],
+            self.__subdomain0_vertices[2],
+            df.Point(0.0, 1.0)]
+
+        # subdomain2
+        self.__subdomain2_vertices = [
+            self.__interface24_vertices[1],
+            self.__subdomain0_vertices[1],
+            self.__interface12_vertices[1],
+            self.__interface23_vertices[1],
+            self.__interface23_vertices[0]]
+
+        self.__subdomain3_vertices = [
+            self.__interface23_vertices[0],
+            self.__interface23_vertices[1],
+            self.__interface13_vertices[0]]
+
+        self.__subdomain4_vertices = [
+            self.__subdomain0_vertices[0],
+            self.__interface24_vertices[1],
+            self.__interface34_vertices[1],
+            self.__interface34_vertices[0],
+            self.__interface45_vertices[0]]
+
+        self.__subdomain5_vertices = [
+            self.__interface45_vertices[0],
+            self.__interface15_vertices[0],
+            self.__interface15_vertices[1],
+            self.__subdomain0_vertices[3]]
+
+        self.subdomain_def_points = [
+            self.__subdomain0_vertices,
+            self.__subdomain1_vertices,
+            self.__subdomain2_vertices,
+            self.__subdomain3_vertices,
+            self.__subdomain4_vertices,
+            self.__subdomain5_vertices,
+            ]
+
+    def __outer_boundary_def_points(self):
+        """Set self._outer_boundary_def_points."""
+        # vertex coordinates of the outer boundaries. If it can not be
+        # specified as a polygon, use an entry per boundary polygon.
+        # This information is used for defining the Dirichlet boundary
+        # conditions. If a domain is completely internal, the
+        # dictionary entry should be 0: None
+        self.__subdomain1_outer_boundary_verts = {
+            0: [self.__interface12_vertices[1],
+                self.__subdomain0_vertices[2],
+                df.Point(0.0, 1.0)]
+            }
+
+        self.__subdomain2_outer_boundary_verts = {
+            0: [self.__interface24_vertices[1],
+                self.__subdomain0_vertices[1],
+                self.__interface12_vertices[1]]
+            }
+
+        self.__subdomain3_outer_boundary_verts = None
+
+        self.__subdomain4_outer_boundary_verts = {
+            0: [self.__interface45_vertices[0],
+                self.__subdomain0_vertices[0],
+                self.__interface24_vertices[1]]
+        }
+
+        self.__subdomain5_outer_boundary_verts = {
+            0: [self.__interface15_vertices[1],
+                self.__subdomain0_vertices[3],
+                self.__interface45_vertices[0]]
+        }
+
+        # if a subdomain has no outer boundary write None instead, i.e.
+        # i: None
+        # if i is the index of the inner subdomain.
+        self.outer_boundary_def_points = {
+            1: self.__subdomain1_outer_boundary_verts,
+            2: self.__subdomain2_outer_boundary_verts,
+            3: self.__subdomain3_outer_boundary_verts,
+            4: self.__subdomain4_outer_boundary_verts,
+            5: self.__subdomain5_outer_boundary_verts,
+        }
diff --git a/Two-phase-Richards/multi-patch/five_patch_domain_with_inner_patch/TP-R-multi-patch-with-inner-patch.py b/Two-phase-Richards/multi-patch/five_patch_domain_with_inner_patch/TP-R-multi-patch-with-inner-patch.py
index 15f9e9d..3f846e6 100755
--- a/Two-phase-Richards/multi-patch/five_patch_domain_with_inner_patch/TP-R-multi-patch-with-inner-patch.py
+++ b/Two-phase-Richards/multi-patch/five_patch_domain_with_inner_patch/TP-R-multi-patch-with-inner-patch.py
@@ -3,7 +3,6 @@
 
 This program sets up an LDD simulation
 """
-
 import dolfin as df
 import sympy as sym
 import functools as ft
@@ -12,8 +11,15 @@ import helpers as hlp
 import datetime
 import os
 import pandas as pd
+import multiprocessing as mp
+import domainSubstructuring as dss
+
+# init sympy session
+sym.init_printing()
 
-# check if output directory exists
+# PREREQUISITS  ###############################################################
+# check if output directory "./output" exists. This will be used in
+# the generation of the output string.
 if not os.path.exists('./output'):
     os.mkdir('./output')
     print("Directory ", './output',  " created ")
@@ -24,37 +30,38 @@ else:
 date = datetime.datetime.now()
 datestr = date.strftime("%Y-%m-%d")
 
