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tutorial.h.in
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// ---------------------------------------------------------------------
//
// Copyright (C) 2005 - 2019 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.
//
// ---------------------------------------------------------------------
/**
* @page Tutorial Tutorial programs
*
* New to deal.II? You might want to start with tutorial Step-1 and work
* your way up to Step-5. At that point you can explore what features you
* are interested in and look at the large collection of programs listed
* below.
*
* The deal.II tutorial contains a collection of programs, each more or
* less built atop of previous ones, which demonstrate various aspects of
* the library. Each such example has the following structure:
* <ol>
* <li> <b>Introduction:</b> What the program does, including
* the mathematical model, and
* what programming techniques are new.
* <li> <b>The commented program:</b> An extensively documented listing of the
* source code.
* <li> <b>Results:</b> The output of the program, with comments and
* interpretation.
* <li> <b>The plain program:</b> The source code stripped of
* all comments.
* </ol>
* You can browse the available tutorial programs
* <ol>
* <li> as <b><a href="#graph">a graph</a></b> that shows how tutorial programs build upon each other.
* <li> as <b><a href="#list">a list</a></b> that provides a short
* synopsis of each program.
* <li> or <b><a href="#topic">grouped by topic</a></b>.
* </ol>
*
* The programs are in the <code>examples/</code> directory of your local
* deal.II installation. After compiling the library itself, if you go into
* one of the tutorial directories, you can configure the program by typing
* <code>cmake .</code>, build it via <code>make</code> and run it using
* <code>make run</code>. The latter command also compiles the program if
* that has not already been done. The CMakeLists.txt files in the
* different directories are based on the
* <a href="../../users/cmakelists.html#cmakeauto" target="_top">autopilot
* style CMakeLists.txt example</a>.
*
* @note Some of the tutorial programs also jointly form
* the <a href="../../doxygen/deal.II/group__geodynamics.html">geodynamics
* demonstration suite</a>. More, often more complex but less well documented,
* deal.II-based programs than the ones that form the tutorial can also be
* found in the @ref CodeGallery .
*
*
* <a name="graph"></a>
* @anchor TutorialConnectionGraph
* <h3>Connections between tutorial programs</h3>
*
* The following graph shows the connections between tutorial programs and
* how they build on each other.
* Click on any of the boxes to go to one of the programs. If you hover
* your mouse pointer over a box, a brief description of the program
* should appear.
* @dot
@@TUTORIAL_MAP@@
* @enddot
*
* <b>Legend:</b><br />
* @dot
@@TUTORIAL_LEGEND@@
* @enddot
*
* <a name="list"></a>
* <h3>Tutorial programs listed by number</h3>
*
* <table align="center" width="90%">
* <tr valign="top">
* <td width="100px">step-1</td>
* <td> Creating a grid. A simple way to write it to a file.
* <br/> Keywords: Triangulation, GridGenerator::hyper_cube,
* GridGenerator::hyper_shell, GridOut,
* Triangulation::execute_coarsening_and_refinement
* </td></tr>
*
* <tr valign="top">
* <td>step-2</td>
* <td> Associate degrees of freedom to
* each vertex and compute the resulting sparsity pattern of
* matrices. Show that renumbering reduces the bandwidth of
* matrices significantly, i.e. clusters nonzero entries around the
* diagonal.
* <br/> Keywords: FE_Q, DynamicSparsityPattern,
* DoFTools::make_sparsity_pattern, DoFHandler::distribute_dofs,
* DoFRenumbering, SparsityPattern
* </td></tr>
*
* <tr valign="top">
* <td>step-3</td>
* <td> Actually solve Laplace's
* problem. Object-orientation. Assembling matrices and
* vectors. Boundary values.
* <br/> Keywords: FEValues, VectorTools::interpolate_boundary_values,
* MatrixTools::apply_boundary_values, SolverCG, Vector<double>,
* SparseMatrix<double>, DataOut
* </td></tr>
*
* <tr valign="top">
* <td>step-4</td>
* <td> This example is programmed in a
* way that it is independent of the dimension for which we want to
* solve Laplace's equation; we will solve the equation in 2D and
* 3D, although the program is exactly the same. Non-constant right
* hand side function. Non-homogeneous boundary values.
