Problem Class¶

The problem definitions in TTiP are designed to be extensible, this is done through multiple inheritance and mixin classes.

The two main parts to a problem class in TTiP are the base class and the mixins.

Base Class¶

The base class (found in core/problem.py) defines a set of methods that create, set (replace), and bound firedrake functions. It also defines a set of functions such as the flux and ionisation terms which are used in multiple mixins.

The formula that the problem defines is given by:

$a - L = 0$

$a$ is the sum of terms containing both $T$ and $v$ , whereas $L$ does not contain $T$ explicitly (some parameters can be dependant on temperature).

Mixins¶

The mixins are fundamental to creating a sensible problem.

A variety of mixins can be found in the problem_mixins directory.

Mixins are used to add functionality such as time dependancies, flux limits, specific conductivity formulations, and many others.

The key concept of a mixin for the problem class is that it should edit the existing variables rather than replacing them, either by adding terms or by using the set_function method from the parent class (which will be available at runtime as the mixin will only ever be used with the base problem class). Some examples of this are the time dependancy mixin which adds a term to the a attribute, and the conductivity limiter which imposes bounds on the existing conductivity.

Usage¶

Some examples of how to define new problem classes can be seen at the bottom of the core/problem.py file as well as a utility function to dynamically create new problem classes.

Extending¶

To add new functionality to the problem class, define a new mixin (using the template in problem_mixins) this can then be used in any custom scripts. To make the new mixin more accessible, it should be added to the create_problem_class method in the problem file.