mapping.discrete#

Functions#

random_string(n)

Classes#

Inheritance diagram of psydac.mapping.discrete

`NurbsMapping`(args, *kwargs)
`SplineMapping`(args, *kwargs)

Details#

class SplineMapping(*args: Any, **kwargs: Any)[source]#

Bases: BasicCallableMapping

property name#

set_name(name)[source]#

classmethod from_mapping(tensor_space, mapping)[source]#

classmethod from_control_points(tensor_space, control_points)[source]#

jacobian(*eta)[source]#

jacobian_inv(*eta)[source]#

metric(*eta)[source]#

metric_det(*eta)[source]#

property ldim#

property pdim#

build_mesh(grid, npts_per_cell=None, overlap=0)[source]#

Evaluation of the mapping on the given grid.

Parameters:

gridList of ndarray: Grid on which to evaluate the fields. Each array in this list corresponds to one logical coordinate.
npts_per_cell: int, tuple of int or None, optional: Number of evaluation points in each cell. If an integer is given, then assume that it is the same in every direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

mesh: tuple: ldim ldim-D arrays. One for each component.

See also

psydac.fem.tensor.TensorFemSpace.eval_fields: More information about the grid parameter.

jac_mat_grid(grid, npts_per_cell=None, overlap=0)[source]#

Evaluates the Jacobian matrix of the mapping at the given location(s) grid.

Parameters:

gridList of array_like: Grid on which to evaluate the fields
npts_per_cell: int or tuple of int or None, optional: number of evaluation points in each cell. If an integer is given, then assume that it is the same in every direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

array_like: Jacobian matrix at the location(s) grid.

See also

mapping.SplineMapping.inv_jac_mat_grid: Evaluates the inverse of the Jacobian matrix of the mapping at the given location(s) grid.
mapping.SplineMapping.metric_det_grid: Evaluates the metric determinant of the mapping at the given location(s) grid.

jac_mat_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian matrix on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

jac_mat_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian matrix on an irregular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

inv_jac_mat_grid(grid, npts_per_cell=None, overlap=0)[source]#

Evaluates the inverse of the Jacobian matrix of the mapping at the given location(s) grid.

Parameters:

gridList of array_like: Grid on which to evaluate the fields
npts_per_cell: int or tuple of int or None, optional: number of evaluation points in each cell. If an integer is given, then assume that it is the same in every direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

array_like: Inverse of the Jacobian matrix at the location(s) grid.

See also

mapping.SplineMapping.jac_mat_grid: Evaluates the Jacobian matrix of the mapping at the given location(s) grid.
mapping.SplineMapping.metric_det_grid: Evaluates the metric determinant of the mapping at the given location(s) grid.

inv_jac_mat_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the inverse of the Jacobian matrix on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

inv_jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the inverse of the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

inv_jac_mat_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the inverse of the Jacobian matrix on an irregular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

inv_jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the inverse of the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

jac_det_grid(grid, npts_per_cell=None, overlap=0)[source]#

Evaluates the Jacobian determinant of the mapping at the given location(s) grid.

Parameters:

gridList of array_like: Grid on which to evaluate the fields
npts_per_cell: int or tuple of int or None, optional: number of evaluation points in each cell. If an integer is given, then assume that it is the same in every direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

array_like: Jacobian determinant at the location(s) grid.

See also

mapping.SplineMapping.jac_mat_grid: Evaluates the Jacobian matrix of the mapping at the given location(s) grid.
mapping.SplineMapping.inv_jac_mat_grid: Evaluates the inverse of the Jacobian matrix of the mapping at the given location(s) grid.

jac_det_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian determinant on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_detsndarray: self.ldim D array of shape (n_x_1, ..., n_x_ldim). jac_dets[x_1, ..., x_ldim] is the Jacobian determinant at the location corresponding to (x_1, ..., x_ldim).

jac_det_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian determinant on an irregular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_detsndarray: self.ldim D array of shape (n_x_1, ..., n_x_ldim). jac_dets[x_1, ..., x_ldim] is the Jacobian determinant at the location corresponding to (x_1, ..., x_ldim).

jacobian_det(*eta)[source]#

property space#

property fields#

property control_points#

export(filename)[source]#

Export tensor-product spline space and mapping to geometry file in HDF5 format (single-patch only).

Parameters:

filenamestr: Name of HDF5 output file.

class ControlPoints(mapping)[source]#

Bases: object

Convenience object to access control points.

property mapping#

class NurbsMapping(*args: Any, **kwargs: Any)[source]#

Bases: SplineMapping

classmethod from_control_points_weights(tensor_space, control_points, weights)[source]#

jacobian(*eta)[source]#

build_mesh(grid, npts_per_cell=None, overlap=0)[source]#

Evaluation of the mapping on the given grid.

Parameters:

gridList of ndarray: Each array in the list should correspond to a logical coordinate.
npts_per_cellint, tuple of int or None, optional
overlapint: How much to overlap. Only used in the distributed context.

Returns:

mesh: tuple: ldim ldim-D arrays. One for each component.

See also

psydac.fem.tensor.TensorFemSpace.eval_fields: More information about the grid parameter.

jac_mat_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian matrix on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

jac_mat_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian matrix on an irregular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

inv_jac_mat_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the inverse of the Jacobian matrix on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

inv_jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the inverse of the Jacobian matrix a at the location corresponding to (x_1, ..., x_ldim).

inv_jac_mat_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the inverse of the Jacobian matrix on an irregular tensor product grid.

Parameters:

gridList of ndarray: List of 1D arrays representing each direction of the grid.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

inv_jac_matsndarray: self.ldim + 2 D array of shape (n_x_1, ..., n_x_ldim, ldim, ldim). jac_mats[x_1, ..., x_ldim] is the inverse of the Jacobian matrix at the location corresponding to (x_1, ..., x_ldim).

jac_det_regular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian determinant on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_detsndarray: self.ldim D array of shape (n_x_1, ..., n_x_ldim). jac_dets[x_1, ..., x_ldim] is the Jacobian determinant at the location corresponding to (x_1, ..., x_ldim).

jac_det_irregular_tensor_grid(grid, overlap=0)[source]#

Evaluates the Jacobian determinant on a regular tensor product grid.

Parameters:

gridList of ndarray: List of 2D arrays representing each direction of the grid. Each of these arrays should have shape (ne_xi, nv_xi) where ne_xi is the number of cells in the domain in the direction xi and nv_xi is the number of evaluation points in the same direction.
overlapint: How much to overlap. Only used in the distributed context.

Returns:

jac_detsndarray: self.ldim D array of shape (n_x_1, ..., n_x_ldim). jac_dets[x_1, ..., x_ldim] is the Jacobian determinant at the location corresponding to (x_1, ..., x_ldim).

property weights_field#

property weights#

export(filename)[source]#

Export tensor-product spline space and mapping to geometry file in HDF5 format (single-patch only).

Parameters:

filenamestr: Name of HDF5 output file.

class Weights(mapping)[source]#

Bases: object

Convenience object to access weights.

property mapping#