* <br/> Keywords: VectorTools::point_value,
* VectorTools::compute_mean_value
* </td></tr>
*
* <tr valign="top">
* <td>step-5</td>
* <td> Computations on successively
* refined grids. Reading a grid from disk. Some optimizations.
* Using assertions. Non-constant coefficient in
* the elliptic operator (yielding the extended Poisson
* equation). Preconditioning the CG solver for the
* linear system of equations.
* <br/> Keywords: PreconditionSSOR, GridIn, SphericalManifold
* </td></tr>
*
* <tr valign="top">
* <td>step-6</td>
* <td> Adaptive local
* refinement. Handling of hanging nodes. Higher order elements.
* Catching exceptions in the <code>main</code>; function.
* <br/> Keywords: DoFTools::make_hanging_node_constraints,
* AffineConstraints::distribute_local_to_global, KellyErrorEstimator,
* GridRefinement::refine_and_coarsen_fixed_number
* </td></tr>
*
* <tr valign="top">
* <td>step-7</td>
* <td> Helmholtz
* equation. Non-homogeneous Neumann boundary conditions and
* boundary integrals. Verification of correctness of computed
* solutions. Computing the error between exact and numerical
* solution and output of the data in tables. Using counted pointers.
* <br/> Keywords: FEFaceValues, VectorTools::integrate_difference,
* VectorTools::compute_global_error, TableHandler
* </td></tr>
*
* <tr valign="top">
* <td>step-8</td>
* <td> The elasticity equations will be
* solved instead of Laplace's equation. The solution is
* vector-valued and the equations form a system with as many
* equations as the dimension of the space in which it is posed.
* <br/> Keywords: FESystem
* </td></tr>
*
* <tr valign="top">
* <td>step-9</td>
* <td> Linear advection equation, assembling
* the system of equations in parallel using multi-threading,
* implementing a refinement criterion based on a finite difference
* approximation of the gradient.
* <br/> Keywords: TensorFunction, WorkStream::run, SolverGMRES
* </td></tr>
*
* <tr valign="top">
* <td>step-10</td>
* <td> Higher order mappings. Do not
* solve equations, but rather compute the value of pi to high
* accuracy.
* </td></tr>
*
* <tr valign="top">
* <td>step-11</td>
* <td> Solving a Laplace problem with
* higher order mappings. Using mean value constraints and
* intermediate representations of sparsity patterns.
* </td></tr>
*
* <tr valign="top">
* <td>step-12</td>
* <td> Discontinuous Galerkin methods for linear advection problems.
* </td></tr>
*
* <tr valign="top">
* <td>step-13</td>
* <td> Software design questions and
* how to write a modular, extensible finite element program.
* </td></tr>
*
* <tr valign="top">
* <td>step-14</td>
* <td> Duality based error estimators,
* more strategies to write a modular, extensible finite element
* program.
* </td></tr>
*
* <tr valign="top">
* <td>step-15</td>
* <td> A nonlinear elliptic problem: The minimal surface equation.
* Newton's method. Transferring a solution across mesh refinement.
* </td></tr>
*
* <tr valign="top">
* <td>step-16</td>
* <td> Multigrid preconditioning of the Laplace equation on adaptive
* meshes.
* </td></tr>
*
* <tr valign="top">
* <td>step-16b</td>
* <td> A variant of step-16 but with MeshWorker for assembly: Multigrid
* preconditioning of the Laplace equation on adaptive meshes.
* </td></tr>
*
* <tr valign="top">
* <td>step-17</td>
* <td> Using PETSc for linear algebra; running
* in parallel on clusters of computers linked together by MPI.
* </td></tr>
*
* <tr valign="top">
* <td>step-18</td>
* <td> A time dependent problem; using a much
* simplified version of implementing elasticity; moving meshes; handling
* large scale output of parallel programs.
* </td></tr>
*
* <tr valign="top">
* <td>step-19</td>
* <td> Input parameter file handling. Merging
* output of a parallel program.
