fdtdx.PerfectlyMatchedLayer

Contents

fdtdx.PerfectlyMatchedLayer#

class fdtdx.PerfectlyMatchedLayer(*, partial_real_shape=(None, None, None), partial_real_position=(None, None, None), partial_grid_shape=(None, None, None), color=Color(r=0.21176470588235294, g=0.21568627450980393, b=0.21568627450980393), name=None, max_random_real_offsets=(0, 0, 0), max_random_grid_offsets=(0, 0, 0), axis=null, direction=null, alpha_start=None, alpha_end=None, alpha_order=None, kappa_start=None, kappa_end=None, kappa_order=None, sigma_start=None, sigma_end=None, sigma_order=None)[source]#

Bases: BaseBoundary

Implements a Convolutional Perfectly Matched Layer (CPML) boundary condition.

The CPML absorbs outgoing electromagnetic waves with minimal reflection by using a complex coordinate stretching approach. This implementation supports arbitrary axis orientation and both positive/negative directions.

Quick Reference#

Attributes

Methods

Attributes#

PerfectlyMatchedLayer.alpha_end: float | None#

Final loss parameter for complex frequency shifting. Defaults to 0.0 if not provided.

PerfectlyMatchedLayer.alpha_order: float | None#

Polynomial order for alpha grading. Defaults to 1.0 if not provided.

PerfectlyMatchedLayer.alpha_start: float | None#

Initial loss parameter for complex frequency shifting. Defaults to 0.01 * 2 * jnp.pi * c / wavelength * eps0 if not provided.

PerfectlyMatchedLayer.axis: int#

Principal axis for boundary (0=x, 1=y, 2=z)

PerfectlyMatchedLayer.color: Color | None#

RGB color tuple for visualization. defaults to dark grey.

PerfectlyMatchedLayer.descriptive_name#

Gets a human-readable name describing this PML boundary’s location.

Returns:

Description like “min_x” or “max_z” indicating position

Return type:

str

PerfectlyMatchedLayer.direction: Literal['+', '-']#

Direction along axis (“+” or “-“)

PerfectlyMatchedLayer.grid_shape#
PerfectlyMatchedLayer.grid_slice#
PerfectlyMatchedLayer.grid_slice_tuple#
PerfectlyMatchedLayer.kappa_end: float | None#

Final kappa stretching coefficient. Defaults to 0.0 if not provided.

PerfectlyMatchedLayer.kappa_order: float | None#

Polynomial order for kappa grading. Defaults to 1.0 if not provided.

PerfectlyMatchedLayer.kappa_start: float | None#

Initial kappa stretching coefficient. Defaults to 0.0 if not provided.

PerfectlyMatchedLayer.max_random_grid_offsets: tuple[int, int, int]#

Maximum random offset values that can be applied to the object’s position in grid coordinates for each axis (x, y, z). Defaults to (0, 0, 0) for no random offset.

PerfectlyMatchedLayer.max_random_real_offsets: tuple[float, float, float]#

Maximum random offset values that can be applied to the object’s position in real coordinates for each axis (x, y, z). Defaults to (0, 0, 0) for no random offset.

PerfectlyMatchedLayer.name: str#

Unique identifier for the object. Automatically enforced to be unique through the UniqueName validator. The user can also set a name manually.

PerfectlyMatchedLayer.partial_grid_shape: PartialGridShape3D#

The object’s shape in grid coordinates. Defaults to UNDEFINED_SHAPE_3D if not specified.

PerfectlyMatchedLayer.partial_real_position: PartialRealShape3D#

The object’s position in real-world coordinates. Defaults to UNDEFINED_SHAPE_3D if not specified.

PerfectlyMatchedLayer.partial_real_shape: PartialRealShape3D#

The object’s shape in real-world coordinates. Defaults to UNDEFINED_SHAPE_3D if not specified.

