This tutorial covers some simple but common examples for discretizing PDEs and pre-/post processing the discrete data on a grid.

  1. Grids and Discrete Functions: Learn how to define a grid as a discretization of the domain and a discrete function of that grid. How to tranverse the grid elements and assign data to the discrete functions.

  2. Working with the Problem class: Create a problem class as a container for the grid, basis, solution vector and linear system and many more. What can a problem class do for your workflow.

  3. Backup and Restore Write intermediate states of your lengthy conmputations to file and resume the simulation from a backup file.

  4. Operators: Define your PDE in terms of operator terms. Learn how to add operators to a problem and how to define your own operators.

  5. Block Matrices and Vectors Use block matrices and vectors instead of the default flat versions.

  6. Boundary Conditions: Select parts of the grid boundary and assign boundary conditions or boundary operators. Learn how to specify the boundary parts and how to set different types of boundary conditions, like Dirichlet or periodic conditions, or Neumann/Robin-type boundary integrals.

  7. Linear Solvers: Control the solution of the assembled linear system, which linear solver to use and which preconditioner. How to control solver parameters and how to add an own linear solver.

  8. Adaptivity and Grid Refinement: Grid adaptivity needs control of marking and refinement strategies. Learn how to define and add a marker to the problem, learn about interpolation during grid adaptivity and how to load balance your grid.

  9. FileWriters: Output and backup/restore of data is an important topic for simulations and for postprocessing. Different Writers are introduced and the configuration and control of these writers discussed.