Merge pull request #6 from luca-heltai/lab-03

Added lab 03.

.github/workflows/tests.yml

@@ -26,6 +26,7 @@ jobs:
       run: |
          cd labs/lab-01/build_linux_debug
          ./gtest
+    
     - name: Build lab 02
       run: |
          cd labs/lab-02
@@ -36,4 +37,16 @@ jobs:
     - name: Run gtest on lab 02 
       run: |
          cd labs/lab-02/build_linux_debug
+         ./gtest
+
+    - name: Build lab 03
+      run: |
+         cd labs/lab-03
+         rm -rf build_linux_debug
+         mkdir build_linux_debug 
+         cd build_linux_debug
+         cmake .. -GNinja -DCMAKE_BUILD_TYPE=Debug; ninja
+    - name: Run gtest on lab 03 
+      run: |
+         cd labs/lab-03/build_linux_debug
          ./gtest

.gitignore

@@ -1,2 +1,3 @@
 compile_commands.json
 build-container
+doc/html

labs/lab-03/CMakeLists.txt

@@ -0,0 +1,29 @@
+CMAKE_MINIMUM_REQUIRED(VERSION 3.15)
+
+PROJECT(gtest)
+
+FIND_PACKAGE(deal.II 9.3 REQUIRED
+HINTS ${deal.II_DIR} ${DEAL_II_DIR} ../ ../../ $ENV{DEAL_II_DIR})
+
+DEAL_II_INITIALIZE_CACHED_VARIABLES()
+
+# Executable
+FILE(GLOB executable_files source/*cc)
+ADD_EXECUTABLE(step-3 ${executable_files})
+DEAL_II_SETUP_TARGET(step-3)
+
+# Library of the executable
+ADD_LIBRARY(step-3-lib SHARED $<TARGET_OBJECTS:step-3>)
+DEAL_II_SETUP_TARGET(step-3-lib)
+
+# Tester executable
+FIND_PACKAGE(GTest REQUIRED)
+FILE(GLOB test_files tests/*cc)
+ADD_EXECUTABLE(gtest ${test_files})
+TARGET_LINK_LIBRARIES(gtest ${GTEST_LIBRARY} ${GTEST_MAIN_LIBRARY} step-3-lib)   
+DEAL_II_SETUP_TARGET(gtest)
+
+INCLUDE_DIRECTORIES(${GTEST_INCLUDE_DIRS} ./include/)
+
+ENABLE_TESTING()
+GTEST_DISCOVER_TESTS(gtest)

labs/lab-03/LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2021 Theory and Practice of FEM
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