PerfectlyMatchedLayer.real_shape#

Physical side lengths covered by this object’s placed grid slice.

The value is derived from SimulationConfig.grid when available. That keeps object geometry tied to physical edge coordinates instead of a global scalar resolution. During early placement, before a concrete grid has been attached to the config, the legacy uniform-resolution fallback is still used for compatibility.

PerfectlyMatchedLayer.sigma_end: float | None#

Final sigma value. Defaults to 1.0 if not provided.

PerfectlyMatchedLayer.sigma_order: float | None#

Polynomial order for sigma grading. Defaults to 3.0 if not provided.

PerfectlyMatchedLayer.sigma_start: float | None#

Initial sigma value. Defaults to 0.0 if not provided.

PerfectlyMatchedLayer.thickness#

Gets the thickness of the PML layer in grid points.

Returns:

Number of grid points in the PML along its axis

Return type:

int

PerfectlyMatchedLayer.uses_wrap_padding#

Whether this boundary’s axis should use wrap (periodic) padding.

Returns True for boundaries that connect opposite sides of the domain (periodic, Bloch). Returns False for terminating boundaries (PEC, PMC, PML).

Methods#

PerfectlyMatchedLayer.apply(key, inv_permittivities, inv_permeabilities, dispersive_c1=None, dispersive_c2=None, dispersive_c3=None)#
Return type:

Self

PerfectlyMatchedLayer.apply_field_reset(fields)[source]#

Zero all field components within the PML region.

Return type:

dict[str, Array]

PerfectlyMatchedLayer.apply_pad_correction(padded_fields, volume_shape, resolution)#

Apply boundary-specific correction to padded fields.

Called after basic wrap/constant padding. Default is a no-op. Subclasses like BlochBoundary override this to apply phase shifts to ghost cells.

Parameters:

  • padded_fields (Array) – Padded field array of shape (3, Nx+2, Ny+2, Nz+2)

  • volume_shape (tuple[int, int, int]) – Full simulation volume shape (Nx, Ny, Nz)

  • resolution (float) – Grid resolution in meters

Return type:

Array

Returns:

Padded fields with boundary-specific corrections applied

PerfectlyMatchedLayer.apply_post_E_update(E)#

Apply boundary-specific enforcement after E field update.

Called after each E field update (forward and reverse). Default is a no-op. Subclasses like PEC override this to zero tangential E components.

Parameters:

E (Array) – Electric field array of shape (3, Nx, Ny, Nz)

Return type:

Array

Returns:

E field with boundary conditions enforced

PerfectlyMatchedLayer.apply_post_H_update(H)#

Apply boundary-specific enforcement after H field update.

Called after each H field update (forward and reverse). Default is a no-op. Subclasses like PMC override this to zero tangential H components.

Parameters:

H (Array) – Magnetic field array of shape (3, Nx, Ny, Nz)

Return type:

Array

Returns:

H field with boundary conditions enforced

PerfectlyMatchedLayer.aset(attr_name, val, create_new_ok=False)#

Sets an attribute of this class. In contrast to the classical .at[].set(), this method updates the class attribute directly and does not only operate on jax pytree leaf nodes. Instead, replaces the full attribute with the new value.

The attribute can either be the attribute name of this class, or for nested classes it can also be the attribute name of a class, which itself is an attribute of this class. The syntax for this operation could look like this: “a->b->[0]->[‘name’]”. Here, the current class has an attribute a, which has an attribute b, which is a list, which we index at index 0, which is an element of type dictionary, which we index using the dictionary key ‘name’.

Note that dictionary keys cannot contain square brackets or single quotes (even if they are escaped).

Parameters:

  • attr_name (str) – Name of attribute to set

  • val (Any) – Value to set the attribute to

  • create_new_ok (bool, optional) – If false (default), throw an error if the attribute does not exist. If true, creates a new attribute if the attribute name does not exist yet.