* </td></tr>
*
* <tr valign="top">
* <td>step-20</td>
* <td> Mixed finite elements. Using block
* matrices and block vectors to define more complicated solvers and
* preconditioners working on the Schur complement.
* </td></tr>
*
* <tr valign="top">
* <td>step-21</td>
* <td> The time dependent two-phase flow in
* porous media. Extensions of mixed Laplace discretizations. More
* complicated block solvers. Simple time stepping.
* </td></tr>
*
* <tr valign="top">
* <td>step-22</td>
* <td> Solving the Stokes equations of slow fluid flow on adaptive
* meshes. More on Schur complement solvers. Advanced use of the
* AffineConstraints class.
* </td></tr>
*
* <tr valign="top">
* <td>step-23</td>
* <td> Finally a "real" time dependent problem, the wave equation.
* </td></tr>
*
* <tr valign="top">
* <td>step-24</td>
* <td> A variant of step-23 with absorbing
* boundary conditions, and extracting practically useful data.
* </td></tr>
*
* <tr valign="top">
* <td>step-25</td>
* <td> The sine-Gordon
* soliton equation, which is a nonlinear variant of the time
* dependent wave equation covered in step-23 and step-24.
* </td></tr>
*
* <tr valign="top">
* <td>step-26</td>
* <td> The heat equation, solved on a mesh that is adapted
* every few time steps.
* </td></tr>
*
* <tr valign="top">
* <td>step-27</td>
* <td> The hp finite element method.
* </td></tr>
*
* <tr valign="top">
* <td>step-28</td>
* <td> Multiple grids for solving a multigroup diffusion equation
* in nuclear physics simulating a nuclear reactor core.
* </td></tr>
*
* <tr valign="top">
* <td>step-29</td>
* <td> Solving a complex-valued Helmholtz equation. Sparse direct
* solvers. Dealing with parameter files. </td></tr>
*
* <tr valign="top">
* <td>step-30</td>
* <td> Anisotropic refinement for DG finite element methods.
* </td></tr>
*
* <tr valign="top">
* <td>step-31</td>
* <td> Time-dependent Stokes flow driven by temperature
* differences in a fluid. Adaptive meshes that change between time
* steps.
* </td></tr>
*
* <tr valign="top">
* <td>step-32</td>
* <td> A massively parallel solver for time-dependent Stokes flow driven
* by temperature differences in a fluid. Adapting methods for real-world
* equations.
* </td></tr>
*
* <tr valign="top">
* <td>step-33</td>
* <td> A nonlinear hyperbolic conservation law: The Euler equations of
* compressible gas dynamics.
* </td></tr>
*
* <tr valign="top">
* <td>step-34</td>
* <td> Boundary element methods (BEM) of low order: Exterior irrotational
* flow. The ParsedFunction class.
* </td></tr>
*
* <tr valign="top">
* <td>step-35</td>
* <td> A projection solver for the Navier–Stokes equations.
* </td></tr>
*
* <tr valign="top">
* <td>step-36</td>
* <td> Using SLEPc for linear algebra; solving an eigenspectrum
* problem. The Schrödinger wave equation.
* </td></tr>
*
* <tr valign="top">
* <td>step-37</td>
* <td> Solving a Poisson problem with a multilevel preconditioner without
* explicitly storing the matrix (a matrix-free method) in a massively
* parallel context.
* </td></tr>
*
* <tr valign="top">
* <td>step-38</td>
* <td>Solving the Laplace-Beltrami equation on curved manifolds embedded
* in higher dimensional spaces.
* </td></tr>
*
* <tr valign="top">
* <td>step-39</td>
* <td> Solving Poisson's equation once more, this time with the
* interior penalty method, one of the discontinuous Galerkin
* methods developed for this problem. Error estimator, adaptive
* meshes, and multigrid preconditioner, all using the MeshWorker
* framework.
* </td></tr>
*
* <tr valign="top">
* <td>step-40</td>
* <td> Techniques for the massively parallel solution of the Laplace
* equation (up to 10,000s of processors).
