Update the demo for volume projection in topology optimization

demos/documented/topology_optimization/projection/config.ini

@@ -1,58 +1,22 @@
 [StateSystem]
 is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
 
 [OptimizationRoutine]
 algorithm = bfgs
 rtol = 1e-10
-atol = 0.0
-max_iter = 1000
-gradient_method = direct
-gradient_tol = 1e-9
 soft_exit = True
 
 [LineSearch]
-;method = polynomial
 initial_stepsize = 1e-3
 safeguard_stepsize = False
 epsilon_armijo = 1e-20
-beta_armijo = 2.0
 
 [AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
 bfgs_periodic_restart = 3
 
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
-
 [Output]
 verbose = True
 save_results = False
 save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-time_suffix = False
 
 

demos/documented/topology_optimization/projection/demo_projection.py

@@ -69,6 +69,14 @@
 # {math}`\lambda` are the Lamé parameters which satisfy {math}`\mu \geq 0` and
 # {math}`2\mu + d \lambda > 0`, where {math}`d` is the dimension of the problem.
 #
+# The volume constraint is treated by projecting the level-set function so
+# that the updated level-set function satisfies the volume constraint, similar to
+# a projected gradient method. For more details, we refer to our preprint
+# [Baeck, Blauth, Leithäuser, Pinnau, and Sturm - A Novel Deflation Approach for
+# Topology Optimization and Application for Optimization of Bipolar Plates of
+# Electrolysis Cells](https://arxiv.org/abs/2406.17491), where the used method is
+# described detailedly.
+#
 # ## Implementation
 #
 # The complete python code can be found in the file {download}`demo_projection.py
@@ -151,6 +159,8 @@ def value_shape(self):
 
 J = cashocs.IntegralFunctional(alpha * inner(sigma(u), eps(u)) * dx)
 
+# Note, that this is indeed the same as in {ref}`demo_cantilever` for the case that
+# :math:`\gamma = 0`.
 # Finally, we specify the generalized topological derivative of the problem
 # with the lines
 
@@ -177,7 +187,8 @@ def value_shape(self):
 )
 # -
 # This generalized topological derivative is again similar to {ref}`demo_cantilever`
-# without the last term resulting from the volume penalty term in the objective.
+# without the last term resulting from the volume penalty term in the objective, as
+# :math:`\gamma = 0` in this demo since the volume constraint is dealt with differently.
 
 # The update routine for the level-set function reads
 
@@ -193,7 +204,7 @@ def update_level_set():
 
 vol_low = 0.5
 vol_up = 1.25
-vol = (vol_low, vol_up)
+volume_restriction = (vol_low, vol_up)
 
 # Now, we are able to define the
 # {py:class}`TopologyOptimizationProblem <cashocs.TopologyOptimizationProblem>`.
@@ -208,7 +219,7 @@ def update_level_set():
     dJ_in,
     dJ_out,
     update_level_set,
-    volume_restriction=vol,
+    volume_restriction=volume_restriction,
     config=cfg,
 )
 
@@ -219,12 +230,13 @@ def update_level_set():
 
 # ::::{note}
 # In the case of an equality constraint for the volume of {math}`\Omega` we
-# have to exchange `vol` by a float describing the desired volume, in this
-# case we choose 1.0.
+# have to use a float for `volume_restriction` instead of a tuple. For example, if
+# we consider a volume equality with target volume of 1, then we would have to use the
+# following definition
 # :::{code-block} python
-# vol = 1.0
+# volume_restriction = 1.0
 # top = cashocs.TopologyOptimizationProblem(
-#    F, bcs, J, u, v, psi, dJ_in, dJ_out, update_level_set, volume_restriction=vol, config=cfg
+#    F, bcs, J, u, v, psi, dJ_in, dJ_out, update_level_set, volume_restriction=volume_restriction, config=cfg
 # )
 # :::
 # ::::