cashocs.geometry.mesh#

Basic mesh generation.

Functions

interval_mesh([n, start, end, partitions, comm])

Creates an 1D interval mesh starting at x=0 to x=length.

regular_box_mesh([n, start_x, start_y, ...])

Creates a mesh corresponding to a rectangle or cube.

regular_mesh([n, length_x, length_y, ...])

Creates a mesh corresponding to a rectangle or cube.

Classes

Any(*args, **kwargs)

Special type indicating an unconstrained type.
cashocs.geometry.mesh.interval_mesh(n=10, start=0.0, end=1.0, partitions=None, comm=None)[source]#

Creates an 1D interval mesh starting at x=0 to x=length.

This function creates a uniform mesh of a 1D interval, starting at the start and ending at end. The resulting mesh uses n sub-intervals to discretize the geometry. The boundary markers are as follows:

  • 1 corresponds to \(x=start\)

  • 2 corresponds to \(x=end\)

Parameters:

  • n (int) – Number of elements for discretizing the interval, default is 10

  • start (float) – The start of the interval, default is 0.0

  • end (float) – The end of the interval, default is 1.0

  • partitions (Optional[List[float]]) – Points in the interval at which a partition in subdomains should be made. The resulting volume measure is sorted ascendingly according to the sub-intervals defined in partitions (starting at 1). Defaults to None.

  • comm (Optional[MPI.Comm]) – MPI communicator that is to be used for creating the mesh.

Returns:

A tuple (mesh, subdomains, boundaries, dx, ds, dS), where mesh is the imported FEM mesh, subdomains is a mesh function for the subdomains, boundaries is a mesh function for the boundaries, dx is a volume measure, ds is a surface measure, and dS is a measure for the interior facets.

Return type:

_typing.MeshTuple

cashocs.geometry.mesh.regular_box_mesh(n=10, start_x=0.0, start_y=0.0, start_z=None, end_x=1.0, end_y=1.0, end_z=None, diagonal='right', comm=None)[source]#

Creates a mesh corresponding to a rectangle or cube.

This function creates a uniform mesh of either a rectangle or a cube, with specified start (S_) and end points (E_). The resulting mesh uses n elements along the shortest direction and accordingly many along the longer ones. The resulting domain is

\[\begin{split}\begin{alignedat}{2} &[start_x, end_x] \times [start_y, end_y] \quad &&\text{ in } 2D, \\ &[start_x, end_x] \times [start_y, end_y] \times [start_z, end_z] \quad &&\text{ in } 3D. \end{alignedat}\end{split}\]

The boundary markers are ordered as follows:

  • 1 corresponds to \(x=start_x\).

  • 2 corresponds to \(x=end_x\).

  • 3 corresponds to \(y=start_y\).

  • 4 corresponds to \(y=end_y\).

  • 5 corresponds to \(z=start_z\) (only in 3D).

  • 6 corresponds to \(z=end_z\) (only in 3D).

Parameters:

  • n (int) – Number of elements in the shortest coordinate direction.

  • start_x (float) – Start of the x-interval.

  • start_y (float) – Start of the y-interval.

  • start_z (Optional[float]) – Start of the z-interval, mesh is 2D if this is None (default is None).

  • end_x (float) – End of the x-interval.

  • end_y (float) – End of the y-interval.

  • end_z (Optional[float]) – End of the z-interval, mesh is 2D if this is None (default is None).

  • diagonal (Literal['right', 'left', 'left/right', 'right/left', 'crossed']) – This defines the type of diagonal used to create the box mesh in 2D. This can be one of "right", "left", "left/right", "right/left" or "crossed".

  • comm (Optional[MPI.Comm]) – MPI communicator that is to be used for creating the mesh.

Returns:

A tuple (mesh, subdomains, boundaries, dx, ds, dS), where mesh is the imported FEM mesh, subdomains is a mesh function for the subdomains, boundaries is a mesh function for the boundaries, dx is a volume measure, ds is a surface measure, and dS is a measure for the interior facets.

Return type:

_typing.MeshTuple

cashocs.geometry.mesh.regular_mesh(n=10, length_x=1.0, length_y=1.0, length_z=None, diagonal='right', comm=None)[source]#

Creates a mesh corresponding to a rectangle or cube.

This function creates a uniform mesh of either a rectangle or a cube, starting at the origin and having length specified in length_x, length_y, and length_z. The resulting mesh uses n elements along the shortest direction and accordingly many along the longer ones. The resulting domain is

\[\begin{split}\begin{alignedat}{2} &[0, length_x] \times [0, length_y] \quad &&\text{ in } 2D, \\ &[0, length_x] \times [0, length_y] \times [0, length_z] \quad &&\text{ in } 3D. \end{alignedat}\end{split}\]

The boundary markers are ordered as follows:

  • 1 corresponds to \(x=0\).

  • 2 corresponds to \(x=length_x\).

  • 3 corresponds to \(y=0\).

  • 4 corresponds to \(y=length_y\).

  • 5 corresponds to \(z=0\) (only in 3D).

  • 6 corresponds to \(z=length_z\) (only in 3D).

Parameters:

  • n (int) – Number of elements in the shortest coordinate direction.

  • length_x (float) – Length in x-direction.

  • length_y (float) – Length in y-direction.

  • length_z (Optional[float]) – Length in z-direction, if this is None, then the geometry will be two-dimensional (default is None).

  • diagonal (Literal['left', 'right', 'left/right', 'right/left', 'crossed']) – This defines the type of diagonal used to create the box mesh in 2D. This can be one of "right", "left", "left/right", "right/left" or "crossed".

  • comm (Optional[MPI.Comm]) – MPI communicator that is to be used for creating the mesh.

Returns:

A tuple (mesh, subdomains, boundaries, dx, ds, dS), where mesh is the imported FEM mesh, subdomains is a mesh function for the subdomains, boundaries is a mesh function for the boundaries, dx is a volume measure, ds is a surface measure, and dS is a measure for the interior facets.

Return type:

_typing.MeshTuple