]> https://gitweb.dealii.org/ - dealii.git/commitdiff
First draft of results
authorLuca Heltai <luca.heltai@sissa.it>
Mon, 11 May 2020 10:55:42 +0000 (12:55 +0200)
committerMatthias Maier <tamiko@43-1.org>
Fri, 15 May 2020 03:16:37 +0000 (22:16 -0500)
doc/doxygen/tutorial/tutorial.h.in
examples/step-70/doc/builds-on
examples/step-70/doc/results.dox
examples/step-70/impeller.step [new file with mode: 0644]
examples/step-70/impeller.vtk [new file with mode: 0644]
examples/step-70/parameters_23.prm [new file with mode: 0644]
examples/step-70/step-70.cc

index bf11db9e01e0a2f661d6341c8e42d50697b5f144..be99036d6e14c56cf571e00cc3f76135631f854a 100644 (file)
  *       step-42,
  *       step-50,
  *       step-55,
- *       step-60,
  *       step-70
  *     </td>
  *   </tr>
  *       step-42,
  *       step-50,
  *       step-55,
- *       step-59,
+ *       step-59
  *     </td>
  *   </tr>
  *
index d69f25861c8d1d2cc4007f1e113472e9e8696f53..5aa1b0eb9539302862d4495f3bb6fae29cbe7f1b 100644 (file)
@@ -1 +1 @@
-step-6 step-22 step-32 step-55 step-60
+step-32 step-60
index 6e9a8159ad6adaec0f5054d015e8bff21ca465bf..bb66b8a2fbaf9550526412f283996f9205153a6c 100644 (file)
@@ -1,9 +1,18 @@
 <h1>Results</h1>
 
-The directory in which this program is run does not contain a parameter file by
-default. On the other hand, this program wants to read its parameters from a
-file called parameters.prm -- and so, when you execute it the first time, you
-will get an exception that no such file can be found:
+The directory in which this program is run contains a number of sample parameter
+files that you can use to reproduce the results presented in this section. If
+you do not specify a parameter file as an argument on command line, the program
+will try to read the file "parameters.prm" by default, and will execute the two
+dimensional version of the code. As explained before, if your file name contains
+the string "23", then the program will run a three dimensional problem, with
+immersed solid of co-dimension one. If it contains the string "3", it will run
+a three dimensional problem, with immersed solid of co-dimension zero, otherwise
+it will run a two dimensional problem with immersed solid of co-dimension zero.
+
+Regardless of the specific parameter file name, if the specified file does not
+exist, when you execute the program you will get an exception that no such file
+can be found:
 
 @code
 ----------------------------------------------------
@@ -23,71 +32,181 @@ Aborting!
 @endcode
 
 However, as the error message already states, the code that triggers the
-exception will also generate a parameters.prm file that simply contains the
-default values for all parameters this program cares about. By inspection of the
-parameter file, we see the following:
+exception will also generate the specified file ("parameters.prm" in this
+case) that simply contains the default values for all parameters this program
+cares about (for the correct dimension and co-dimension, according to the
+wether a string "23" or "3" is contained in the file name).
+By inspection of the default parameter file, we see the following:
 
 @code
+# Listing of Parameters
+# ---------------------
 subsection Stokes Immersed Problem
-  set Final time                         = 1
-  set Homogeneous Dirichlet boundary ids = 0, 1, 2, 3
-  set Initial fluid refinement           = 4
-  set Initial solid refinement           = 4
-  set Particle insertion refinement      = 4
-  set Nitsche penalty term               = 1000
-  set Number of time steps               = 501
-  set Velocity degree                    = 2
-  set Viscosity                          = 1
+  set Final time                            = 1
+  # Extraction level of the rtree used to construct global bounding boxes
+  set Fluid bounding boxes extraction level = 1
+
+  # Boundary Ids over which homogeneous Dirichlet boundary conditions are
+  # applied
+  set Homogeneous Dirichlet boundary ids    = 0
+
+  # Initial mesh refinement used for the fluid domain Omega
+  set Initial fluid refinement              = 3
+
+  # Initial mesh refinement used for the solid domain Gamma
+  set Initial solid refinement              = 3
+  set Nitsche penalty term                  = 10
+  set Number of time steps                  = 11
+  set Output frequency                      = 1
+
+  # Refinement of the volumetric mesh used to insert the particles
+  set Particle insertion refinement         = 1
+  set Velocity degree                       = 2
+  set Viscosity                             = 1
+
+
   subsection Angular velocity
-    set Function constants  =
-    set Function expression = t < .5 ? 5 : -5
+    # Sometimes it is convenient to use symbolic constants in the expression
+    # that describes the function, rather than having to use its numeric value
+    # everywhere the constant appears. These values can be defined using this
+    # parameter, in the form `var1=value1, var2=value2, ...'.
+    # 
+    # A typical example would be to set this runtime parameter to
+    # `pi=3.1415926536' and then use `pi' in the expression of the actual
+    # formula. (That said, for convenience this class actually defines both
+    # `pi' and `Pi' by default, but you get the idea.)
+    set Function constants  = 
+
+    # The formula that denotes the function you want to evaluate for
+    # particular values of the independent variables. This expression may
+    # contain any of the usual operations such as addition or multiplication,
+    # as well as all of the common functions such as `sin' or `cos'. In
+    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
+    # expression evaluates to the second argument if the first argument is
+    # true, and to the third argument otherwise. For a full overview of
+    # possible expressions accepted see the documentation of the muparser
+    # library at http://muparser.beltoforion.de/.
+    # 
+    # If the function you are describing represents a vector-valued function
+    # with multiple components, then separate the expressions for individual
+    # components by a semicolon.
+    set Function expression = t < .500001 ? 5 : -5 # default: 0
+
+    # The names of the variables as they will be used in the function,
+    # separated by commas. By default, the names of variables at which the
+    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
+    # 3d) for spatial coordinates and `t' for time. You can then use these
+    # variable names in your function expression and they will be replaced by
+    # the values of these variables at which the function is currently
+    # evaluated. However, you can also choose a different set of names for the
+    # independent variables at which to evaluate your function expression. For
+    # example, if you work in spherical coordinates, you may wish to set this
+    # input parameter to `r,phi,theta,t' and then use these variable names in
+    # your function expression.
     set Variable names      = x,y,t
   end
+
   subsection Grid generation
-    set Grid one generator                = hyper_cube
-    set Grid one generator arguments      = -1: 1: false
-    set Grid two generator                = hyper_rectangle
-    set Grid two generator arguments      = -.5, -.1: .5, .1: false
+    set Fluid grid generator              = hyper_cube
+    set Fluid grid generator arguments    = -1: 1: false
     set Particle grid generator           = hyper_ball
     set Particle grid generator arguments = 0.3, 0.3: 0.1: false
+    set Solid grid generator              = hyper_rectangle
+    set Solid grid generator arguments    = -.5, -.1: .5, .1: false
   end
+
+  subsection Refinement and remeshing
+    set Maximum number of cells        = 1000
+    set Refinement coarsening fraction = 0.3
+    set Refinement fraction            = 0.3
+    set Refinement maximal level       = 5
+    set Refinement step frequency      = 5
+    set Refinement strategy            = fixed_fraction
+  end
+
   subsection Right hand side
-    set Function constants  =
+    # Sometimes it is convenient to use symbolic constants in the expression
+    # that describes the function, rather than having to use its numeric value
+    # everywhere the constant appears. These values can be defined using this
+    # parameter, in the form `var1=value1, var2=value2, ...'.
+    # 
+    # A typical example would be to set this runtime parameter to
+    # `pi=3.1415926536' and then use `pi' in the expression of the actual
+    # formula. (That said, for convenience this class actually defines both
+    # `pi' and `Pi' by default, but you get the idea.)
+    set Function constants  = 
+
+    # The formula that denotes the function you want to evaluate for
+    # particular values of the independent variables. This expression may
+    # contain any of the usual operations such as addition or multiplication,
+    # as well as all of the common functions such as `sin' or `cos'. In
+    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
+    # expression evaluates to the second argument if the first argument is
+    # true, and to the third argument otherwise. For a full overview of
+    # possible expressions accepted see the documentation of the muparser
+    # library at http://muparser.beltoforion.de/.
+    # 
+    # If the function you are describing represents a vector-valued function
+    # with multiple components, then separate the expressions for individual
+    # components by a semicolon.
     set Function expression = 0; 0; 0
+
+    # The names of the variables as they will be used in the function,
+    # separated by commas. By default, the names of variables at which the
+    # function will be evaluated are `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
+    # 3d) for spatial coordinates and `t' for time. You can then use these
+    # variable names in your function expression and they will be replaced by
+    # the values of these variables at which the function is currently
+    # evaluated. However, you can also choose a different set of names for the
+    # independent variables at which to evaluate your function expression. For
+    # example, if you work in spherical coordinates, you may wish to set this
+    # input parameter to `r,phi,theta,t' and then use these variable names in
+    # your function expression.
     set Variable names      = x,y,t
   end
+
 end
 @endcode
 
