scimba_torch.domain.meshless_domain.base¶

Base module for meshless domains.

Classes

`SurfacicDomain`(domain_type, ...)	Base class for representing the boundary of a domain.
`VolumetricDomain`(domain_type, dim, sdf, bounds)	Base class for the volumetric meshless domains.

class VolumetricDomain(domain_type, dim, sdf, bounds, is_main_domain=False)[source]¶

Bases: object

Base class for the volumetric meshless domains.

\[\Omega = \{ x \in \text{bounds} \subset \mathbb{R}^n \, | \, \text{sdf}(x) < - \text{sdf.threshold} \}\]

Note

Mapped domain is only allowed on the main domain.
You should only call the domain.set_mapping once on the main domain (it will be applied to all subdomains and bc_domain).
For holes, if you want them unmapped you should use copy_mapping=False when adding the hole.
If some holes are already added, you can specified to_holes=False when setting the mapping to the main domain, it wont be applied to any of the holes already added.
The best pratices is to create the main domain, set the mapping if any, then add subdomains/holes/boundary domains.
If you want to change the mapping, it will be applied only to the holes that were mapped if you pass to_holes=False.
So basically a hole will always have the main domain mapping or never be mapped

Parameters:

domain_type (str) – Type of the domain.
dim (int) – Dimension of the domain.
sdf (SignedDistance) – Signed distance function that defines the domain.
bounds (list[tuple[float, float]] | Tensor) – Tensor of shape (dim, 2) representing an hypercube that contains the domain.
is_main_domain (bool) – A flag to indicate if the domain can have subdomains and holes.

domain_type: str¶: Type of the domain.

dim: int¶: Dimension of the domain (before mapping).

list_bc_domains: list[SurfacicDomain]¶: The list of boundary domains specified by the user.

is_mapped: bool¶: Flag to indicate if the domain is mapped.

dim_postmap: int¶: The dimension of the domain (after mapping).

mapping: None | Mapping¶: The mapping of the domain (if any).

bounds_postmap: Tensor¶: Tensor of shape (dim_postmap, 2) representing a box that contains the domain (after mapping).

is_main_domain: bool¶: A flag to indicate if the domain can have subdomains and holes.

list_subdomains: list[VolumetricDomain]¶: A list of subdomains that are inside the main domain (ONLY IF is_main_domain is True).

list_holes: list[VolumetricDomain]¶: A list of holes that are inside the main domain (ONLY IF is_main_domain is True).

is_inside(x)[source]¶

Test if N points x are inside the domain (before mapping if any).

Parameters:: x (Tensor) – Tensor of shape (N, dim) representing the points to test.
Return type:: Tensor
Returns:: Boolean tensor of shape (N,) indicating if the points are inside the domain.

is_outside(x)[source]¶

Test if N points x are outside the domain (before mapping if any).

Parameters:

x (Tensor) – Tensor of shape (N, dim) representing the points to test.

Return type:

Tensor

Returns:

Boolean tensor of shape (N,) indicating if the points are outside: the domain.

is_outside_np(x)[source]¶

Test if N points x are outside the domain (before mapping if any).

Parameters:

x (ndarray) – Tensor of shape (N, dim) representing the points to test.

Return type:

ndarray

Returns:

Boolean tensor of shape (N,) indicating if the points are outside: the domain.

is_on_boundary(x, tol=0.0001)[source]¶

Test if N points x are on the boundary of the domain (before mapping if any).

Parameters:

x (Tensor) – Tensor of shape (N, dim) representing the points to test.
tol (float) – Tolerance for the test (Default value = 1e-4).

Return type:

Tensor

Returns:

Boolean tensor of shape (N,) indicating if the points are on the boundary.

is_inside_postmap(x)[source]¶

Test if N points x are inside the domain (after mapping if any).

Parameters:: x (Tensor) – Tensor of shape (N, dim_postmap) representing the points to test.
Return type:: Tensor
Returns:: Boolean tensor of shape (N,) indicating if the points are inside the domain.

is_inside_postmap_np(x)[source]¶

Test if N points x are inside the domain (after mapping if any).

Parameters:: x (ndarray) – Tensor of shape (N, dim_postmap) representing the points to test.
Return type:: ndarray
Returns:: Boolean tensor of shape (N,) indicating if the points are inside the domain.

is_outside_postmap(x)[source]¶

Test if N points x are outside the domain (after mapping if any).

Parameters:

x (Tensor) – Tensor of shape (N, dim_postmap) representing the points to test.

Return type:

Tensor

Returns:

Boolean tensor of shape (N,) indicating if the points are outside: the domain.

is_outside_postmap_np(x)[source]¶

Test if N points x are outside the domain (after mapping if any).

Parameters:: x (ndarray) – Array of shape (N, dim_postmap) representing the points to test.
Return type:: ndarray
Returns:: Boolean array of shape (N,) indicating if the points are outside the domain.

is_on_boundary_postmap(x, tol=0.0001)[source]¶

Test if N points x are on the boundary of the domain (after mapping if any).