* </td></tr>
*
* <tr valign="top">
* <td>step-41</td>
* <td> Solving the obstacle problem, a variational inequality.
* </td></tr>
*
* <tr valign="top">
* <td>step-42</td>
* <td> A solver for an elasto-plastic contact problem, running on
* parallel machines.
* </td></tr>
*
* <tr valign="top">
* <td>step-43</td>
* <td> Advanced techniques for the simulation of porous media flow.
* </td></tr>
*
* <tr valign="top">
* <td>step-44</td>
* <td> Finite strain hyperelasticity based on a three-field formulation.
* <br/> Keywords: CellDataStorage, FEValuesExtractors, WorkStream::run,
* BlockSparseMatrix, BlockVector, ComponentSelectFunction,
* Physics::Elasticity, FullMatrix::extract_submatrix_from,
* FullMatrix::scatter_matrix_to, LinearOperator, SolverSelector,
* PreconditionSelector, ReductionControl, MappingQEulerian
* </td></tr>
*
* <tr valign="top">
* <td>step-45</td>
* <td> Periodic boundary conditions.
* </td></tr>
*
* <tr valign="top">
* <td>step-46</td>
* <td> Coupling different kinds of equations in different parts of the domain.
* </td></tr>
*
* <tr valign="top">
* <td>step-48</td>
* <td> Explicit time stepping for the Sine–Gordon equation based on
* a diagonal mass matrix. Efficient implementation of (nonlinear) finite
* element operators.
* </td></tr>
*
* <tr valign="top">
* <td>step-49</td>
* <td> Advanced mesh creation and manipulation techniques.
* </td></tr>
*
* <tr valign="top">
* <td>step-51</td>
* <td> Solving the convection-diffusion equation with a hybridizable
* discontinuous Galerkin method using face elements.
* </td></tr>
*
* <tr valign="top">
* <td>step-52</td>
* <td> Solving the time dependent neutron diffusion equation using
* Runge-Kutta methods.
* </td></tr>
*
* <tr valign="top">
* <td>step-53</td>
* <td> Describing the geometry of complex domains and curved boundaries.
* </td></tr>
*
* <tr valign="top">
* <td>step-54</td>
* <td> Using CAD files to describe the boundary of your domain.
* </td></tr>
*
* <tr valign="top">
* <td>step-55</td>
* <td> Solving the Stokes problem in parallel.
* </td></tr>
*
* <tr valign="top">
* <td>step-56</td>
* <td> Geometric Multigrid for Stokes.
* </td></tr>
*
* <tr valign="top">
* <td>step-57</td>
* <td> Incompressible, stationary Navier Stokes equations.
* </td></tr>
*
* <tr valign="top">
* <td>step-59</td>
* <td> Solving a Poisson problem discretized with an interior penalty DG
* method and a multilevel preconditioner in a matrix-free fashion using
* a massively parallel implementation.
* </td></tr>
*
* <tr valign="top">
* <td>step-60</td>
* <td> Distributed Lagrange multipliers for the solution of
* Poisson problems in complex domains with constraints defined
* on non-matching grids.
* </td></tr>
*
* <tr valign="top">
* <td>step-61</td>
* <td> Solving the Poisson problem with the "weak Galerkin" finite element
* method.
* </td></tr>
*
* <tr valign="top">
* <td>step-62</td>
* <td> Resonance frequency and bandgap of a phononic crystal. Elastic
* wave equation in the frequency domain with Perfectly Matched Layer
* boundary conditions. Parallelization via MUMPS and MPI.
* </td></tr>
*
* <tr valign="top">
* <td>step-63</td>
* <td>Block smoothers for geometric multigrid. A scalar convection
* diffusion equation is solved with different additive or
* multiplicative multigrid smoothers.
* </td></tr>
*
* <tr valign="top">
* <td>step-64</td>
* <td> Solving a Helmholtz problem using matrix-free methods on the GPU
* with MPI parallelization.