-If you now run the program, you will get a file called `used_parameters.prm`,
+If you now run the program, you will get a file called `parameters_used.prm`,
 containing a shorter version of the above parameters (without comments and
 documentation), documenting all parameters that were used to run your program:
 @code
 subsection Stokes Immersed Problem
-  set Final time                         = 1
-  set Homogeneous Dirichlet boundary ids = 0, 1, 2, 3
-  set Initial fluid refinement           = 4
-  set Initial solid refinement           = 4
-  set Particle insertion refinement      = 4
-  set Nitsche penalty term               = 1000
-  set Number of time steps               = 501
-  set Velocity degree                    = 2
-  set Viscosity                          = 1
+  set Final time                            = 1
+  set Fluid bounding boxes extraction level = 1
+  set Homogeneous Dirichlet boundary ids    = 0
+  set Initial fluid refinement              = 5
+  set Initial solid refinement              = 3
+  set Nitsche penalty term                  = 100
+  set Number of time steps                  = 501
+  set Output frequency                      = 1
+  set Particle insertion refinement         = 3
+  set Velocity degree                       = 2
+  set Viscosity                             = 1
   subsection Angular velocity
-    set Function constants  =
-    set Function expression = t < .5 ? 5 : -5
+    set Function constants  = 
+    set Function expression = t < .500001 ? 5 : -5
     set Variable names      = x,y,t
   end
   subsection Grid generation
-    set Grid one generator                = hyper_cube
-    set Grid one generator arguments      = -1: 1: false
-    set Grid two generator                = hyper_rectangle
-    set Grid two generator arguments      = -.5, -.1: .5, .1: false
+    set Fluid grid generator              = hyper_cube
+    set Fluid grid generator arguments    = -1: 1: false
     set Particle grid generator           = hyper_ball
     set Particle grid generator arguments = 0.3, 0.3: 0.1: false
+    set Solid grid generator              = hyper_rectangle
+    set Solid grid generator arguments    = -.5, -.1: .5, .1: false
+  end
+  subsection Refinement and remeshing
+    set Maximum number of cells        = 1000
+    set Refinement coarsening fraction = 0.3
+    set Refinement fraction            = 0.3
+    set Refinement maximal level       = 7
+    set Refinement step frequency      = 5
+    set Refinement strategy            = fixed_fraction
   end
   subsection Right hand side
-    set Function constants  =
+    set Function constants  = 
     set Function expression = 0; 0; 0
     set Variable names      = x,y,t
   end
@@ -95,211 +214,198 @@ end
 @endcode
 
 The rationale behind creating first `parameters.prm` file (the first time the
-program is run) and then a `used_parameters.prm` (every other times you run the
+program is run) and then a `parameters_used.prm` (every other times you run the
 program), is because you may want to leave most parameters to their default
 values, and only modify a handful of them.
 
 For example, you could use the following (perfectly valid) parameter file with
 this tutorial program:
 @code
-SHORTER VERSION HERE
+subsection Stokes Immersed Problem
+  set Final time                         = 1
+  set Nitsche penalty term               = 10
+  set Number of time steps               = 101
+  set Velocity degree                    = 3
+end
 @endcode
 
-and you would obtain exactly the same results as in test case 1 below.
+and you would run the program with Q3/Q2 Taylor-Hood finite elements,
+for 101 steps, using a Nistche penalty of `10`, and leaving all the other
+parameters to their default value.
 
-<h3> Test case 1: </h3>
+<h3> Two dimensional test case </h3>
 
-For the default problem the value of $u$ on $\Gamma$ is set to the constant $1$:
-this is like imposing a constant Dirichlet boundary condition on $\Gamma$, seen
-as boundary of the portion of $\Omega$ inside $\Gamma$. Similarly on $\partial
-\Omega$ we have zero Dirichlet boundary conditions.
+The default problem generates a co-dimension zero impeller, consisting of a
+rotating rectangular grid, where the rotation is for half a second in one
+direction, and half a second in the opposite direction, with constant angular
+velocity equal to five.
 
 
-<div class="twocolumn" style="width: 80%">
-  <div class="parent">
-    <div class="img" align="center">
-      <img src="https://www.dealii.org/images/steps/developer/step-60.1_no_grid.png"
+<p align="center">
+   <div class="img" align="center">
+      <img src="https://www.dealii.org/images/steps/developer/step-70.2d.gif"
            alt = ""
            width="500">
     </div>
-  </div>
-  <div class="parent">
-    <div class="img" align="center">
-      <img src="https://www.dealii.org/images/steps/developer/step-60.1_grid.png"
-           alt = ""
-           width="500">
-    </div>
-  </div>
-</div>
+</p>
 
 The output of the program will look like the following:
 
 @code
-
+bash$ mpirun -np 8 ./step-70 test.prm
+Running StokesImmersedProblem<2> using Trilinos.
+Cycle 0:
+Time : 0, time step: 0.002
+   Number of degrees of freedom: 9539 (8450+1089 -- 0+0)
+Tracer particles: 753
+Solid particles: 576
+   Solved in 142 iterations.
+   Number of degrees of freedom: 3790 (3354+436 -- 576+753)
+Cycle 1:
+Time : 0.002, time step: 0.002
+   Solved in 133 iterations.
+Cycle 2:
+Time : 0.004, time step: 0.002
+   Solved in 148 iterations.
+Cycle 3:
+
+...
+
+Cycle 499:
+Time : 0.998, time step: 0.002
+   Solved in 167 iterations.
+Cycle 500:
+Time : 1, time step: 0.002
+   Solved in 156 iterations.
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start    |      46.9s |            |
+|                                             |            |            |
+| Section                         | no. calls |  wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble Nitsche terms          |       501 |      0.73s |       1.6% |
+| Assemble Stokes terms           |       501 |      1.34s |       2.8% |
+| Initial setup                   |         1 |  0.000827s |         0% |
+| Output fluid                    |       502 |      2.92s |       6.2% |
+| Output solid particles          |       502 |      1.58s |       3.4% |
+| Output tracer particles         |       502 |      2.04s |       4.4% |
+| Refine                          |       100 |       1.2s |       2.6% |
+| Set solid particle position     |       500 |     0.213s |      0.45% |
+| Set tracer particle motion      |       501 |      1.13s |       2.4% |
+| Setup dofs                      |       101 |      0.82s |       1.7% |
+| Solve                           |       501 |      35.4s |        76% |
++---------------------------------+-----------+------------+------------+
 @endcode
 
-You may notice that, in terms of CPU time, assembling the coupling system is
-twice as expensive as assembling the standard Poisson system, even though the
-matrix is smaller. This is due to the non-matching nature of the discretization.
-Whether this is acceptable or not, depends on the applications.
+You may notice that assembling the coupling system is roughly as expensive as
+assemblying the Stokes part, and roughly as expensive as tracking the motion
+of the particles.
 