-
-# init sympy session
-sym.init_printing()
-# solver_tol = 6E-7
+# Name of the usecase that will be printed during simulation.
 use_case = "TP-R-five-domain-with-inner-patch-realistic"
-# name of this very file. Needed for log output.
+# The name of this very file. Needed for creating log output.
 thisfile = "TP-R-multi-patch-with-inner-patch.py"
+
+# GENERAL SOLVER CONFIG  ######################################################
+# maximal iteration per timestep
 max_iter_num = 700
 FEM_Lagrange_degree = 1
+
+# GRID AND MESH STUDY SPECIFICATIONS  #########################################
 mesh_study = False
 resolutions = {
-                # 1: 2e-6,  # h=2
-                # 2: 2e-6,  # h=1.1180
-                # 4: 2e-6,  # h=0.5590
-                # 8: 2e-6,  # h=0.2814
-                # 16: 8e-6, # h=0.1412
-                32: 5e-6,
+                # 1: 1e-6,
+                # 2: 1e-6,
+                # 4: 1e-6,
+                8: 1e-5,
+                # 16: 5e-6,
+                # 32: 5e-6,
                 # 64: 2e-6,
-                # 128: 2e-6
+                # 128: 1e-6,
+                # 256: 1e-6,
                 }
 
-# GRID #######################
-# mesh_resolution = 20
-timestep_size = 0.001
-number_of_timesteps = 1000
-plot_timestep_every = 2
-# decide how many timesteps you want analysed. Analysed means, that we write
-# out subsequent errors of the L-iteration within the timestep.
-number_of_timesteps_to_analyse = 8
+# starttimes gives a list of starttimes to run the simulation from.
+# The list is looped over and a simulation is run with t_0 as initial time
+#  for each element t_0 in starttimes.
 starttimes = [0.0]
+timestep_size = 0.001
+number_of_timesteps = 5
 
+# LDD scheme parameters  ######################################################
 Lw1 = 0.5  # /timestep_size
 Lnw1 = Lw1
 
@@ -94,23 +101,41 @@ lambda15_nw = 4
 
 
 include_gravity = True
-debugflag = False
+debugflag = True
 analyse_condition = False
 
-output_string = "./output/{}-{}_timesteps{}_P{}".format(
-    datestr, use_case, number_of_timesteps, FEM_Lagrange_degree
-    )
-
-
-# toggle what should be written to files
+# I/O CONFIG  #################################################################
+# when number_of_timesteps is high, it might take a long time to write all
+# timesteps to disk. Therefore, you can choose to only write data of every
+# plot_timestep_every timestep to disk.
+plot_timestep_every = 1
+# Decide how many timesteps you want analysed. Analysed means, that
+# subsequent errors of the L-iteration within the timestep are written out.
+number_of_timesteps_to_analyse = 1
+
+# fine grained control over data to be written to disk in the mesh study case
+# as well as for a regular simuation for a fixed grid.
 if mesh_study:
     write_to_file = {
+        # output the relative errornorm (integration in space) w.r.t. an exact
+        # solution for each timestep into a csv file.
         'space_errornorms': True,
+        # save the mesh and marker functions to disk
         'meshes_and_markers': True,
+        # save xdmf/h5 data for each LDD iteration for timesteps determined by
+        # number_of_timesteps_to_analyse. I/O intensive!
         'L_iterations_per_timestep': False,
+        # save solution to xdmf/h5.
         'solutions': True,
+        # save absolute differences w.r.t an exact solution to xdmf/h5 file
+        # to monitor where on the domains errors happen
         'absolute_differences': True,
+        # analyise condition numbers for timesteps determined by
+        # number_of_timesteps_to_analyse and save them over time to csv.
         'condition_numbers': analyse_condition,
+        # output subsequent iteration errors measured in L^2  to csv for
+        # timesteps determined by number_of_timesteps_to_analyse.
+        # Usefull to monitor convergence of the acutal LDD solver.
         'subsequent_errors': True
     }
 else:
@@ -124,134 +149,115 @@ else:
         'subsequent_errors': True
     }
 
+# OUTPUT FILE STRING  #########################################################
+output_string = "./output/{}-{}_timesteps{}_P{}".format(
+    datestr, use_case, number_of_timesteps, FEM_Lagrange_degree
+    )
 
