Mesh Generation Helpers

mesh_generation

Helper functions that produce simple 2D rectangular meshes that can be used for testing.

fimjax.util.mesh_generation.Mesh

dataclass for holding everything that belongs to the mesh. Note that this only supports keyword arguments due to Chex. Use it like: mesh = Mesh(points=points, elements=elements)

N: Number of elements in a mesh (i.e. triangles) d_e: Number of points in an element M: Number of points in a mesh d: Dimension of the underlying space

Attributes:

Name	Type	Description
points	np.ndarray	[M, d] array of points
elements	np.ndarray	[N, d_e] array of indices into points that correspond to elements in a mesh
points_triangle	np.ndarray	[N, d_e, d] like elements, but with the points instead of indices

__init__

__init__(points: np.ndarray, elements: np.ndarray)

Constructor.

Parameters:

Name	Type	Description	Default
points	np.ndarray	[M, d] array of points	required
elements	np.ndarray	[N] array of	required

fimjax.util.mesh_generation.tensor_field

tensor_field(alpha: float, num_elems: int, dimension: int, dtype=jnp.double) -> np.ndarray

generates identity

Parameters:

Name	Type	Description	Default
alpha	float	description	required
num_elems	int	description	required
dimension	int	description	required
dtype	_type_	description. Defaults to jnp.double.	jnp.double

Returns:

Type	Description
np.ndarray	np.ndarray: description

fimjax.util.mesh_generation.generate_random_2d_mesh

generate_random_2d_mesh(discretization: int) -> tuple[Mesh, np.ndarray]

Generates a random 2D mesh with random metrics (positive definite with eigenvalues between 1 and 5)

Parameters:

Name	Type	Description	Default
discretization	int	Number of points in each dimension	required

fimjax.util.mesh_generation.generate_identity_2d_mesh

generate_identity_2d_mesh(discretization: int) -> tuple[Mesh, np.ndarray]

Generates a 2D mesh with isotropic metrics with velocity 1 (identity tensor)

Parameters:

Name	Type	Description	Default
discretization	int	Number of points in each dimension	required

fimjax.util.mesh_generation.generate_benchmark_data

generate_benchmark_data(dir: str = 'data')

Generates benchmark data for benchmarking and also for finite difference validation

Parameters:

Name	Type	Description	Default
dir	optional	directory to store meshes and tensor. Defaults to "data".	'data'

fimjax.util.mesh_generation.read_benchmark_data

read_benchmark_data(dir: str = 'data', maximal_discretization: int = np.inf) -> tuple[dict[int, tuple[Mesh, np.ndarray]], dict[int, tuple[Mesh, np.ndarray]]]

Reads benchmark data from directory

Parameters:

Name	Type	Description	Default
dir	optional	directory where benchmark data is stored. Defaults to "data".	'data'

Returns:

Type	Description
tuple[dict[int, tuple[Mesh, np.ndarray]], dict[int, tuple[Mesh, np.ndarray]]]	dict[int, tuple[Mesh, np.ndarray]]: Dictionary with discretization as key and tuple of mesh and tensor as value