-If the problem was set in a three-dimensional setting, and the immersed mesh was
-time dependent, it would be much more expensive to recreate the mesh at each
-step rather than use the technique we present here. Moreover, you may be able to
-create a very fast and optimized solver on a uniformly refined square or cubic
-grid, and embed the domain where you want to perform your computation using the
-technique presented here. This would require you to only have a surface
-representatio of your domain (a much cheaper and easier mesh to produce).
+To play around a little bit, we complicate the fictitious domain (taken from
+https://grabcad.com/library/lungstors-blower-1), and run a co-dimension one
+simulation in three space dimensions, using the following
+"parameters_23.prm" file:
 
-To play around a little bit, we are going to complicate a little the fictitious
-domain as well as the boundary conditions we impose on it.
-
-<h3> Test case 2 and 3: </h3>
-
-If we use the following parameter file:
 @code
-subsection Distributed Lagrange<1,2>
-  set Coupling quadrature order                    = 3
-  set Embedded configuration finite element degree = 1
-  set Embedded space finite element degree         = 1
-  set Embedding space finite element degree        = 1
-  set Homogeneous Dirichlet boundary ids           = 0,1,2,3
-  set Initial embedded space refinement            = 8
-  set Initial embedding space refinement           = 4
-  set Local refinements steps near embedded domain = 4
-  set Use displacement in embedded interface       = false
-  set Verbosity level                              = 10
-  subsection Embedded configuration
-    set Function constants  = R=.3, Cx=.5, Cy=.5, r=.1, w=12
-    set Function expression = (R+r*cos(w*pi*x))*cos(2*pi*x)+Cx; (R+r*cos(w*pi*x))*sin(2*pi*x)+Cy
-    set Variable names      = x,y,t
+subsection Stokes Immersed Problem
+  set Final time                            = 1
+  set Homogeneous Dirichlet boundary ids    = 0
+  set Fluid bounding boxes extraction level = 1
+  set Initial fluid refinement              = 3
+  set Initial solid refinement              = 0
+  set Nitsche penalty term                  = 10
+  set Number of time steps                  = 101
+  set Output frequency                      = 1
+  set Particle insertion refinement         = 3
+  set Velocity degree                       = 2
+  set Viscosity                             = 1
+  subsection Angular velocity
+    set Function constants  = 
+    set Function expression = t < .500001 ? 5 : -5
+    set Variable names      = x,y,z,t
   end
-  subsection Embedded value
-    set Function constants  =
-    set Function expression = x-.5
-    set Variable names      = x,y,t
+  subsection Grid generation
+    set Fluid grid generator              = hyper_rectangle
+    set Fluid grid generator arguments    = -50,-50, -10: 50, 50, 40: false
+    set Solid grid generator              = impeller.vtk
+    set Solid grid generator arguments    = 1:impeller.step
+    set Particle grid generator           = hyper_ball
+    set Particle grid generator arguments = 30, 30, 20: 10: false
+  end
+  subsection Refinement and remeshing
+    set Maximum number of cells        = 100000
+    set Refinement coarsening fraction = 0.3
+    set Refinement fraction            = 0.3
+    set Refinement maximal level       = 6
+    set Refinement step frequency      = 5
+    set Refinement strategy            = fixed_fraction
   end
-  subsection Schur solver control
-    set Log frequency = 1
-    set Log history   = false
-    set Log result    = true
-    set Max steps     = 100000
-    set Reduction     = 1.e-12
-    set Tolerance     = 1.e-12
+  subsection Right hand side
+    set Function constants  = 
+    set Function expression = 0; 0; 0; 0
+    set Variable names      = x,y,z,t
   end
 end
 @endcode
 
-We get a "flowery" looking domain, where we impose a linear boundary condition
-$g=x-.5$. This test shows that the method is actually quite accurate in
-recovering an exactly linear function from its boundary conditions, and even
-though the meshes are not aligned, we obtain a pretty good result.
+In this case, the timing outputs are a bit different:
 
-Replacing $x-.5$ with $2(x-.5)^2-2(y-.5)^2$, i.e., modifying the parameter file
-such that we have
 @code
-  ...
-  subsection Embedded value
-    set Function constants  =
-    set Function expression = 2*(x-.5)^2-2*(y-.5)^2
-    set Variable names      = x,y,t
-  end
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start    |  5.54e+03s |            |
+|                                             |            |            |
+| Section                         | no. calls |  wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble Nitsche terms          |       101 |       111s |         2% |
+| Assemble Stokes terms           |       101 |       208s |       3.8% |
+| Initial setup                   |         1 |   0.00187s |         0% |
+| Output fluid                    |       102 |      15.5s |      0.28% |
+| Output solid particles          |       102 |      2.63s |         0% |
+| Output tracer particles         |       102 |      2.49s |         0% |
+| Refine                          |        20 |      18.4s |      0.33% |
+| Set solid particle position     |       100 |       6.1s |      0.11% |
+| Set tracer particle motion      |       101 |      10.8s |       0.2% |
+| Setup dofs                      |        21 |      13.9s |      0.25% |
+| Solve                           |       101 |  5.16e+03s |        93% |
++---------------------------------+-----------+------------+------------+
 @endcode
-produces the saddle on the right.
 
-<div class="twocolumn" style="width: 80%">
-  <div class="parent">
-    <div class="img" align="center">
-      <img src="https://www.dealii.org/images/steps/developer/step-60.3_grid.png"
-           alt = ""
-           width="500">
-    </div>
-  </div>
-  <div class="parent">
-    <div class="img" align="center">
-      <img src="https://www.dealii.org/images/steps/developer/step-60.4_grid.png"
+showing how the solver is taking most of the solution time in three dimensions,
+and that the particle motion and Nitsche assembly remain under control.
+
+<p align="center">
+   <div class="img" align="center">
+      <img src="https://www.dealii.org/images/steps/developer/step-70.2d-3d.gif"
            alt = ""
            width="500">
     </div>
-  </div>
-</div>
+</p>
 