* </td></tr>
*
* </table>
*
* <a name="topic"></a>
* <h3>Tutorial programs grouped by topics</h3>
*
* <h4><b>Basic techniques</b></h4>
* <table align="center" width="90%">
*
* <tr valign="top">
* <td width="400px"> Creating a grid. A simple way to write it to a file
* <td>step-1</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Degrees of freedom
* <td>step-2</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Solve the Laplace equation
* <td>step-3</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Dimension independent programming, non-zero data
* <td>step-4</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Computing on uniformly refined meshes
* <td>step-5</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Adaptivity
* <td>step-6, step-26</td>
* </td>
* </tr>
*
* <tr valign="top">
* <td> Evaluating errors
* <td>step-7</td>
* </td>
*
* <tr valign="top">
* <td> Nonlinear problems, Newton's method
* </td>
* <td>step-15</td>
* </tr>
*
* </table>
* <h4><b>Advanced techniques</b></h4>
* <table align="center" width="90%">
*
* <tr valign="top">
* <td width="400px"> Multithreading
* </td>
* <td>
* step-9,
* step-28,
* step-32,
* step-44,
* step-48,
* step-51
* </td>
* </tr>
*
* <tr valign="top">
* <td> Block solvers and preconditioners
* </td>
* <td>
* step-20,
* step-21,
* step-22,
* step-31,
* step-32,
* step-43,
* step-44,
* step-55,
* step-56,
* step-57
* </td>
* </tr>
*
* <tr valign="top">
* <td> Using Trilinos
* </td>
* <td>
* step-31,
* step-32,
* step-33,
* step-41,
* step-42,
* step-43,
* step-55
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallelization via PETSc and MPI
* </td>
* <td>
* step-17,
* step-18,
* step-19,
* step-40,
* step-55
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallelization via Trilinos and MPI
* </td>
* <td>
* step-32,
* step-42,
* step-55
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallelization via MUMPS and MPI
* </td>
* <td>
* step-62
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallelization via CUDA and MPI
* </td>
* <td>
* step-64
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallelization on very large numbers of processors
* </td>
* <td>
* step-32,
* step-37,
* step-40,
* step-42,
* step-55,
* step-59
* </td>
* </tr>
*
* <tr valign="top">
* <td> Input parameter handling
* </td>
* <td>
* step-19,
* step-28,
* step-29,
* step-32,
* step-33,
* step-34,
* step-35,
* step-36,
* step-42,
* step-44,
* step-60,
* step-62
* </td>
* </tr>
*
* <tr valign="top">
* <td> Higher order mappings
* </td>
* <td>
* step-10,
* step-11,
* step-32,
* step-60
* </td>
* </tr>
*
* <tr valign="top">
* <td> Error indicators and estimators
* </td>
* <td>
* step-6,
* step-9,
* step-14,
* step-39
* </td>
* </tr>
*
* <tr valign="top">
* <td> Transferring solutions across mesh refinement
* </td>
* <td>
* step-15,
* step-28,
* step-31,
* step-32,
* step-33,
* step-42,
* step-43,
* step-57
* </td>
* </tr>
*
* <tr valign="top">
* <td> Discontinuous Galerkin methods
* </td>
* <td>
* step-12,
* step-21,
* step-39,
* step-46,
* step-51,
* step-59,
* step-61
* </td>
* </tr>
*
* <tr valign="top">
* <td> hp finite elements
* </td>
* <td>
* step-27,
* step-46
* </td>
* </tr>
*
* <tr valign="top">
* <td> Anisotropic refinement for DG finite element methods
* </td>
* <td>step-30</td>
* </tr>
*
* <tr valign="top">
* <td> Computing Jacobians from residuals, automatic differentiation
