optymus.benchmark.TopologicalDomain

class optymus.benchmark.TopologicalDomain(name, domain_bounding_box, signed_distance_function, domain_boundary_conditions=None, domain_fixed_points=[])

Represents a mathematically defined domain for polygonal mesh.

This class defines a mathematically defined domain based on its name, bounding box, signed distance function (signed_distance_function), boundary conditions (domain_boundary_conditions), and fixed points (domain_fixed_points).

name

The name of the mathematically defined domain.

Type:

str

domain_bounding_box

The bounding box of the domain, defined as [xmin, xmax, ymin, ymax].

Type:

list

signed_distance_function

The signed distance function that provides the distance values.

Type:

callable

domain_boundary_conditions

The function for setting boundary conditions. Default is None.

Type:

callable, optional

domain_fixed_points

List of fixed points within the domain. Default is an empty list.

Type:

list, optional

signed_distance(P)

Computes the distance value for a point P using the signed distance function.

boundary_conditions(Node)

Determines the boundary conditions for a given node within the domain.

compute_area(n=1_000_000)

Calculates the approximate area of the domain using the Monte Carlo method

__init__(name, domain_bounding_box, signed_distance_function, domain_boundary_conditions=None, domain_fixed_points=[])

Initializes a Domain object with the provided attributes.

Parameters:

• name (str) – The name of the computational domain.

• domain_bounding_box (list) – The bounding box of the domain, defined as [xmin, xmax, ymin, ymax].

• signed_distance_function (callable) – The signed distance function that provides the distance values.

• domain_boundary_conditions (callable, optional) – The function for setting boundary conditions. Default is None.

• domain_fixed_points (list, optional) – List of fixed points within the domain. Default is an empty list.

Methods

__init__(name, domain_bounding_box, ...[, ...])	Initializes a Domain object with the provided attributes.
boundary_conditions(Node)	Determines the boundary conditions for a given node within the domain.
compute_area([n])	Calculates the approximate area of the domain using the Monte Carlo method.
signed_distance(P)	Computes the distance value for a point P using the signed distance function.

boundary_conditions(Node)

Determines the boundary conditions for a given node within the domain.

Parameters:

Node (tuple) – The coordinates of a node (x, y).

Returns:

A list containing boundary conditions for the node. It may include None values.

Return type:

list

compute_area(n=1000000)

Calculates the approximate area of the domain using the Monte Carlo method.

Parameters:

n (int, optional) – The number of random points to use. Default is 1,000,000.

Returns:

The calculated approximate area of the domain.

Return type:

float

signed_distance(P)

Computes the distance value for a point P using the signed distance function.

Parameters:

P (numpy.ndarray) – A point or an array of points for which the distance is to be calculated.

Returns:

An array of distance values corresponding to the input points.

Return type:

numpy.ndarray