 <a name="extensions"></a>
 <h3>Possibilities for extensions</h3>
 
-<h4> Running with `spacedim` equal to three</h4>
-
-While the current tutorial program is written for `spacedim` equal to two, there
-are only minor changes you have to do in order for the program to run in
-different combinations of dimensions.
-
-If you want to run with `spacedim` equal to three and `dim` equal to two, then
-you will almost certainly want to perform the following changes:
-
-- use a different reference domain for the embedded grid, maybe reading it from
-  a file. It is not possible to construct a smooth closed surface with one
-  single parametrization of a square domain, therefore you'll most likely want
-  to use a reference domain that is topologically equivalent to a the boundary
-  of a sphere.
-
-- use a displacement instead of the deformation to map $\Gamma_0$ into $\Gamma$
-
-<h4> More general domains </h4>
-
-We have seen in other tutorials (for example in step-5 and step-54) how to read
-grids from input files. A nice generalization for this tutorial program would be
-to allow the user to select a grid to read from the parameter file itself,
-instead of hardcoding the mesh type in the tutorial program itself.
-
-<h4> Preconditioner</h4>
-
-At the moment, we have no preconditioner on the Schur complement. This is ok for
-two dimensional problems, where a few hundred iterations bring the residual down
-to the machine precision, but it's not going to work in three dimensions.
-
-It is not obvious what a good preconditioner would be here. The physical problem
-we are solving with the Schur complement, is to associate to the Dirichlet data
-$g$, the value of the Lagrange multiplier $\lambda$. $\lambda$ can be
-interpreted as the *jump* in the normal gradient that needs to be imposed on $u$
-across $\Gamma$, in order to obtain the Dirichlet data $g$.
-
-So $S$ is some sort of Neumann to Dirichlet map, and we would like to have a
-good approximation for the Dirichlet to Neumann map. A possibility would be to
-use a Boundary Element approximation of the problem on $\Gamma$, and construct a
-rough approximation of the hyper-singular operator for the Poisson problem
-associated to $\Gamma$, which is precisely a Dirichlet to Neumann map.
-
-<h4> Parallel Code </h4>
-
-The simple code proposed here can serve as a starting point for more
-complex problems which, to be solved, need to be run on parallel
-code, possibly using distributed meshes (see step-17, step-40, and the
-documentation for parallel::shared::Triangulation and
-parallel::distributed::Triangulation).
-
-When using non-matching grids in parallel a problem arises: to compute the
-matrix $C$ a process needs information about both meshes on the same portion of
-real space but, when working with distributed meshes, this information may not
-be available, because the locally owned part of the $\Omega$ triangulation
-stored on a given processor may not be physically co-located with the locally
-owned part of the $\Gamma$ triangulation stored on the same processor.
-
-Various strategies can be implemented to tackle this problem:
-
-- distribute the two meshes so that this constraint is satisfied;
-
-- use communication for the parts of real space where the constraint is not
-  satisfied;
-
-- use a distributed triangulation for the embedding space, and a shared
-  triangulation for the emdedded configuration.
-
-The latter strategy is clearly the easiest to implement, as most of the
-functions used in this tutorial program will work unchanged also in the parallel
-case. Of course one could use the reversal strategy (that is, have a distributed
-embedded Triangulation and a shared embedding Triangulation).
-
-However, this strategy is most likely going to be more expensive, since by
-definition the embedding grid is larger than the embedded grid, and it makes
-more sense to distribute the largest of the two grids, maintaining the smallest
-one shared among all processors.
+The current tutorial program shows a one-way coupling between the fluid and the
+solid, where the solid motion is imposed (and not solved for), and read in the
+solid domain by exploiting the location and the weights of the solid quadrature
+points.
+
+The structure of the code already allows one to implement a two-way coupling,
+by exploiting the possibility to read values of the fluid velocity on the
+quadrature points of the solid grid. For this to be more efficient in terms
+of MPI communication patterns, one should maintain ownership of the quadrature
+points on the solid processor that owns them. In the current code, it is
+sufficient to define the IndexSet of the vectors used to exchange information
+of the quadrature points by using the solid partition instead of the initial
+fluid partition.
+
+This allows the combination of the technique used in this tutorial program
+with those presented in the tutorial step-60 to solve a fluid structure
+interaction problem with distributed Lagrange multipliers, on
+parallel::distributed::Triangulation objects.
+
+The timings above show that the current preconditioning strategy does not work
+well for Nitsche penalisation, and we should come up with a better
+preconditioner if we want to aim at larger problems. Moreover, a checkpoint
+restart strategy should be implemented to allow for longer simulations to be
+interrupted and restored, as it is done for example in the tutorial step-69.
diff --git a/examples/step-70/impeller.step b/examples/step-70/impeller.step
new file mode 100644 (file)
index 0000000..7e6125b
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+#52433 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52434 = ADVANCED_FACE('',(#52435),#20572,.T.);\r
+#52435 = FACE_BOUND('',#52436,.T.);\r
+#52436 = EDGE_LOOP('',(#52437,#52459,#52460));\r
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+#52440 = CIRCLE('',#52441,40.);\r
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+#52442 = CARTESIAN_POINT('',(0.,0.,-3.));\r
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+#52445 = PCURVE('',#20572,#52446);\r
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+#52450 = DIRECTION('',(1.,0.));\r
+#52451 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52452 = PCURVE('',#51634,#52453);\r
+#52453 = DEFINITIONAL_REPRESENTATION('',(#52454),#52458);\r
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+#52457 = DIRECTION('',(1.,0.));\r
+#52458 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+    #53360,#53361,#53362,#53389));\r
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+#52471 = LINE('',#52472,#52473);\r
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+#52475 = PCURVE('',#20542,#52476);\r
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+#52480 = DIRECTION('',(0.,1.));\r
+#52481 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52482 = PCURVE('',#51634,#52483);\r
+#52483 = DEFINITIONAL_REPRESENTATION('',(#52484),#52488);\r
+#52484 = LINE('',#52485,#52486);\r
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+#52487 = DIRECTION('',(0.,1.));\r
+#52488 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52489 = ORIENTED_EDGE('',*,*,#52490,.F.);\r
+#52490 = EDGE_CURVE('',#52491,#52468,#52493,.T.);\r
+#52491 = VERTEX_POINT('',#52492);\r
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+#52494 = CIRCLE('',#52495,40.);\r
+#52495 = AXIS2_PLACEMENT_3D('',#52496,#52497,#52498);\r
+#52496 = CARTESIAN_POINT('',(3.3E-16,-3.3E-16,-4.));\r
+#52497 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
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+#52499 = PCURVE('',#20542,#52500);\r
+#52500 = DEFINITIONAL_REPRESENTATION('',(#52501),#52505);\r
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+#52502 = CARTESIAN_POINT('',(0.,1.));\r
+#52503 = VECTOR('',#52504,1.);\r
+#52504 = DIRECTION('',(1.,0.));\r
+#52505 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52506 = PCURVE('',#52507,#52512);\r
+#52507 = PLANE('',#52508);\r
+#52508 = AXIS2_PLACEMENT_3D('',#52509,#52510,#52511);\r
+#52509 = CARTESIAN_POINT('',(3.3E-16,-3.3E-16,-4.));\r
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+#52512 = DEFINITIONAL_REPRESENTATION('',(#52513),#52521);\r
+#52513 = ( BOUNDED_CURVE() B_SPLINE_CURVE(2,(#52514,#52515,#52516,#52517\r
+    ,#52518,#52519,#52520),.UNSPECIFIED.,.T.,.F.) \r
+B_SPLINE_CURVE_WITH_KNOTS((1,2,2,2,2,1),(-2.094395102393,0.,\r
+    2.094395102393,4.188790204786,6.28318530718,8.377580409573),\r
+.UNSPECIFIED.) CURVE() GEOMETRIC_REPRESENTATION_ITEM() \r