labs/lab-03/README.md

@@ -0,0 +1,161 @@
+#  Lab 03 - Poisson Problem
+## The finite element method using deal.II
+
+**Luca Heltai** <[email protected]>
+
+* * * * *
+
+## General Instructions
+
+For each of the point below, extend the `step-3` class with functions that 
+perform the indicated tasks, trying to minimize the amount of code you copy
+and paste, possibly restructuring existing code by adding arguments to existing
+functions, and generating wrappers similar to the `run` method (e.g., 
+`run_exercise_3`).
+
+Once you created a function that performs the given task, add it to the 
+`step-3-tester.cc` file, and make sure all the exercises are run through
+the `gtest` executable, e.g., adding a test for each exercise, as in the 
+following snippet: 
+
+```C++
+TEST_F(Step3Tester, Exercise3) {
+   run_exercise_3();
+}
+```
+
+By the end of this laboratory, you will have a code that solves a Poisson 
+problem in two dimensions, on different domain types, with arbitrary right hand
+side, arbitrary Dirichlet boundary conditions, variable finite element degree, 
+and different levels of refinement.
+
+The program will read parameter files for its execution. This is the minimal 
+starting point for simple but extensible Finite Element applications, and 
+touches already many important and fundamental characteristics of general and 
+extensible Finite Element codes.
+
+## Lab-03 
+
+### step-3
+
+1.  See documentation of step-3 at
+    <https://www.dealii.org/current/doxygen/deal.II/step_3.html>
+
+2.  Compile and run step-3. Examine the source and header files. Move all 
+    `#include<...>` directives that you can from the header `step-3.h` to
+    the source file `step-3.cc`.
+
+3.  Open the vtk output and visualize the solution in paraview or visit. 
+    Figure out how to warp the solution by the solution variable. Save a picture
+    of your visualization on the `figures` subdirectory, named `step-3-0.png`, 
+    and commit it to your repository.
+
+4.  Follow the instructions in “Modify the type of boundary condition”
+    in the description of the tutorial, plot your output, and save a figure in
+    the `figures`  subdirectory, named `step-3-1.png`, and commit it to your
+    repository. Make sure the test is run through `gtest`.
+
+5.  Now also do “A slight variation of the last point” but use the value
+    -0.5 for the boundary with indicator 1. Save your output as `step-3-2.png`, 
+    and commit it to the `figures` directory in your repository. Make sure the
+    test is run through `gtest`.
+
+6.  Change the setup to have $f=0$. Save your output as `step-3-3.png`, 
+    and commit it to the `figures` directory in your repository. Make sure the
+    test is run through `gtest`.
+
+7.  Switch to an L-shaped domain and experiment with a combination of
+    Dirichlet and Neumann boundary conditions. By experimentation, identify
+    the faces adjacent to the re-entrant corner and apply Dirichlet conditions
+    only there. Save your output as `step-3-4.png`, 
+    and commit it to the `figures` directory in your repository. Make sure the
+    test is run through `gtest`.
+
+8.  Bonus: Do “Convergence of the mean”. Can you see the order $h^2$?
+    Increase the polynomial order (you need to increase all orders of
+    the quadratures in the program!) and check the convergence of the
+    mean now. Make sure the test is run through `gtest`.
+
+### ParameterHandler
+
+1.  Follow the documentation of the class `ParameterAcceptor` 
+    (from "A typical usage of this class"). Derive your `Step3` class from 
+    `ParameterAcceptor`, and initialize the `ParameterAcceptor` class using 
+    the string `"Step3"`. Add a function that initializes the class given a 
+    parameter file name, i.e., `initialize("parameters.prm")`, by calling 
+    `ParameterAcceptor::initialize(...)`
+    
+2.  Add the following parameters to your `Step3` class, and make sure they 
+    are used throughout your code
+
+      - Finite element degree
+      - Number of global refinements
+      - Output filename
+
+    Notice that the `FE_Q` class will need to be built *after* the 
+    initialization of the Finite element degree variable. You can create
+    it right before you use it, and then reference to it by 
+    `DoFHandler::get_fe()` when you need it later.
+
+3.  Add two `FunctionParser<2>` members to your `Step3` class, one for the 
+    boundary conditions, and one for the forcing term. Add two `std::string` 
+    members, representing their mathematical expressions, and a 
+    `std::map<std::string, double>` representing the constants to use in your
+    mathematical expression, and make sure they are added as parameters of your 
+    class as
+    
+      - Forcing term expression
+      - Boundary condition expression
+      - Problem constants
+    
+    and initialize the two `FunctionParser<2>` objects with the given 
+    expressions and the given constants. Make sure your `Step3` class uses 
+    these two functions where the boundary conditions are computed and where
+    the right hand side is assembled
+
+4.  Following the ideas in `step-70`, add two additional parameters to the 
+    `Step3` class to select at run time what grid to create, and with what 
+    arguments. Use as parameters
+
+      - Grid generator function
+      - Grid generator arguments
+
+5.  Test your application with all the files in the `parameters` subdirectory,
+    (running the test through the `gtest` application), and create a 
+    visualization for each of the given parameters, with the same
+    name of the parameter file, i.e., the visualization of the test that runs
+    `parameters/hyper_shell.prm` should be saved on an image named `figures/hyper_shell.png`. Commits all your generated figures.
+    Notice that for older versions of google test, you may need to run each
+    test individually (this is a known issue between google testsuite and the
+    `ParameterAcceptor` class). To run an individual test, you can use the 
+    `--gtest_filter` command line option, i.e., the following command
+
+    ```
+    ./gtest --gtest_filter=Step3Tester.HyperShell
+    ```
+
+    will run only the test `Step3Tester.HyperShell`.
+
+    If you want to run all tests one after the other you can call the `ctest` 
+    utility, which will execute the `gtest` command passing the gtest filter for
+    each of the tests you provided, producing, for example, an output similar 
+    to:
+
+    ```
+    dealii@66c3be678611:/workspace/sissa-mhpc-lab-03/build-container$ ctest
+    Test project /workspace/sissa-mhpc-lab-03/build-container
+        Start 1: Step3Tester.MakeGrid
+    1/6 Test #1: Step3Tester.MakeGrid .............   Passed    0.68 sec
+        Start 2: Step3Tester.HyperCube
+    2/6 Test #2: Step3Tester.HyperCube ............   Passed    0.78 sec
+        Start 3: Step3Tester.HyperShell
+    3/6 Test #3: Step3Tester.HyperShell ...........   Passed    1.90 sec
+        Start 4: Step3Tester.HyperBall
+    4/6 Test #4: Step3Tester.HyperBall ............   Passed    1.28 sec
+        Start 5: Step3Tester.SinRhs
+    5/6 Test #5: Step3Tester.SinRhs ...............   Passed    0.79 sec
+        Start 6: Step3Tester.SinBc
+    6/6 Test #6: Step3Tester.SinBc ................   Passed    1.26 sec
+    
+    100% tests passed, 0 tests failed out of 6
+    ```