Returns:

Updated instance with new attribute value

Return type:

Self

PerfectlyMatchedLayer.check_overlap(other)#
Return type:

bool

PerfectlyMatchedLayer.extend_to(other, axis, direction, other_position=None, offset=0, grid_offset=0)#

Creates a SizeExtensionConstraint that extends this object along a specified axis until it reaches another object or the simulation boundary. The extension can be in either positive or negative direction.

Parameters:

  • other (str | None) – Target object to extend to, or None to extend to simulation boundary

  • axis (int) – Which axis to extend along (0, 1, or 2)

  • direction (Literal["+", "-"]) – Direction to extend in (‘+’ or ‘-‘)

  • other_position (float | None, optional) – Relative position on target object (-1 to 1) to extend to. If None, defaults to the corresponding side (-1 for ‘+’ direction, 1 for ‘-’ direction). Defaults to None.

  • offset (float, optional) – Additional offset in meters to apply after extension. Ignored when extending to simulation boundary. Defaults to zero.

  • grid_offset (int, optional) – Additional offset in Yee-grid voxels to apply after extension. Ignored when extending to simulation boundary. Defaults to zero.

Returns:

Constraint defining how the object extends

Return type:

SizeExtensionConstraint

PerfectlyMatchedLayer.face_to_face_negative_direction(other, axes, margins=None, grid_margins=None)#

Creates a PositionConstraint that places this object facing another object in the negative direction of specified axes. The objects will touch at their facing boundaries unless margins are specified.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int) – Either a single integer or a tuple describing which axes to align on

  • margins (tuple[float, ...] | float | None, optional) – Additional margins in meters between the facing surfaces. Must have same length as axes. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional margins in Yee-grid voxels between the facing surfaces. Must have same length as axes. If None, no margin is used. Defaults to None.

Returns:

Position constraint aligning objects face-to-face in negative direction

Return type:

PositionConstraint

PerfectlyMatchedLayer.face_to_face_positive_direction(other, axes, margins=None, grid_margins=None)#

Creates a PositionConstraint that places this object facing another object in the positive direction of specified axes. The objects will touch at their facing boundaries unless margins are specified.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int) – Either a single integer or a tuple describing which axes to align on

  • margins (tuple[float, ...] | float | None, optional) – Additional margins in meters between the facing surfaces. Must have same length as axes. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional margins in Yee-grid voxels between the facing surfaces. Must have same length as axes. If None, no margin is used. Defaults to None

Returns:

Position constraint aligning objects face-to-face in positive direction

Return type:

PositionConstraint

PerfectlyMatchedLayer.get_class_fields()#
Return type:

list[TreeClassField]

PerfectlyMatchedLayer.get_public_fields()#
Return type:

list[TreeClassField]

PerfectlyMatchedLayer.interface_grid_shape()#
Return type:

tuple[int, int, int]

PerfectlyMatchedLayer.interface_slice()#
Return type:

tuple[slice, slice, slice]

PerfectlyMatchedLayer.interface_slice_tuple()#
Return type:

tuple[tuple[int, int], tuple[int, int], tuple[int, int]]

PerfectlyMatchedLayer.modify_arrays(alpha, kappa, sigma, electric_conductivity, magnetic_conductivity)[source]#

Modifies simulation arrays to include PML parameters.

Parameters:

  • alpha (Array) – Alpha array for PML calculations (shape: (3, *volume_shape))

  • kappa (Array) – Kappa array for PML calculations (shape: (3, *volume_shape))

  • sigma (Array) – Sigma array for PML calculations (shape: (3, *volume_shape))

  • electric_conductivity – Electric conductivity array (shape: volume_shape)

  • magnetic_conductivity – Magnetic conductivity array (shape: volume_shape)

Returns:

Dictionary with modified ‘alpha’, ‘kappa’, and ‘sigma’ arrays

Return type:

dict

PerfectlyMatchedLayer.place_above(other, margins=None, grid_margins=None)#

Creates a PositionConstraint that places this object above another object along the z-axis. This is a convenience wrapper around face_to_face_positive_direction() for axis 2 (z-axis).