+RATIONAL_B_SPLINE_CURVE((1.,0.5,1.,0.5,1.,0.5,1.)) REPRESENTATION_ITEM(\r
+  '') );\r
+#52514 = CARTESIAN_POINT('',(-40.,-1.97128336478E-32));\r
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+#52520 = CARTESIAN_POINT('',(-40.,-1.97128336478E-32));\r
+#52521 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52522 = ORIENTED_EDGE('',*,*,#52523,.F.);\r
+#52523 = EDGE_CURVE('',#20526,#52491,#52524,.T.);\r
+#52524 = SURFACE_CURVE('',#52525,(#52529,#52536),.PCURVE_S1.);\r
+#52525 = LINE('',#52526,#52527);\r
+#52526 = CARTESIAN_POINT('',(40.,0.,-3.));\r
+#52527 = VECTOR('',#52528,1.);\r
+#52528 = DIRECTION('',(0.,0.,-1.));\r
+#52529 = PCURVE('',#20542,#52530);\r
+#52530 = DEFINITIONAL_REPRESENTATION('',(#52531),#52535);\r
+#52531 = LINE('',#52532,#52533);\r
+#52532 = CARTESIAN_POINT('',(0.,0.));\r
+#52533 = VECTOR('',#52534,1.);\r
+#52534 = DIRECTION('',(0.,1.));\r
+#52535 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52536 = PCURVE('',#51634,#52537);\r
+#52537 = DEFINITIONAL_REPRESENTATION('',(#52538),#52542);\r
+#52538 = LINE('',#52539,#52540);\r
+#52539 = CARTESIAN_POINT('',(6.28318530718,0.));\r
+#52540 = VECTOR('',#52541,1.);\r
+#52541 = DIRECTION('',(0.,1.));\r
+#52542 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52543 = ORIENTED_EDGE('',*,*,#20525,.T.);\r
+#52544 = ORIENTED_EDGE('',*,*,#52545,.T.);\r
+#52545 = EDGE_CURVE('',#20308,#21501,#52546,.T.);\r
+#52546 = SURFACE_CURVE('',#52547,(#52552,#52559),.PCURVE_S1.);\r
+#52547 = CIRCLE('',#52548,40.);\r
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+#52549 = CARTESIAN_POINT('',(0.,0.,-3.));\r
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+#52552 = PCURVE('',#20542,#52553);\r
+#52553 = DEFINITIONAL_REPRESENTATION('',(#52554),#52558);\r
+#52554 = LINE('',#52555,#52556);\r
+#52555 = CARTESIAN_POINT('',(0.,0.));\r
+#52556 = VECTOR('',#52557,1.);\r
+#52557 = DIRECTION('',(1.,0.));\r
+#52558 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52559 = PCURVE('',#20832,#52560);\r
+#52560 = DEFINITIONAL_REPRESENTATION('',(#52561),#52565);\r
+#52561 = LINE('',#52562,#52563);\r
+#52562 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52563 = VECTOR('',#52564,1.);\r
+#52564 = DIRECTION('',(1.,-0.));\r
+#52565 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52566 = ORIENTED_EDGE('',*,*,#22008,.T.);\r
+#52567 = ORIENTED_EDGE('',*,*,#52568,.T.);\r
+#52568 = EDGE_CURVE('',#21769,#22419,#52569,.T.);\r
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+#52570 = CIRCLE('',#52571,40.);\r
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+#52572 = CARTESIAN_POINT('',(0.,0.,-3.));\r
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+#52575 = PCURVE('',#20542,#52576);\r
+#52576 = DEFINITIONAL_REPRESENTATION('',(#52577),#52581);\r
+#52577 = LINE('',#52578,#52579);\r
+#52578 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52579 = VECTOR('',#52580,1.);\r
+#52580 = DIRECTION('',(1.,0.));\r
+#52581 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52582 = PCURVE('',#52583,#52588);\r
+#52583 = CYLINDRICAL_SURFACE('',#52584,40.);\r
+#52584 = AXIS2_PLACEMENT_3D('',#52585,#52586,#52587);\r
+#52585 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
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+#52588 = DEFINITIONAL_REPRESENTATION('',(#52589),#52593);\r
+#52589 = LINE('',#52590,#52591);\r
+#52590 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52591 = VECTOR('',#52592,1.);\r
+#52592 = DIRECTION('',(1.,-0.));\r
+#52593 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52594 = ORIENTED_EDGE('',*,*,#22418,.T.);\r
+#52595 = ORIENTED_EDGE('',*,*,#52596,.T.);\r
+#52596 = EDGE_CURVE('',#22201,#23377,#52597,.T.);\r
+#52597 = SURFACE_CURVE('',#52598,(#52603,#52610),.PCURVE_S1.);\r
+#52598 = CIRCLE('',#52599,40.);\r
+#52599 = AXIS2_PLACEMENT_3D('',#52600,#52601,#52602);\r
+#52600 = CARTESIAN_POINT('',(0.,0.,-3.));\r
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+#52603 = PCURVE('',#20542,#52604);\r
+#52604 = DEFINITIONAL_REPRESENTATION('',(#52605),#52609);\r
+#52605 = LINE('',#52606,#52607);\r
+#52606 = CARTESIAN_POINT('',(0.,0.));\r
+#52607 = VECTOR('',#52608,1.);\r
+#52608 = DIRECTION('',(1.,0.));\r
+#52609 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52610 = PCURVE('',#22941,#52611);\r
+#52611 = DEFINITIONAL_REPRESENTATION('',(#52612),#52616);\r
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+#52613 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
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+#52615 = DIRECTION('',(1.,-0.));\r
+#52616 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52617 = ORIENTED_EDGE('',*,*,#23887,.T.);\r
+#52618 = ORIENTED_EDGE('',*,*,#52619,.T.);\r
+#52619 = EDGE_CURVE('',#23648,#24298,#52620,.T.);\r
+#52620 = SURFACE_CURVE('',#52621,(#52626,#52633),.PCURVE_S1.);\r
+#52621 = CIRCLE('',#52622,40.);\r
+#52622 = AXIS2_PLACEMENT_3D('',#52623,#52624,#52625);\r
+#52623 = CARTESIAN_POINT('',(0.,0.,-3.));\r
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+#52626 = PCURVE('',#20542,#52627);\r
+#52627 = DEFINITIONAL_REPRESENTATION('',(#52628),#52632);\r
+#52628 = LINE('',#52629,#52630);\r
+#52629 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52630 = VECTOR('',#52631,1.);\r
+#52631 = DIRECTION('',(1.,0.));\r
+#52632 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52633 = PCURVE('',#52634,#52639);\r
+#52634 = CYLINDRICAL_SURFACE('',#52635,40.);\r
+#52635 = AXIS2_PLACEMENT_3D('',#52636,#52637,#52638);\r
+#52636 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52637 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52638 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52639 = DEFINITIONAL_REPRESENTATION('',(#52640),#52644);\r
+#52640 = LINE('',#52641,#52642);\r
+#52641 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52642 = VECTOR('',#52643,1.);\r
+#52643 = DIRECTION('',(1.,-0.));\r
+#52644 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52645 = ORIENTED_EDGE('',*,*,#24297,.T.);\r
+#52646 = ORIENTED_EDGE('',*,*,#52647,.T.);\r
+#52647 = EDGE_CURVE('',#24080,#25256,#52648,.T.);\r
+#52648 = SURFACE_CURVE('',#52649,(#52654,#52661),.PCURVE_S1.);\r
+#52649 = CIRCLE('',#52650,40.);\r
+#52650 = AXIS2_PLACEMENT_3D('',#52651,#52652,#52653);\r
+#52651 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52652 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52653 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52654 = PCURVE('',#20542,#52655);\r
+#52655 = DEFINITIONAL_REPRESENTATION('',(#52656),#52660);\r
+#52656 = LINE('',#52657,#52658);\r
+#52657 = CARTESIAN_POINT('',(0.,0.));\r
+#52658 = VECTOR('',#52659,1.);\r
+#52659 = DIRECTION('',(1.,0.));\r
+#52660 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52661 = PCURVE('',#24590,#52662);\r
+#52662 = DEFINITIONAL_REPRESENTATION('',(#52663),#52667);\r
+#52663 = LINE('',#52664,#52665);\r
+#52664 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52665 = VECTOR('',#52666,1.);\r
+#52666 = DIRECTION('',(1.,-0.));\r
+#52667 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52668 = ORIENTED_EDGE('',*,*,#25766,.T.);\r
+#52669 = ORIENTED_EDGE('',*,*,#52670,.T.);\r
+#52670 = EDGE_CURVE('',#25527,#26177,#52671,.T.);\r
+#52671 = SURFACE_CURVE('',#52672,(#52677,#52684),.PCURVE_S1.);\r
+#52672 = CIRCLE('',#52673,40.);\r
+#52673 = AXIS2_PLACEMENT_3D('',#52674,#52675,#52676);\r
+#52674 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52675 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52676 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52677 = PCURVE('',#20542,#52678);\r
+#52678 = DEFINITIONAL_REPRESENTATION('',(#52679),#52683);\r
+#52679 = LINE('',#52680,#52681);\r
+#52680 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52681 = VECTOR('',#52682,1.);\r
+#52682 = DIRECTION('',(1.,0.));\r
+#52683 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52684 = PCURVE('',#52685,#52690);\r
+#52685 = CYLINDRICAL_SURFACE('',#52686,40.);\r
+#52686 = AXIS2_PLACEMENT_3D('',#52687,#52688,#52689);\r
+#52687 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52688 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52689 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52690 = DEFINITIONAL_REPRESENTATION('',(#52691),#52695);\r
+#52691 = LINE('',#52692,#52693);\r
+#52692 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52693 = VECTOR('',#52694,1.);\r
+#52694 = DIRECTION('',(1.,-0.));\r
+#52695 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52696 = ORIENTED_EDGE('',*,*,#26176,.T.);\r
