deal.II laboratories

This section documents the C++/deal.II laboratory infrastructure used in the course for finite element experiments on PDE-constrained optimal control problems.

The source tree lives in codes/dealii. It is organized as a course testbench: a small, inspectable code base that students can compile, modify, test, and extend during the laboratories.

Purpose¶

The deal.II laboratory track complements the Python notebooks in jupyterbook/codes.

• The notebooks are used for fast experimentation and visualization.

• The deal.II code is used for realistic finite element implementations.

• The goal is to let students move from reduced models to research-style PDE control prototypes.

Testbench structure¶

The directory is meant to contain:

• reference finite element applications for state, adjoint, and coupled optimality systems;

• a CMake build system with dimension-dependent executables;

• regression tests in deal.II style under codes/dealii/tests;

• unit tests under codes/dealii/gtests;

• a Doxygen configuration under codes/dealii/doc.

Planned evolution¶

The testbench hosts laboratories on:

• distributed control of elliptic equations;

• state, adjoint, and gradient assembly;

• reduced cost functionals and optimization loops;

• box constraints and active-set ideas;

• solver design, preconditioning, and performance comparisons;

• verification with tests that are simple enough to be read and modified by students.

Working model for the laboratories¶

Students should be able to:

1. configure and compile the code;

2. run a reference state or optimality-system problem;

3. inspect the finite element assembly;

4. extend the code to include controls, constraints, and optimization algorithms;

5. validate changes through tests and documented experiments.

Repository guide¶

For a directory-level overview and build instructions, see codes/dealii/README.md.

The generated API documentation is available in the companion page API reference.