scimba_torch.domain.mesh_based_domain.cuboid

Defines the Cuboid domain and its components.

Classes

Cuboid(bounds[, is_main_domain])

Cuboid domain in n dimensions.

class Cuboid(bounds, is_main_domain=True, **kwargs)

Bases: object

Cuboid domain in n dimensions.

At the moment, boundaries, inclusions and holes are not supported.

Parameters:

• bounds (list[tuple[float, float]]) – The bounds of the cuboid.

• is_main_domain (bool) – Whether the domain is the main domain or not.

• **kwargs (Any) – Additional arguments.

Examples

1D Cuboid

import torch
from scimba_torch.domain.meshless_domain.domain_1d import Segment1D
from scimba_torch.domain.mesh_based_domain.cuboid import Cuboid

n = 10

domain_1d = Cuboid([(0, 1)], is_main_domain=True)
mesh_1d = domain_1d.uniform_mesh(n)
assert mesh_1d.shape == (n, 1)

V_domain_1d = domain_1d.to_volumetric_domain()
assert isinstance(V_domain_1d, Segment1D)
assert torch.all(domain_1d.bounds == V_domain_1d.bounds)

2D Cuboid

import torch
from scimba_torch.domain.meshless_domain.domain_2d import Square2D
from scimba_torch.domain.mesh_based_domain.cuboid import Cuboid

n, n_2 = 10, 5

domain_2d = Cuboid([(0, 1), (-1, 2)], is_main_domain=True)
mesh_2d = domain_2d.uniform_mesh(n**2)
assert mesh_2d.shape == (n**2, 2)

V_domain_2d = domain_2d.to_volumetric_domain()
assert isinstance(V_domain_2d, Square2D)
assert torch.all(domain_2d.bounds == V_domain_2d.bounds)

domain_2d = Cuboid([(0, 1), (-1, 2)], is_main_domain=True)
mesh_2d = domain_2d.uniform_mesh((n, n_2))
assert mesh_2d.shape == (n * n_2, 2)

3D Cuboid

import torch
from scimba_torch.domain.meshless_domain.domain_3d import Cube3D
from scimba_torch.domain.mesh_based_domain.cuboid import Cuboid

n, n_2, n_3 = 10, 5, 3

domain_3d = Cuboid([(0, 1), (-1, 2), (-10, 10)], is_main_domain=True)
mesh_3d = domain_3d.uniform_mesh(n**3)
assert mesh_3d.shape == (n**3, 3)

domain_3d = Cuboid([(0, 1), (-1, 2), (-10, 10)], is_main_domain=True)
mesh_3d = domain_3d.uniform_mesh((n, n_2, n_3))
assert mesh_3d.shape == (n * n_2 * n_3, 3)

V_domain_3d = domain_3d.to_volumetric_domain()
assert isinstance(V_domain_3d, Cube3D)
assert torch.all(domain_3d.bounds == V_domain_3d.bounds)

uniform_mesh(n, **kwargs)

Uniformly meshes the domain.

Parameters:

• n (int | list | tuple) – Total number of mesh points. If the same number of points is used in each dimension, equal to n ** (1 / dim). If list or tuple, the number of points in each dimension.

• **kwargs (Any) – Additional arguments.

Return type:

LabelTensor

Returns:

The mesh points.

flatten_mesh(mesh, mesh_size)

Flattens a mesh.

Parameters:

• mesh (tuple[Tensor, ...]) – The mesh.

• mesh_size (int) – The size of the mesh.

Return type:

Tensor

Returns:

The flattened mesh.

to_volumetric_domain()

Converts the cuboid to a volumetric domain.

Return type:

VolumetricDomain

Returns:

The volumetric domain.

Raises:

NotImplementedError – If the dimension is not supported.