+#52697 = ORIENTED_EDGE('',*,*,#52698,.T.);\r
+#52698 = EDGE_CURVE('',#25959,#27135,#52699,.T.);\r
+#52699 = SURFACE_CURVE('',#52700,(#52705,#52712),.PCURVE_S1.);\r
+#52700 = CIRCLE('',#52701,40.);\r
+#52701 = AXIS2_PLACEMENT_3D('',#52702,#52703,#52704);\r
+#52702 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52703 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52704 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52705 = PCURVE('',#20542,#52706);\r
+#52706 = DEFINITIONAL_REPRESENTATION('',(#52707),#52711);\r
+#52707 = LINE('',#52708,#52709);\r
+#52708 = CARTESIAN_POINT('',(0.,0.));\r
+#52709 = VECTOR('',#52710,1.);\r
+#52710 = DIRECTION('',(1.,0.));\r
+#52711 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52712 = PCURVE('',#26469,#52713);\r
+#52713 = DEFINITIONAL_REPRESENTATION('',(#52714),#52718);\r
+#52714 = LINE('',#52715,#52716);\r
+#52715 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52716 = VECTOR('',#52717,1.);\r
+#52717 = DIRECTION('',(1.,-0.));\r
+#52718 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52719 = ORIENTED_EDGE('',*,*,#27645,.T.);\r
+#52720 = ORIENTED_EDGE('',*,*,#52721,.T.);\r
+#52721 = EDGE_CURVE('',#27406,#28056,#52722,.T.);\r
+#52722 = SURFACE_CURVE('',#52723,(#52728,#52735),.PCURVE_S1.);\r
+#52723 = CIRCLE('',#52724,40.);\r
+#52724 = AXIS2_PLACEMENT_3D('',#52725,#52726,#52727);\r
+#52725 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52726 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52727 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52728 = PCURVE('',#20542,#52729);\r
+#52729 = DEFINITIONAL_REPRESENTATION('',(#52730),#52734);\r
+#52730 = LINE('',#52731,#52732);\r
+#52731 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52732 = VECTOR('',#52733,1.);\r
+#52733 = DIRECTION('',(1.,0.));\r
+#52734 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52735 = PCURVE('',#52736,#52741);\r
+#52736 = CYLINDRICAL_SURFACE('',#52737,40.);\r
+#52737 = AXIS2_PLACEMENT_3D('',#52738,#52739,#52740);\r
+#52738 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52739 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52740 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52741 = DEFINITIONAL_REPRESENTATION('',(#52742),#52746);\r
+#52742 = LINE('',#52743,#52744);\r
+#52743 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52744 = VECTOR('',#52745,1.);\r
+#52745 = DIRECTION('',(1.,-0.));\r
+#52746 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52747 = ORIENTED_EDGE('',*,*,#28055,.T.);\r
+#52748 = ORIENTED_EDGE('',*,*,#52749,.T.);\r
+#52749 = EDGE_CURVE('',#27838,#29014,#52750,.T.);\r
+#52750 = SURFACE_CURVE('',#52751,(#52756,#52763),.PCURVE_S1.);\r
+#52751 = CIRCLE('',#52752,40.);\r
+#52752 = AXIS2_PLACEMENT_3D('',#52753,#52754,#52755);\r
+#52753 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52754 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52755 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52756 = PCURVE('',#20542,#52757);\r
+#52757 = DEFINITIONAL_REPRESENTATION('',(#52758),#52762);\r
+#52758 = LINE('',#52759,#52760);\r
+#52759 = CARTESIAN_POINT('',(0.,0.));\r
+#52760 = VECTOR('',#52761,1.);\r
+#52761 = DIRECTION('',(1.,0.));\r
+#52762 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52763 = PCURVE('',#28348,#52764);\r
+#52764 = DEFINITIONAL_REPRESENTATION('',(#52765),#52769);\r
+#52765 = LINE('',#52766,#52767);\r
+#52766 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52767 = VECTOR('',#52768,1.);\r
+#52768 = DIRECTION('',(1.,-0.));\r
+#52769 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52770 = ORIENTED_EDGE('',*,*,#29524,.T.);\r
+#52771 = ORIENTED_EDGE('',*,*,#52772,.T.);\r
+#52772 = EDGE_CURVE('',#29285,#29935,#52773,.T.);\r
+#52773 = SURFACE_CURVE('',#52774,(#52779,#52786),.PCURVE_S1.);\r
+#52774 = CIRCLE('',#52775,40.);\r
+#52775 = AXIS2_PLACEMENT_3D('',#52776,#52777,#52778);\r
+#52776 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52777 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52778 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52779 = PCURVE('',#20542,#52780);\r
+#52780 = DEFINITIONAL_REPRESENTATION('',(#52781),#52785);\r
+#52781 = LINE('',#52782,#52783);\r
+#52782 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52783 = VECTOR('',#52784,1.);\r
+#52784 = DIRECTION('',(1.,0.));\r
+#52785 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52786 = PCURVE('',#52787,#52792);\r
+#52787 = CYLINDRICAL_SURFACE('',#52788,40.);\r
+#52788 = AXIS2_PLACEMENT_3D('',#52789,#52790,#52791);\r
+#52789 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52790 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52791 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52792 = DEFINITIONAL_REPRESENTATION('',(#52793),#52797);\r
+#52793 = LINE('',#52794,#52795);\r
+#52794 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52795 = VECTOR('',#52796,1.);\r
+#52796 = DIRECTION('',(1.,-0.));\r
+#52797 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52798 = ORIENTED_EDGE('',*,*,#29934,.T.);\r
+#52799 = ORIENTED_EDGE('',*,*,#52800,.T.);\r
+#52800 = EDGE_CURVE('',#29717,#30893,#52801,.T.);\r
+#52801 = SURFACE_CURVE('',#52802,(#52807,#52814),.PCURVE_S1.);\r
+#52802 = CIRCLE('',#52803,40.);\r
+#52803 = AXIS2_PLACEMENT_3D('',#52804,#52805,#52806);\r
+#52804 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52805 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52806 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52807 = PCURVE('',#20542,#52808);\r
+#52808 = DEFINITIONAL_REPRESENTATION('',(#52809),#52813);\r
+#52809 = LINE('',#52810,#52811);\r
+#52810 = CARTESIAN_POINT('',(0.,0.));\r
+#52811 = VECTOR('',#52812,1.);\r
+#52812 = DIRECTION('',(1.,0.));\r
+#52813 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52814 = PCURVE('',#30227,#52815);\r
+#52815 = DEFINITIONAL_REPRESENTATION('',(#52816),#52820);\r
+#52816 = LINE('',#52817,#52818);\r
+#52817 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52818 = VECTOR('',#52819,1.);\r
+#52819 = DIRECTION('',(1.,-0.));\r
+#52820 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52821 = ORIENTED_EDGE('',*,*,#31403,.T.);\r
+#52822 = ORIENTED_EDGE('',*,*,#52823,.T.);\r
+#52823 = EDGE_CURVE('',#31164,#31814,#52824,.T.);\r
+#52824 = SURFACE_CURVE('',#52825,(#52830,#52837),.PCURVE_S1.);\r
+#52825 = CIRCLE('',#52826,40.);\r
+#52826 = AXIS2_PLACEMENT_3D('',#52827,#52828,#52829);\r
+#52827 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52828 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52829 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52830 = PCURVE('',#20542,#52831);\r
+#52831 = DEFINITIONAL_REPRESENTATION('',(#52832),#52836);\r
+#52832 = LINE('',#52833,#52834);\r
+#52833 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52834 = VECTOR('',#52835,1.);\r
+#52835 = DIRECTION('',(1.,0.));\r
+#52836 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52837 = PCURVE('',#52838,#52843);\r
+#52838 = CYLINDRICAL_SURFACE('',#52839,40.);\r
+#52839 = AXIS2_PLACEMENT_3D('',#52840,#52841,#52842);\r
+#52840 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52841 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52842 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52843 = DEFINITIONAL_REPRESENTATION('',(#52844),#52848);\r
+#52844 = LINE('',#52845,#52846);\r
+#52845 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52846 = VECTOR('',#52847,1.);\r
+#52847 = DIRECTION('',(1.,-0.));\r
+#52848 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52849 = ORIENTED_EDGE('',*,*,#31813,.T.);\r
+#52850 = ORIENTED_EDGE('',*,*,#52851,.T.);\r
+#52851 = EDGE_CURVE('',#31596,#32772,#52852,.T.);\r
+#52852 = SURFACE_CURVE('',#52853,(#52858,#52865),.PCURVE_S1.);\r
+#52853 = CIRCLE('',#52854,40.);\r
+#52854 = AXIS2_PLACEMENT_3D('',#52855,#52856,#52857);\r
+#52855 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52856 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52857 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52858 = PCURVE('',#20542,#52859);\r
+#52859 = DEFINITIONAL_REPRESENTATION('',(#52860),#52864);\r
+#52860 = LINE('',#52861,#52862);\r
+#52861 = CARTESIAN_POINT('',(0.,0.));\r
+#52862 = VECTOR('',#52863,1.);\r
+#52863 = DIRECTION('',(1.,0.));\r
+#52864 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52865 = PCURVE('',#32106,#52866);\r
+#52866 = DEFINITIONAL_REPRESENTATION('',(#52867),#52871);\r
+#52867 = LINE('',#52868,#52869);\r
+#52868 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52869 = VECTOR('',#52870,1.);\r