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • margins (tuple[float, ...] | float | None, optional) – Additional vertical margins in meters between objects. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional vertical margins in Yee-grid voxels between objects. If None, no margin is used. Defaults to None.

Returns:

Position constraint placing this object above the other

Return type:

PositionConstraint

PerfectlyMatchedLayer.place_at_center(other, axes=(0, 1, 2), own_positions=None, other_positions=None, margins=None, grid_margins=None)#

Creates a PositionConstraint that centers this object relative to another object along specified axes. This is a convenience wrapper around place_relative_to() with default positions at the center (0).

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int, optional) – Either a single integer or a tuple describing which axes to center on. Defaults to all axes (0, 1, 2).

  • own_positions (tuple[float, ...] | float | None, optional) – Relative positions on this object (-1 to 1). If None, uses center (0). Defaults to None.

  • other_positions (tuple[float, ...] | float | None, optional) – Relative positions on other object (-1 to 1). If None, uses center (0). Defaults to None.

  • margins (tuple[float, ...] | float | None, optional) – Additional margins in meters between objects. Must have same length as axes. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional margins in Yee-grid voxels between objects. Must have same length as axes. If None, no margin is used. Defaults to None.

Returns:

Position constraint centering objects relative to each other

Return type:

PositionConstraint

PerfectlyMatchedLayer.place_below(other, margins=None, grid_margins=None)#

Creates a PositionConstraint that places this object below another object along the z-axis. This is a convenience wrapper around face_to_face_negative_direction() for axis 2 (z-axis).

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • margins (tuple[float, ...] | float | None, optional) – Additional vertical margins in meters between objects. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional vertical margins in Yee-grid voxels between objects. If None, no margin is used. Defaults to None.

Returns:

Position constraint placing this object below the other

Return type:

PositionConstraint

PerfectlyMatchedLayer.place_on_grid(grid_slice_tuple, config, key)[source]#

Place the PML on the grid and calculate any remaining defaults.

This is called after initialization, so grid_shape and config are available.

PerfectlyMatchedLayer.place_relative_to(other, axes, own_positions, other_positions, margins=None, grid_margins=None)#

Creates a PositionalConstraint between two objects. The constraint is defined by anchor points on both objects, which are constrained to be at the same position. Anchors are defined in relative coordinates, i.e. a position of -1 is the left object boundary in the respective axis and a position of +1 the right boundary.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int) – Eiter a single integer or a tuple describing the axes of the constraints

  • own_positions (tuple[float, ...] | float) – The positions of the own anchor in the axes. Must have the same lengths as axes

  • other_positions (tuple[float, ...] | float) – The positions of the other objects’ anchor in the axes. Must have the same lengths as axes

  • margins (tuple[float, ...] | float | None, optional) – The margins between the anchors of both objects in meters. Must have the same lengths as axes. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – The margins between the anchors of both objects in Yee-grid voxels. Must have the same lengths as axes. If none, no margin is used. Defaults to None.

Returns:

Positional constraint between this object and the other

Return type:

PositionConstraint

PerfectlyMatchedLayer.same_position(other, axes=(0, 1, 2), own_positions=None, other_positions=None, margins=None, grid_margins=None)#

Creates a PositionConstraint that places this object at the same position as another object. This is a convenience wrapper around place_at_center() for more intuitive naming.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int, optional) – Either a single integer or a tuple describing which axes to match position on. Defaults to all axes (0, 1, 2).

  • own_positions (tuple[float, ...] | float | None, optional) – Relative positions on this object (-1 to 1). If None, uses center (0). Defaults to None.

  • other_positions (tuple[float, ...] | float | None, optional) – Relative positions on other object (-1 to 1). If None, uses center (0). Defaults to None.

