mtnlion.variable module

Variables are used to define the relationship between trial functions, in both time and approximations, to test functions and the mapping between both functions and their FEniCS subdomain mapping.

exception mtnlion.variable.SingleDomainError

Bases: Exception

This exception is raised when the number of domains should have been reduced to one for the operation.

class mtnlion.variable.UVMap

Bases: tuple

Mapping between the trial functions (u), test functions (v), and the mapping of elements to the trial functions.

Trial functions are represented as a list of functions in time. Each element of the list is a dictionary of the applicable domains containing a list of related functions. Test functions are not effected by time stepping schemes, so there is no need to provide a list in time. Similarly, the element types are not allowed to change with each step in time.

element_map

Alias for field number 2

test_function

Alias for field number 1

trial_function

Alias for field number 0

class mtnlion.variable.UVMapSingleDomain

Bases: tuple

Mapping between the trial functions (u), test functions (v), and the mapping of elements to the trial functions restricted to a single domain.

Trial functions are represented as a list of functions in time. Each element of the list is a list of related functions. Test functions are not effected by time stepping schemes, so there is no need to provide a list in time. Similarly, the element types are not allowed to change with each step in time.

element_map

Alias for field number 2

test_function

Alias for field number 1

trial_function

Alias for field number 0

class mtnlion.variable.UndefinedDomain(domain: str)

Bases: object

Used to represent objects with an undefined domain.

class mtnlion.variable.Variable(name: str, domains: Iterable[str], num_functions: int = 1)

Bases: object

This class allows the partial definition of trial functions and test functions allowing them to be defined and used before the relationships in time, function approximations, and element mappings are defined.

Variable’s are able to then define the relationships in formulations without worrying about the specifics of

time discretization schemes or function approximations.

get_domain(domain: str) → mtnlion.variable.Variable

Retrieve a Variable object defined only on the given domain using UVMapSingleDomain.

Parameters

domain – Domain to restrict the variable to

Returns

Variable defined on a single domain

is_defined

Indicates whether or not the variable has been defined by checking the uv map element map.

Returns

true if the elements have been defined

test(subfunction: int = 0, all_funcs: bool = False) → Union[List[Optional[ufl.indexed.Indexed]], ufl.indexed.Indexed, None]

Retrieve the test function for this Variable.

If no constraints are applied, the entire test function will be returned.

Parameters

• subfunction – Index of the desired subfunction

• all_funcs – return all subfunctions

Returns

Desired test function

trial(history: Optional[int] = None, subfunction: int = 0, all_funcs: bool = False) → Union[ufl.indexed.Indexed, None, List[Union[ufl.indexed.Indexed, mtnlion.variable.UndefinedDomain]], List[List[Union[ufl.indexed.Indexed, mtnlion.variable.UndefinedDomain]]]]

Retrieve the trial function for this Variable.

History and subfunction constraints may be applied simultaneously. If no constraints are applied, the entire trial function will be returned.

Parameters

• history – Index in time to retrieve the trial function, 0 represents the current time, one is the previous time step, etc.

• subfunction – Index of the desired subfunction

• all_funcs – return all subfunctions

Returns

Desired trial function

mtnlion.variable.check_single(func: Callable) → Callable

Used to wrap operations of Variable in order to allow variables to be used as parameters in formulas.

Parameters

func – operation to wrap

Returns

wrapped function