+#52870 = DIRECTION('',(1.,-0.));\r
+#52871 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52872 = ORIENTED_EDGE('',*,*,#33282,.T.);\r
+#52873 = ORIENTED_EDGE('',*,*,#52874,.T.);\r
+#52874 = EDGE_CURVE('',#33043,#33693,#52875,.T.);\r
+#52875 = SURFACE_CURVE('',#52876,(#52881,#52888),.PCURVE_S1.);\r
+#52876 = CIRCLE('',#52877,40.);\r
+#52877 = AXIS2_PLACEMENT_3D('',#52878,#52879,#52880);\r
+#52878 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52879 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52880 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52881 = PCURVE('',#20542,#52882);\r
+#52882 = DEFINITIONAL_REPRESENTATION('',(#52883),#52887);\r
+#52883 = LINE('',#52884,#52885);\r
+#52884 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52885 = VECTOR('',#52886,1.);\r
+#52886 = DIRECTION('',(1.,0.));\r
+#52887 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52888 = PCURVE('',#52889,#52894);\r
+#52889 = CYLINDRICAL_SURFACE('',#52890,40.);\r
+#52890 = AXIS2_PLACEMENT_3D('',#52891,#52892,#52893);\r
+#52891 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52892 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52893 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52894 = DEFINITIONAL_REPRESENTATION('',(#52895),#52899);\r
+#52895 = LINE('',#52896,#52897);\r
+#52896 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52897 = VECTOR('',#52898,1.);\r
+#52898 = DIRECTION('',(1.,-0.));\r
+#52899 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52900 = ORIENTED_EDGE('',*,*,#33692,.T.);\r
+#52901 = ORIENTED_EDGE('',*,*,#52902,.T.);\r
+#52902 = EDGE_CURVE('',#33475,#34651,#52903,.T.);\r
+#52903 = SURFACE_CURVE('',#52904,(#52909,#52916),.PCURVE_S1.);\r
+#52904 = CIRCLE('',#52905,40.);\r
+#52905 = AXIS2_PLACEMENT_3D('',#52906,#52907,#52908);\r
+#52906 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52907 = DIRECTION('',(3.3E-16,-3.3E-16,-1.));\r
+#52908 = DIRECTION('',(1.,0.,3.3E-16));\r
+#52909 = PCURVE('',#20542,#52910);\r
+#52910 = DEFINITIONAL_REPRESENTATION('',(#52911),#52915);\r
+#52911 = LINE('',#52912,#52913);\r
+#52912 = CARTESIAN_POINT('',(0.,0.));\r
+#52913 = VECTOR('',#52914,1.);\r
+#52914 = DIRECTION('',(1.,0.));\r
+#52915 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52916 = PCURVE('',#33985,#52917);\r
+#52917 = DEFINITIONAL_REPRESENTATION('',(#52918),#52922);\r
+#52918 = LINE('',#52919,#52920);\r
+#52919 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52920 = VECTOR('',#52921,1.);\r
+#52921 = DIRECTION('',(1.,-0.));\r
+#52922 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52923 = ORIENTED_EDGE('',*,*,#35161,.T.);\r
+#52924 = ORIENTED_EDGE('',*,*,#52925,.T.);\r
+#52925 = EDGE_CURVE('',#34922,#35572,#52926,.T.);\r
+#52926 = SURFACE_CURVE('',#52927,(#52932,#52939),.PCURVE_S1.);\r
+#52927 = CIRCLE('',#52928,40.);\r
+#52928 = AXIS2_PLACEMENT_3D('',#52929,#52930,#52931);\r
+#52929 = CARTESIAN_POINT('',(0.,0.,-3.));\r
+#52930 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52931 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52932 = PCURVE('',#20542,#52933);\r
+#52933 = DEFINITIONAL_REPRESENTATION('',(#52934),#52938);\r
+#52934 = LINE('',#52935,#52936);\r
+#52935 = CARTESIAN_POINT('',(-0.174532925199,0.));\r
+#52936 = VECTOR('',#52937,1.);\r
+#52937 = DIRECTION('',(1.,0.));\r
+#52938 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#52939 = PCURVE('',#52940,#52945);\r
+#52940 = CYLINDRICAL_SURFACE('',#52941,40.);\r
+#52941 = AXIS2_PLACEMENT_3D('',#52942,#52943,#52944);\r
+#52942 = CARTESIAN_POINT('',(-2.316911861358E-15,1.622319150691E-15,3.)\r
+  );\r
+#52943 = DIRECTION('',(3.822904571241E-16,-2.676826598639E-16,-1.));\r
+#52944 = DIRECTION('',(0.984807753012,0.173648177667,3.3E-16));\r
+#52945 = DEFINITIONAL_REPRESENTATION('',(#52946),#52950);\r
+#52946 = LINE('',#52947,#52948);\r
+#52947 = CARTESIAN_POINT('',(-6.28318530718,6.));\r
+#52948 = VECTOR('',#52949,1.);\r
+#52949 = DIRECTION('',(1.,-0.));\r
+#52950 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#52966 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#52973 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#52989 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53001 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53017 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53024 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53039 = DIRECTION('',(1.,0.));\r
+#53040 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
+#53041 = PCURVE('',#53042,#53047);\r
+#53042 = CYLINDRICAL_SURFACE('',#53043,40.);\r
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+#53052 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53068 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53075 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53090 = DIRECTION('',(1.,0.));\r
+#53091 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53093 = CYLINDRICAL_SURFACE('',#53094,40.);\r
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+#53103 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53126 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53142 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53154 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53170 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53177 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53193 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+#53205 = ( GEOMETRIC_REPRESENTATION_CONTEXT(2) \r
+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
+  ) );\r
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+  ) );\r
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+PARAMETRIC_REPRESENTATION_CONTEXT() REPRESENTATION_CONTEXT('2D SPACE',''\r
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+REPRESENTATION_CONTEXT('Context #1',\r
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+    #64118),#64111);\r
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+ENDSEC;\r
+END-ISO-10303-21;\r
diff --git a/examples/step-70/impeller.vtk b/examples/step-70/impeller.vtk
new file mode 100644 (file)
index 0000000..0738096
--- /dev/null
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+CELL_DATA 4167
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diff --git a/examples/step-70/parameters_23.prm b/examples/step-70/parameters_23.prm
new file mode 100644 (file)
index 0000000..b378a73
--- /dev/null
@@ -0,0 +1,39 @@
+subsection Stokes Immersed Problem
+  set Final time                            = 1
+  set Homogeneous Dirichlet boundary ids    = 0
+  set Fluid bounding boxes extraction level = 1
+  set Initial fluid refinement              = 3
+  set Initial solid refinement              = 0
+  set Nitsche penalty term                  = 10
+  set Number of time steps                  = 101
+  set Output frequency                      = 1
+  set Particle insertion refinement         = 3
+  set Velocity degree                       = 2
+  set Viscosity                             = 1
+  subsection Angular velocity
+    set Function constants  = 
+    set Function expression = t < .500001 ? 5 : -5
+    set Variable names      = x,y,z,t
+  end
+  subsection Grid generation
+    set Grid one generator                = hyper_rectangle
+    set Grid one generator arguments      = -50,-50, -10: 50, 50, 40: false
+    set Grid two generator                = ../impeller.vtk
+    set Grid two generator arguments      = 1:../impeller.step
+    set Particle grid generator           = hyper_ball
+    set Particle grid generator arguments = 30, 30, 20: 10: false
+  end
+  subsection Refinement and remeshing
+    set Maximum number of cells        = 100000
+    set Refinement coarsening fraction = 0.3
+    set Refinement fraction            = 0.3
+    set Refinement maximal level       = 6
+    set Refinement step frequency      = 5
+    set Refinement strategy            = fixed_fraction
+  end
+  subsection Right hand side
+    set Function constants  = 
+    set Function expression = 0; 0; 0; 0
+    set Variable names      = x,y,z,t
+  end
+end
index cc1e8068761fc18ff3dd86f9b19c24c1f8e3004e..ff328880b30b46fd960d5edf2465081734d705cd 100644 (file)
@@ -192,7 +192,7 @@ namespace Step70
     // Instead of defining a time step increment, in this tutorial we prefer to
     // let the user choose a final simulation time, and the number of steps in
     // which we want to reach the final time
-    unsigned int number_of_time_steps = 1;
+    unsigned int number_of_time_steps = 501;
     double       final_time           = 1.0;
 