-# ----------------------------------------------------------------------------#
-# ------------------- Domain and Interface -----------------------------------#
-# ----------------------------------------------------------------------------#
-# global simulation domain domain
-sub_domain0_vertices = [df.Point(-1.0, -1.0),
-                        df.Point(1.0, -1.0),
-                        df.Point(1.0, 1.0),
-                        df.Point(-1.0, 1.0)]
-
-# interfaces
-
-interface23_vertices = [df.Point(0.0, -0.6),
-                        df.Point(0.7, 0.0)]
-
-interface12_vertices = [interface23_vertices[1],
-                        df.Point(1.0, 0.0)]
-
-interface13_vertices = [df.Point(0.0, 0.0),
-                        interface23_vertices[1]]
-
-interface15_vertices = [df.Point(0.0, 0.0),
-                        df.Point(0.0, 1.0)]
-
-interface34_vertices = [df.Point(0.0, 0.0),
-                        interface23_vertices[0]]
-
-interface24_vertices = [interface23_vertices[0],
-                        df.Point(0.0, -1.0)]
-
-interface45_vertices = [df.Point(-1.0, 0.0),
-                        df.Point(0.0, 0.0)]
-# subdomain1.
-sub_domain1_vertices = [interface23_vertices[0],
-                        interface23_vertices[1],
-                        interface12_vertices[1],
-                        sub_domain0_vertices[2],
-                        df.Point(0.0, 1.0)]
-
-# vertex coordinates of the outer boundaries. If it can not be specified as a
-# polygon, use an entry per boundary polygon. This information is used for
-# defining the Dirichlet boundary conditions. If a domain is completely inter-
-# nal, the dictionary entry should be 0: None
-subdomain1_outer_boundary_verts = {
-    0: [interface12_vertices[1],
-        sub_domain0_vertices[2],
-        df.Point(0.0, 1.0)]
-}
-# subdomain2
-sub_domain2_vertices = [interface24_vertices[1],
-                        sub_domain0_vertices[1],
-                        interface12_vertices[1],
-                        interface23_vertices[1],
-                        interface23_vertices[0]]
-
-subdomain2_outer_boundary_verts = {
-    0: [interface24_vertices[1],
-        sub_domain0_vertices[1],
-        interface12_vertices[1]]
-}
-
-sub_domain3_vertices = [interface23_vertices[0],
-                        interface23_vertices[1],
-                        interface13_vertices[0]]
-
-subdomain3_outer_boundary_verts = None
-
-
-sub_domain4_vertices = [sub_domain0_vertices[0],
-                        interface24_vertices[1],
-                        interface34_vertices[1],
-                        interface34_vertices[0],
-                        interface45_vertices[0]]
-
-subdomain4_outer_boundary_verts = {
-    0: [interface45_vertices[0],
-        sub_domain0_vertices[0],
-        interface24_vertices[1]]
-}
-
-sub_domain5_vertices = [interface45_vertices[0],
-                        interface15_vertices[0],
-                        interface15_vertices[1],
-                        sub_domain0_vertices[3]]
-
-subdomain5_outer_boundary_verts = {
-    0: [interface15_vertices[1],
-        sub_domain0_vertices[3],
-        interface45_vertices[0]]
-}
-
-# list of subdomains given by the boundary polygon vertices.
-# Subdomains are given as a list of dolfin points forming
-# a closed polygon, such that mshr.Polygon(subdomain_def_points[i]) can be used
-# to create the subdomain. subdomain_def_points[0] contains the
-# vertices of the global simulation domain and subdomain_def_points[i] contains
-# the vertices of the subdomain i.
-subdomain_def_points = [sub_domain0_vertices,
-                        sub_domain1_vertices,
-                        sub_domain2_vertices,
-                        sub_domain3_vertices,
-                        sub_domain4_vertices,
-                        sub_domain5_vertices]
-# in the below list, index 0 corresponds to the 12 interface which has global
-# marker value 1
-interface_def_points = [interface13_vertices,
-                        interface12_vertices,
-                        interface23_vertices,
-                        interface24_vertices,
-                        interface34_vertices,
-                        interface45_vertices,
-                        interface15_vertices,]
-
-# adjacent_subdomains[i] contains the indices of the subdomains sharing the
-# interface i (i.e. given by interface_def_points[i]).
-adjacent_subdomains = [[1, 3], [1, 2], [2, 3], [2, 4], [3, 4], [4, 5], [1, 5]]
-
-# if a subdomain has no outer boundary write None instead, i.e.
-# i: None
-# if i is the index of the inner subdomain.
