pysdic.Mesh.compute_property_interpolation#

Mesh.compute_property_interpolation(property, integration_points, *, skip_m1=True, default=nan)[source]#

Compute the interpolation of a property at given natural coordinates for specified elements in the mesh (convenient method for pysdic.compute_property_interpolation()). The element_type must be specified in the mesh connectivity to compute the shape functions for the elements of the mesh, which are used to perform the interpolation of the property.

In a space of dimension \(E\), we consider a \(K\)-dimensional element (with \(K \leq E\)) defined by \(N_{vpe}\) nodes/vertices.

For an \(K\)-dimensional element defined by \(N_{vpe}\) nodes, points inside the element are represented in a local coordinate system \((\xi, \eta, \zeta, ...)\) also named natural coordinates. Shape functions are defined in this local coordinate system in order to interpolate values at any point within the element based on the values at the nodes.

\[P(\xi, \eta, \zeta, ...) = \sum_{i=1}^{N_{vpe}} N_i(\xi, \eta, \zeta, ...) P_i\]

where \(P\) is the interpolated value at the point, \(N_i\) are the shape functions, and \(P_i\) are the nodal values.

Method to compute the interpolation of a property at given natural coordinates for specified elements in the mesh.

Note

The function is a convenience wrapper around the pysdic.compute_property_interpolation() function.

Important

Hint

To interpolate the position of the vertices use property=mesh.vertices.points.

Warning

No test are performed to check if the provided integration points are consistent with the mesh (i.e., existing element indices). Only shape check is performed. The behavior of the function is undefined if the provided integration points are not consistent with the mesh.

Parameters:

  • property (Union[str, ArrayLike]) – The property to interpolate. If a string is provided, it should correspond to a property name in the mesh (either a vertex property or an element property). If a numpy array is provided, it should have shape (\(N_v\), \(P\)) for vertex properties or shape (\(N_e\), \(P\)) for element properties, where \(N_v\) is the number of vertices, \(N_e\) is the number of elements, and \(P\) is the number of property channels.

  • integration_points (pysdic.objects.IntegrationPoints) – The integration points at which to compute the property interpolation.

  • skip_m1 (bool, optional) – If set to True, any element index of -1 in element_indices will result in the corresponding interpolated property being set to default. Default is True.

  • default (Union[Real, ArrayLike], optional) – The default value to assign to interpolated properties for integration points associated with an element index of -1 when skip_m1 is True. Default is numpy.nan. The input can also be a numpy.ndarray of shape (P,) to assign different default values for each property component.

Returns:

interpolated_properties – An array of shape \((N_{p}, P)\) containing the interpolated property values at each of the \(N_{p}\) integration points.

Return type:

numpy.ndarray

See also

pysdic.compute_shape_functions()

For more information on shape functions and their role in property interpolation.

pysdic.compute_property_interpolation()

For more information on the algorithm used to compute the property interpolation and an example of how to use it.