labs/lab-03/include/step-3.h

@@ -0,0 +1,85 @@
+/* ---------------------------------------------------------------------
+ *
+ * Copyright (C) 1999 - 2020 by the deal.II authors
+ *
+ * This file is part of the deal.II library.
+ *
+ * The deal.II library is free software; you can use it, redistribute
+ * it, and/or modify it under the terms of the GNU Lesser General
+ * Public License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ * The full text of the license can be found in the file LICENSE.md at
+ * the top level directory of deal.II.
+ *
+ * ---------------------------------------------------------------------
+ *
+ * Authors: Wolfgang Bangerth, 1999,
+ *          Guido Kanschat, 2011
+ *          Luca Heltai, 2021
+ */
+
+// Make sure we don't redefine things
+#ifndef step3_include_file
+#define step3_include_file
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+#include <iostream>
+
+// Forward declare the tester class
+class Step3Tester;
+
+using namespace dealii;
+class Step3
+{
+public:
+  Step3();
+  void
+  run();
+
+protected:
+  void
+  make_grid();
+  void
+  setup_system();
+  void
+  assemble_system();
+  void
+  solve();
+  void
+  output_results() const;
+
+  Triangulation<2>     triangulation;
+  FE_Q<2>              fe;
+  DoFHandler<2>        dof_handler;
+  SparsityPattern      sparsity_pattern;
+  SparseMatrix<double> system_matrix;
+  Vector<double>       solution;
+  Vector<double>       system_rhs;
+
+  friend class Step3Tester;
+};
+
+#endif

labs/lab-03/parameters/hyper_ball.prm

@@ -0,0 +1,14 @@
+# Listing of Parameters
+# ---------------------
+subsection Step3
+  set Boundary condition expression = 0
+  set Finite element degree         = 1
+  set Forcing term expression       = 1
+  set Grid generator arguments      = 0,0: 1: false
+  set Grid generator function       = hyper_ball
+  set Number of global refinements  = 4
+  set Output filename               = hyper_ball.vtk
+  set Problem constants             = 
+end
+
+

labs/lab-03/parameters/hyper_cube.prm

@@ -0,0 +1,14 @@
+# Listing of Parameters
+# ---------------------
+subsection Step3
+  set Boundary condition expression = 0
+  set Finite element degree         = 1
+  set Forcing term expression       = 1
+  set Grid generator arguments      = 0: 1: false
+  set Grid generator function       = hyper_cube
+  set Number of global refinements  = 4
+  set Output filename               = hyper_cube.vtk
+  set Problem constants             = 
+end
+
+

labs/lab-03/parameters/hyper_shell.prm

@@ -0,0 +1,14 @@
+# Listing of Parameters
+# ---------------------
+subsection Step3
+  set Boundary condition expression = 0
+  set Finite element degree         = 1
+  set Forcing term expression       = 1
+  set Grid generator arguments      = 0,0: .5: 1.: 0: false
+  set Grid generator function       = hyper_shell
+  set Number of global refinements  = 4
+  set Output filename               = hyper_shell.vtk
+  set Problem constants             = 
+end
+
+

labs/lab-03/parameters/sin_bc.prm

@@ -0,0 +1,14 @@
+# Listing of Parameters
+# ---------------------
+subsection Step3
+  set Boundary condition expression = sin(omega*pi*x)*sin(omega*pi*y)
+  set Finite element degree         = 1
+  set Forcing term expression       = 0
+  set Grid generator arguments      = 0,0: 1: false
+  set Grid generator function       = hyper_ball
+  set Number of global refinements  = 4
+  set Output filename               = sin_bc.vtk
+  set Problem constants             = pi:3.141592653589793, omega:2
+end
+
+