-outer_boundary_def_points = {
-    # subdomain number
-    1: subdomain1_outer_boundary_verts,
-    2: subdomain2_outer_boundary_verts,
-    3: subdomain3_outer_boundary_verts,
-    4: subdomain4_outer_boundary_verts,
-    5: subdomain5_outer_boundary_verts
-}
+# DOMAIN AND INTERFACE  #######################################################
+substructuring = dss.chessBoardInnerPatch()
+interface_def_points = substructuring.interface_def_points
+adjacent_subdomains = substructuring.adjacent_subdomains
+subdomain_def_points = substructuring.subdomain_def_points
+outer_boundary_def_points = substructuring.outer_boundary_def_points
+
+# MODEL CONFIGURATION #########################################################
+# # subdomain1.
+# sub_domain1_vertices = [interface23_vertices[0],
+#                         interface23_vertices[1],
+#                         interface12_vertices[1],
+#                         sub_domain0_vertices[2],
+#                         df.Point(0.0, 1.0)]
+#
+# # vertex coordinates of the outer boundaries. If it can not be specified as a
+# # polygon, use an entry per boundary polygon. This information is used for
+# # defining the Dirichlet boundary conditions. If a domain is completely inter-
+# # nal, the dictionary entry should be 0: None
+# subdomain1_outer_boundary_verts = {
+#     0: [interface12_vertices[1],
+#         sub_domain0_vertices[2],
+#         df.Point(0.0, 1.0)]
+# }
+# # subdomain2
+# sub_domain2_vertices = [interface24_vertices[1],
+#                         sub_domain0_vertices[1],
+#                         interface12_vertices[1],
+#                         interface23_vertices[1],
+#                         interface23_vertices[0]]
+#
+# subdomain2_outer_boundary_verts = {
+#     0: [interface24_vertices[1],
+#         sub_domain0_vertices[1],
+#         interface12_vertices[1]]
+# }
+#
+# sub_domain3_vertices = [interface23_vertices[0],
+#                         interface23_vertices[1],
+#                         interface13_vertices[0]]
+#
+# subdomain3_outer_boundary_verts = None
+#
+#
+# sub_domain4_vertices = [sub_domain0_vertices[0],
+#                         interface24_vertices[1],
+#                         interface34_vertices[1],
+#                         interface34_vertices[0],
+#                         interface45_vertices[0]]
+#
+# subdomain4_outer_boundary_verts = {
+#     0: [interface45_vertices[0],
+#         sub_domain0_vertices[0],
+#         interface24_vertices[1]]
+# }
+#
+# sub_domain5_vertices = [interface45_vertices[0],
+#                         interface15_vertices[0],
+#                         interface15_vertices[1],
+#                         sub_domain0_vertices[3]]
+#
+# subdomain5_outer_boundary_verts = {
+#     0: [interface15_vertices[1],
+#         sub_domain0_vertices[3],
+#         interface45_vertices[0]]
+# }
+#
+# # list of subdomains given by the boundary polygon vertices.
+# # Subdomains are given as a list of dolfin points forming
+# # a closed polygon, such that mshr.Polygon(subdomain_def_points[i]) can be used
+# # to create the subdomain. subdomain_def_points[0] contains the
+# # vertices of the global simulation domain and subdomain_def_points[i] contains
+# # the vertices of the subdomain i.
+# subdomain_def_points = [sub_domain0_vertices,
+#                         sub_domain1_vertices,
+#                         sub_domain2_vertices,
+#                         sub_domain3_vertices,
+#                         sub_domain4_vertices,
+#                         sub_domain5_vertices]
+# # in the below list, index 0 corresponds to the 12 interface which has global
+# # marker value 1
+# interface_def_points = [interface13_vertices,
+#                         interface12_vertices,
+#                         interface23_vertices,
+#                         interface24_vertices,
+#                         interface34_vertices,
+#                         interface45_vertices,
+#                         interface15_vertices,]
+#
+# # adjacent_subdomains[i] contains the indices of the subdomains sharing the
+# # interface i (i.e. given by interface_def_points[i]).
+# adjacent_subdomains = [[1, 3], [1, 2], [2, 3], [2, 4], [3, 4], [4, 5], [1, 5]]
+#
+# # if a subdomain has no outer boundary write None instead, i.e.
+# # i: None
+# # if i is the index of the inner subdomain.
+# outer_boundary_def_points = {
+#     # subdomain number
+#     1: subdomain1_outer_boundary_verts,
+#     2: subdomain2_outer_boundary_verts,
+#     3: subdomain3_outer_boundary_verts,
+#     4: subdomain4_outer_boundary_verts,
+#     5: subdomain5_outer_boundary_verts
+# }
 