     // Instead of producing an output at every time step, we allow the user to
@@ -204,9 +204,9 @@ namespace Step70
     // datum. However it is relatively straightforward to incorporate some
     // elasticity model in this tutorial, and transform it into a fully fledged
     // FSI solver.
-    unsigned int initial_fluid_refinement      = 3;
+    unsigned int initial_fluid_refinement      = 5;
     unsigned int initial_solid_refinement      = 3;
-    unsigned int particle_insertion_refinement = 1;
+    unsigned int particle_insertion_refinement = 3;
 
     // To provide a rough description of the fluid domain, we use the method
     // extract_rtree_level() applied to the tree of bounding boxes of each
@@ -221,7 +221,7 @@ namespace Step70
     // The only two parameters used in the equations are the viscosity of the
     // fluid, and the penalty term used in the Nitsche formulation:
     double viscosity    = 1.0;
-    double penalty_term = 10;
+    double penalty_term = 100;
 
     // By default, we create a hyper_cube without colorisation, and we use
     // homogenous Dirichlet boundary conditions. In this set we store the
@@ -292,7 +292,7 @@ namespace Step70
     //
     // Refinement may be done every few time steps, instead of continuously, and
     // we control this value by the `refinement_frequency` parameter:
-    int          max_level_refinement = 5;
+    int          max_level_refinement = 7;
     std::string  refinement_strategy  = "fixed_fraction";
     double       coarsening_fraction  = 0.3;
     double       refinement_fraction  = 0.3;
@@ -370,7 +370,7 @@ namespace Step70
     {
       Tensor<1, spacedim> displacement = p;
 
-      double dtheta = angular_velocity.value(p, 0) * time_step;
+      double dtheta = angular_velocity.value(p) * time_step;
 
       displacement[0] = std::cos(dtheta) * p[0] - std::sin(dtheta) * p[1];
       displacement[1] = std::sin(dtheta) * p[0] + std::cos(dtheta) * p[1];
@@ -1554,9 +1554,13 @@ namespace Step70
   void StokesImmersedProblem<dim, spacedim>::run()
   {
 #ifdef USE_PETSC_LA
-    pcout << "Running using PETSc." << std::endl;
+    pcout << "Running StokesImmersedProblem<"
+          << Utilities::dim_string(dim, spacedim) << "> using PETSc."
+          << std::endl;
 #else
-    pcout << "Running using Trilinos." << std::endl;
+    pcout << "Running StokesImmersedProblem<"
+          << Utilities::dim_string(dim, spacedim) << "> using Trilinos."
+          << std::endl;
 #endif
 
     ComponentMask velocity_mask(spacedim + 1, true);
@@ -1711,19 +1715,19 @@ namespace Step70
       "Boundary Ids over which homogeneous Dirichlet boundary conditions are applied");
 
     // Next section is dedicated to the parameters used to create the
-    // various grids. We will need three different triangulations: `Grid
-    // one` is used to define the fluid domain, `Grid two` defines the
+    // various grids. We will need three different triangulations: `Fluid grid`
+    // is used to define the fluid domain, `Solid grid` defines the
     // solid domain, and `Particle grid` is used to distribute some tracer
     // particles, that are advected with the velocity and only used as
     // passive tracers.
     enter_my_subsection(this->prm);
     this->prm.enter_subsection("Grid generation");
-    this->prm.add_parameter("Grid one generator", name_of_fluid_grid);
-    this->prm.add_parameter("Grid one generator arguments",
+    this->prm.add_parameter("Fluid grid generator", name_of_fluid_grid);
+    this->prm.add_parameter("Fluid grid generator arguments",
                             arguments_for_fluid_grid);
 
-    this->prm.add_parameter("Grid two generator", name_of_solid_grid);
-    this->prm.add_parameter("Grid two generator arguments",
+    this->prm.add_parameter("Solid grid generator", name_of_solid_grid);
+    this->prm.add_parameter("Solid grid generator arguments",
                             arguments_for_solid_grid);
 
     this->prm.add_parameter("Particle grid generator", name_of_particle_grid);
@@ -1751,21 +1755,29 @@ namespace Step70
     this->prm.leave_subsection();
     leave_my_subsection(this->prm);
 
-    // correct the default dimension for the functions
+    // correct the default dimension for the rhs function
     rhs.declare_parameters_call_back.connect([&]() {
       Functions::ParsedFunction<spacedim>::declare_parameters(this->prm,
                                                               spacedim + 1);
     });
-    angular_velocity.declare_parameters_call_back.connect([&]() {
-      Functions::ParsedFunction<spacedim>::declare_parameters(
-        this->prm, spacedim == 3 ? spacedim : 1);
-    });
+    // and define a meaningful default angular velocity instaed of zero
+    angular_velocity.declare_parameters_call_back.connect(
+      [&]() { this->prm.set("Function expression", "t < .500001 ? 5 : -5"); });
   }
 
 } // namespace Step70
 
 
-// The remainder of the code, the main function, is standard.
+// The remainder of the code, the main function, is standard, with the exception
+// of the handling of input parameter files.
+// We allow the user to specify an optional parameter file as an argument to the
+// program. If nothing is specified, we use the default file "parameters.prm",
+// which is created if non existent.
+// The file name is scanned for the the string "23" first, and "3" afterwards.
+// If the filename contains the string "23", a the problem classes are
+// instantiated with template arguments 2 and 3 respectively. If only the string
+// "3" is found, then both template arguments are set to 3, otherwise both are
+// set to 2.
 int main(int argc, char *argv[])
 {
   using namespace Step70;
@@ -1775,12 +1787,46 @@ int main(int argc, char *argv[])
     {
       Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
 
-      StokesImmersedProblemParameters<2, 3> par;
-      ParameterAcceptor::initialize("parameters_23.prm",
-                                    "used_parameters_23.prm");
+      // Interpret the
+      std::string prm_file;
+      if (argc > 1)
+        {
+          prm_file = argv[1];
+        }
+      else
+        {
+          prm_file = "parameters.prm";
+        }
 
-      StokesImmersedProblem<2, 3> problem(par);
-      problem.run();
+      std::string used_prm_file = prm_file;
+      used_prm_file.insert(used_prm_file.find_last_of("."), "_used");
+
+      // deduce the dimension of the problem from the name of the
+      // parameter file specified at the command line
+      if (prm_file.find("23") != std::string::npos)
+        {
+          StokesImmersedProblemParameters<2, 3> par;
+          ParameterAcceptor::initialize(prm_file, used_prm_file);
+
+          StokesImmersedProblem<2, 3> problem(par);
+          problem.run();
+        }
+      else if (prm_file.find("3") != std::string::npos)
+        {
+          StokesImmersedProblemParameters<3> par;
+          ParameterAcceptor::initialize(prm_file, used_prm_file);
+
+          StokesImmersedProblem<3> problem(par);
+          problem.run();
+        }
+      else
+        {
+          StokesImmersedProblemParameters<2> par;
+          ParameterAcceptor::initialize(prm_file, used_prm_file);
+
+          StokesImmersedProblem<2> problem(par);
+          problem.run();
+        }
     }
   catch (std::exception &exc)
     {

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