  • margins (tuple[float, ...] | float | None, optional) – Additional margins in meters between objects. Must have same length as axes. If None, no margin is used. Defaults to None.

  • grid_margins (tuple[int, ...] | int | None, optional) – Additional margins in Yee-grid voxels between objects. Must have same length as axes. If None, no margin is used. Defaults to None.

Returns:

Position constraint placing objects at the same position

Return type:

PositionConstraint

PerfectlyMatchedLayer.same_position_and_size(other, axes=(0, 1, 2))#

Creates both position and size constraints to make this object match another object’s position and size. This is a convenience wrapper combining place_at_center() and same_size().

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int, optional) – Either a single integer or a tuple describing which axes to match. Defaults to all axes (0, 1, 2).

Returns:

Position and size constraints for matching objects

Return type:

tuple[PositionConstraint, SizeConstraint]

PerfectlyMatchedLayer.same_size(other, axes=(0, 1, 2), offsets=None, grid_offsets=None)#

Creates a SizeConstraint that makes this object the same size as another object along specified axes. This is a convenience wrapper around size_relative_to() with proportions set to 1.0.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int, optional) – Either a single integer or a tuple describing which axes should have the same size. Defaults to all axes (0, 1, 2).

  • offsets (tuple[float, ...] | float | None, optional) – Additional size offsets in meters to apply. Must have same length as axes. If None, no offset is used. Defaults to None.

  • grid_offsets (tuple[int, ...] | int | None, optional) – Additional size offsets in Yee-grid voxels to apply. Must have same length as axes. If None, no offset is used. Defaults to None.

Returns:

Size constraint ensuring equal sizes between objects

Return type:

SizeConstraint

PerfectlyMatchedLayer.set_grid_coordinates(axes, sides, coordinates)#

Creates a GridCoordinateConstraint that forces specific sides of this object to align with given grid coordinates. Used for precise positioning in the discretized simulation space.

Parameters:

  • axes (tuple[int, ...] | int) – Either a single integer or a tuple describing which axes to constrain

  • sides (tuple[Literal["+", "-"], ...] | Literal["+", "-"]) – Either a single string or a tuple of strings (‘+’ or ‘-’) indicating which side of each axis to constrain. Must have same length as axes.

  • coordinates (tuple[int, ...] | int) – Either a single integer or a tuple of integers specifying the grid coordinates to align with. Must have same length as axes.

Returns:

Constraint forcing alignment with specific grid coordinates

Return type:

GridCoordinateConstraint

PerfectlyMatchedLayer.size_relative_to(other, axes, other_axes=None, proportions=None, offsets=None, grid_offsets=None)#

Creates a SizeConstraint between two objects. The constraint defines the size of this object relative to another object, allowing for proportional scaling and offsets in specified axes.

Parameters:

  • other (SimulationObject) – Another object in the simulation scene

  • axes (tuple[int, ...] | int) – Either a single integer or a tuple describing which axes of this object to constrain.

  • other_axes (tuple[int, ...] | int | None, optional) – Either a single integer or a tuple describing which axes of the other object to reference. If None, uses the same axes as specified in ‘axes’. Defaults to None.

  • proportions (tuple[float, ...] | float | None, optional) – Scale factors to apply to the other object’s dimensions. Must have same length as axes. If None, uses 1.0 (same size). Defaults to None.

  • offsets (tuple[float, ...] | float | None, optional) – Additional size offsets in meters to apply after scaling. Must have same length as axes. If None, no offset is used. Defaults to None.

  • grid_offsets (tuple[int, ...] | int | None, optional) – Additional size offsets in Yee-grid voxels to apply after scaling. Must have same length as axes. If None, no offset is used. Defaults to None.

Returns:

Size constraint between this object and the other

Return type:

SizeConstraint

If you find any errors in the documentation, please report them in the Github Issues!

Contents