Parameters:

x (Tensor) – Tensor of shape (N, dim_postmap) representing the points to test.
tol (float) – Tolerance for the test. (Default value = 1e-4)

Return type:

Tensor

Returns:

Boolean tensor of shape (N,) indicating if the points are on the boundary: of the domain.

set_mapping(map, bounds_postmap, to_holes=True)[source]¶

Set the mapping of the main domain.

The mapping is applied to the main domain, subdomains, holes and boundary domains.

If to_holes is False, the mapping is also applied to none of the holes.

Parameters:

map (Mapping) – The mapping to apply to the domain.
bounds_postmap (Tensor) – Tensor of shape (dim_postmap, 2) representing a box that contains the main domain after the mapping.
to_holes (bool) – A flag to indicate if we apply the mapping to the holes. (Default value = True)

del_mapping()[source]¶

Delete the mapping of the domain.

The mapping is removed from the domain and the boundary domains.

When working on a main domain, the mapping is also removed from the subdomains.

add_bc_domain(bc_domain)[source]¶

Add a boundary domain to the domain.

If the domain is mapped, the boundary domain will have the same mapping.

Parameters:: bc_domain (SurfacicDomain) – The boundary domain to add.

add_subdomain(subdomain)[source]¶

Add a subdomain to the domain.

If the domain is mapped, the subdomain will have the same mapping.

Parameters:: subdomain (VolumetricDomain) – The subdomain to add.

add_hole(hole, copy_mapping=True)[source]¶

Add a hole to the domain.

Parameters:

hole (VolumetricDomain) – The hole to add.
copy_mapping (bool) – A flag to indicate if we copy the mapping of the domain to the hole. (Default value = True)

full_bc_domain()[source]¶

Return a list of boundary domains that make up the full domain boundary.

Return type:: list[SurfacicDomain]
Returns:: The list of boundary subdomains.
Raises:: NotImplementedError – If the method is not implemented for the specific class.

property has_bc_domain: bool¶

Check if the domain has boundary domains.

Returns:: True if the domain has boundary domains, False otherwise.

get_all_bc_domains()[source]¶

Return the lists containing all boundary domains.

Return type:: tuple[list[SurfacicDomain], list[SurfacicDomain], list[SurfacicDomain]]
Returns:: The list of boundary domains of the main domain, the holes and the subdomains (if called on the main domain). Otherwise, just the list of boundary domains.

get_extended_bounds(factor=0.05)[source]¶

Return extended bounds of the domain (before mapping if any).

Parameters:: factor (float) – The factor by which to extend the bounds. (Default value = 0.05)
Return type:: ndarray
Returns:: The extended bounds as a numpy array of shape (dim, 2).

get_extended_bounds_postmap(factor=0.05)[source]¶

Return extended bounds of the domain (after mapping if any).

Parameters:: factor (float) – The factor by which to extend the bounds. (Default value = 0.05)
Return type:: ndarray
Returns:: The extended bounds as a numpy array of shape (dim_postmap, 2).

class SurfacicDomain(domain_type, parametric_domain, surface)[source]¶

Bases: object

Base class for representing the boundary of a domain.

\[\partial \Omega = \text{surface}(\text{parametric_domain})\]

Parameters:

domain_type (str) – Type of the domain.
parametric_domain (VolumetricDomain) – The parametric domain.
surface (Mapping) – Mapping from the parametric domain to the domain.

domain_type: str¶: Type of the domain.

dim_parametric: int¶: Dimension of the parametric domain.

dim: int¶: Dimension of the domain (before mapping, =dim_parametric+1).

dim_postmap: int¶: Dimension of the domain (after mapping).

mapping: Mapping | None¶: The mapping of the domain (if any).

surface_o_mapping: Mapping¶: The composition of the surface and the mapping.

del_mapping()[source]¶: Delete the mapping of the domain.

compute_normals(t, **kwargs)[source]¶

Compute the normals of the surface at the points t in the parametric domain.

Parameters:

t (Tensor) – Tensor of shape (N, dim_parametric) representing the points in the parametric domain.
**kwargs (Any) – Additional arguments for the mapping.

Return type:

Tensor

Returns:

Tensor of shape (N, dim_postmap) representing the normals.

get_sdf()[source]¶

Return the signed distance function of the domain.

Return type:: Callable[[Tensor], Tensor]
Returns:: The signed distance function of the domain.
Raises:: NotImplementedError – the domain does not support this method.

is_valid_parametric_point_np(x)[source]¶

Check wether tensor is a valid (batch of) point(s) in the parametric domain.

Parameters:: x (ndarray | Any) – input point
Return type:: bool
Returns:: True if and only if x is a valid point not outside the parametric domain.
Raises:: ValueError – if the input value can not be broadcasted to a valid shape.