 isRichards = {
     1: True,
@@ -650,17 +656,11 @@ p_e_sym = {
         'nonwetting': 0*t },
 }
 
-pc_e_sym = dict()
-for subdomain, isR in isRichards.items():
-    if isR:
-        pc_e_sym.update({subdomain: -p_e_sym[subdomain]['wetting']})
-    else:
-        pc_e_sym.update(
-            {subdomain: p_e_sym[subdomain]['nonwetting']
-                - p_e_sym[subdomain]['wetting']}
+pc_e_sym = hlp.generate_exact_symbolic_pc(
+                isRichards=isRichards,
+                symbolic_pressure=p_e_sym
             )
 
-
 symbols = {"x": x,
            "y": y,
            "t": t}
@@ -685,35 +685,18 @@ source_expression = exact_solution_example['source']
 exact_solution = exact_solution_example['exact_solution']
 initial_condition = exact_solution_example['initial_condition']
 
-# Dictionary of dirichlet boundary conditions.
-dirichletBC = dict()
-# similarly to the outer boundary dictionary, if a patch has no outer boundary
-# None should be written instead of an expression.
-# This is a bit of a brainfuck:
-# dirichletBC[ind] gives a dictionary of the outer boundaries of subdomain ind.
-# Since a domain patch can have several disjoint outer boundary parts, the
-# expressions need to get an enumaration index which starts at 0.
-# So dirichletBC[ind][j] is the dictionary of outer dirichlet conditions of
-# subdomain ind and boundary part j.
-# Finally, dirichletBC[ind][j]['wetting'] and dirichletBC[ind][j]['nonwetting']
-# return the actual expression needed for the dirichlet condition for both
-# phases if present.
-
-# subdomain index: {outer boudary part index: {phase: expression}}
-for subdomain in isRichards.keys():
-    # if subdomain has no outer boundary, outer_boundary_def_points[subdomain]
-    # is None
-    if outer_boundary_def_points[subdomain] is None:
-        dirichletBC.update({subdomain: None})
-    else:
-        dirichletBC.update({subdomain: dict()})
-        # set the dirichlet conditions to be the same code as exact solution on
-        # the subdomain.
-        for outer_boundary_ind in outer_boundary_def_points[subdomain].keys():
-            dirichletBC[subdomain].update(
-                {outer_boundary_ind: exact_solution[subdomain]}
-                )
-
+# BOUNDARY CONDITIONS #########################################################
+# Dictionary of dirichlet boundary conditions. If an exact solution case is
+# used, use the hlp.generate_exact_DirichletBC() method to generate the
+# Dirichlet Boundary conditions from the exact solution.
+dirichletBC = hlp.generate_exact_DirichletBC(
+        isRichards=isRichards,
+        outer_boundary_def_points=outer_boundary_def_points,
+        exact_solution=exact_solution
+    )
+# If no exact solution is provided you need to provide a dictionary of boundary
+# conditions. See the definiton of hlp.generate_exact_DirichletBC() to see
+# the structure.
 
 # LOG FILE OUTPUT #############################################################
 # read this file and print it to std out. This way the simulation can produce a
@@ -723,88 +706,63 @@ print(f.read())
 f.close()
 