* </td>
* <td>step-33</td>
* </tr>
*
* <tr valign="top">
* <td> Boundary element methods, curved manifolds
* </td>
* <td>
* step-32,
* step-34,
* step-38,
* step-53,
* step-54
* </td>
* </tr>
*
* <tr valign="top">
* <td> Periodic boundary conditions
* </td>
* <td>
* step-45,
* step-59
* </td>
* </tr>
*
* <tr valign="top">
* <td> Matrix-free methods with sum factorization
* </td>
* <td>
* step-37,
* step-48,
* step-59
* </td>
* </tr>
*
* <tr valign="top">
* <td> Advanced meshes and geometries
* </td>
* <td>
* step-49,
* step-53,
* step-54
* </td>
* </tr>
*
* <tr valign="top">
* <td> Non matching algorithms
* </td>
* <td>
* step-60
* </td>
* </tr>
*
* <tr valign="top">
* <td> HDF5 and Python
* </td>
* <td>
* step-62
* </td>
* </tr>
*
* </table>
* <h4><b>Linear solvers</b></h4>
* <table align="center" width="90%">
*
* <tr valign="top">
* <td width="400px"> Conjugate Gradient solver
* </td>
* <td>step-3</td>
* </tr>
*
* <tr valign="top">
* <td> Preconditioned CG solver
* </td>
* <td>step-5</td>
* </tr>
*
* <tr valign="top">
* <td> BiCGStab
* </td>
* <td>step-9</td>
* </tr>
*
* <tr valign="top">
* <td> Multilevel preconditioners
* </td>
* <td>
* step-16,
* step-16b
* step-31,
* step-32,
* step-37,
* step-39,
* step-41,
* step-42,
* step-43,
* step-56,
* step-59,
* step-63
* </td>
* </tr>
*
* <tr valign="top">
* <td> Parallel solvers
* </td>
* <td>
* step-17,
* step-18,
* step-32,
* step-37,
* step-40,
* step-42,
* step-55,
* step-59
* </td>
* </tr>
*
* <tr valign="top">
* <td> Block and Schur complement solvers
* </td>
* <td>
* step-20,
* step-21,
* step-22,
* step-31,
* step-32,
* step-43,
* step-55,
* step-56,
* step-57,
* step-60
* </td>
* </tr>
*
* <tr valign="top">
* <td> Decoupled projection solvers
* </td>
* <td>step-35</td>
* </tr>
*
* <tr valign="top">
* <td> Linear Newton systems from nonlinear equations
* </td>
* <td>
* step-33,
* step-41,
* step-42,
* step-44,
* step-57
* </td>
* </tr>
*
* <tr valign="top">
* <td> Eigenvalue solvers
* </td>
* <td>step-36</td>
* </tr>
*
* <tr valign="top">
* <td> Linear operators
* </td>
* <td>
* step-44,
* step-60
* </td>
* </tr>
*
* </table>
* <h4><b>Other equations</b></h4>
* <table align="center" width="90%">
*
* <tr valign="top">
* <td width="400px"> Helmholtz equation
* </td>
* <td>
* step-7,
* step-29,
* step-62,
* step-64
* </td>
* </tr>
*
* <tr valign="top">
* <td> Elasticity and elasto-plasticity equations
* </td>
* <td>
* step-8,
* step-42,
* step-46,
* step-62
* </td>
* </tr>
*
* <tr valign="top">
* <td> The heat equation
* </td>
* <td>
* step-26
* </td>
* </tr>
*
* <tr valign="top">
* <td> Minimal surface equation
* </td>
* <td>
* step-15
* </td>
* </tr>
*
* <tr valign="top">
* <td> Quasi-static elasticity equations
* </td>
* <td>
* step-18,
* step-44
* </td>
* </tr>
*
* <tr valign="top">
* <td> Transport (advection) equations
* </td>
* <td>step-9,
* step-21,
* step-31,
* step-32,
* step-43,
* step-51
* </td>
* </tr>
*
* <tr valign="top">
* <td> The nonlinear hyperbolic Euler system of compressible gas dynamics
* </td>
* <td>step-33</td>
* </tr>
*
* <tr valign="top">
* <td> Mixed Laplace, Darcy, Porous media
* </td>
* <td>
* step-20,
* step-21,
* step-43
* </td>
* </tr>
*
* <tr valign="top">
* <td> Stokes and incompressible Navier-Stokes flow
* </td>
* <td>
* step-22,
* step-31,
* step-32,
* step-35,
* step-46,
* step-55,
* step-56,
* step-57