 
-# RUN #########################################################################
-for starttime in starttimes:
-    for mesh_resolution, solver_tol in resolutions.items():
-        # initialise LDD simulation class
-        simulation = ldd.LDDsimulation(
-            tol=1E-14,
-            LDDsolver_tol=solver_tol,
-            debug=debugflag,
-            max_iter_num=max_iter_num,
-            FEM_Lagrange_degree=FEM_Lagrange_degree,
-            mesh_study=mesh_study
-            )
-
-        simulation.set_parameters(
-            use_case=use_case,
-            output_dir=output_string,
-            subdomain_def_points=subdomain_def_points,
-            isRichards=isRichards,
-            interface_def_points=interface_def_points,
-            outer_boundary_def_points=outer_boundary_def_points,
-            adjacent_subdomains=adjacent_subdomains,
-            mesh_resolution=mesh_resolution,
-            viscosity=viscosity,
-            porosity=porosity,
-            L=L,
-            lambda_param=lambda_param,
-            relative_permeability=relative_permeability,
-            saturation=sat_pressure_relationship,
-            starttime=starttime,
-            number_of_timesteps=number_of_timesteps,
-            number_of_timesteps_to_analyse=number_of_timesteps_to_analyse,
-            plot_timestep_every=plot_timestep_every,
-            timestep_size=timestep_size,
-            sources=source_expression,
-            initial_conditions=initial_condition,
-            dirichletBC_expression_strings=dirichletBC,
-            exact_solution=exact_solution,
-            densities=densities,
-            include_gravity=include_gravity,
-            gravity_acceleration=gravity_acceleration,
-            write2file=write_to_file,
-            )
-
-        simulation.initialise()
-        output_dir = simulation.output_dir
-        # simulation.write_exact_solution_to_xdmf()
-        output = simulation.run(analyse_condition=analyse_condition)
-        for subdomain_index, subdomain_output in output.items():
-            mesh_h = subdomain_output['mesh_size']
-            for phase, error_dict in subdomain_output['errornorm'].items():
-                filename = output_dir \
-                    + "subdomain{}".format(subdomain_index)\
-                    + "-space-time-errornorm-{}-phase.csv".format(phase)
-                # for errortype, errornorm in error_dict.items():
-
-                # eocfile = open("eoc_filename", "a")
-                # eocfile.write( str(mesh_h) + " " + str(errornorm) + "\n" )
-                # eocfile.close()
-                # if subdomain.isRichards:mesh_h
-                data_dict = {
-                    'mesh_parameter': mesh_resolution,
-                    'mesh_h': mesh_h,
-                }
-                for norm_type, errornorm in error_dict.items():
-                    data_dict.update(
-                        {norm_type: errornorm}
-                    )
-                errors = pd.DataFrame(data_dict, index=[mesh_resolution])
-                # check if file exists
-                if os.path.isfile(filename) is True:
-                    with open(filename, 'a') as f:
-                        errors.to_csv(
-                            f,
-                            header=False,
-                            sep='\t',
-                            encoding='utf-8',
-                            index=False
+# MAIN ########################################################################
+if __name__ == '__main__':
+    # dictionary of simualation parameters to pass to the run function.
+    # mesh_resolution and starttime are excluded, as they get passed explicitly
+    # to achieve parallelisation in these parameters in these parameters for
+    # mesh studies etc.
+    simulation_parameter = {
+        "tol": 1E-14,
+        "debugflag": debugflag,
+        "max_iter_num": max_iter_num,
+        "FEM_Lagrange_degree": FEM_Lagrange_degree,
+        "mesh_study": mesh_study,
+        "use_case": use_case,
+        "output_string": output_string,
+        "subdomain_def_points": subdomain_def_points,
+        "isRichards": isRichards,
+        "interface_def_points": interface_def_points,
+        "outer_boundary_def_points": outer_boundary_def_points,
+        "adjacent_subdomains": adjacent_subdomains,
+        # "mesh_resolution": mesh_resolution,
+        "viscosity": viscosity,
+        "porosity": porosity,
+        "L": L,
+        "lambda_param": lambda_param,
+        "relative_permeability": relative_permeability,
+        "sat_pressure_relationship": sat_pressure_relationship,
+        # "starttime": starttime,
+        "number_of_timesteps": number_of_timesteps,
+        "number_of_timesteps_to_analyse": number_of_timesteps_to_analyse,
+        "plot_timestep_every": plot_timestep_every,
+        "timestep_size": timestep_size,
+        "source_expression": source_expression,
+        "initial_condition": initial_condition,
+        "dirichletBC": dirichletBC,
+        "exact_solution": exact_solution,
+        "densities": densities,
+        "include_gravity": include_gravity,
+        "gravity_acceleration": gravity_acceleration,
+        "write_to_file": write_to_file,
+        "analyse_condition": analyse_condition
+    }
+    for starttime in starttimes:
+        for mesh_resolution, solver_tol in resolutions.items():
+            simulation_parameter.update({"solver_tol": solver_tol})
+            hlp.info(simulation_parameter["use_case"])
+            LDDsim = mp.Process(
+                        target=hlp.run_simulation,
+                        args=(
+                            simulation_parameter,
+                            starttime,
+                            mesh_resolution
                             )
-                else:
-                    errors.to_csv(
-                        filename,
-                        sep='\t',
-                        encoding='utf-8',
-                        index=False
                         )
+            LDDsim.start()
+            LDDsim.join()
+            # hlp.run_simulation(
+            #     mesh_resolution=mesh_resolution,
+            #     starttime=starttime,
+            #     parameter=simulation_parameter
+            #     )
-- 
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