fastvpinns.FE.fe_transformation_2d module
This module provides an interface for the transformation methods used in the 2D finite element analysis. The transformation is essential for mapping element geometry in the reference domain to the actual physical domain. The primary functionalities encapsulated within this class include:
set_cell() - To set the physical coordinates of the cell. These coordinates are essential for subsequent computations involving Jacobians and transformations.
get_original_from_ref(xi, eta) - Given reference coordinates (xi, eta), this method returns the corresponding coordinates in the physical domain.
get_jacobian(xi, eta) - For a given point in the reference domain, represented by (xi, eta), this method calculates and returns the Jacobian of the transformation, which provides information about the local stretching, rotation, and skewing of the element. Further implementations of this class for specific element types (like quad and triangular elements) can incorporate more detailed and element-specific transformation techniques.
Author: Thivin Anandh D
Date: 20/Sep/2023
History: First version - 20/Sep/2023 - Thivin Anandh
- class fastvpinns.FE.fe_transformation_2d.FETransforamtion2D[source]
Bases:
objectThis class represents a 2D finite element transformation.
- abstract get_jacobian(xi, eta)[source]
This method returns the Jacobian of the transformation.
- Parameters:
xi (float) – The xi coordinate.
eta (float) – The eta coordinate.
- Returns:
The Jacobian matrix.
- Return type:
numpy.ndarray
- abstract get_original_from_ref(xi, eta)[source]
This method returns the original coordinates from the reference coordinates.
- Parameters:
xi (float) – The xi value of the reference coordinates.
eta (float) – The eta value of the reference coordinates.
- Returns:
The original coordinates corresponding to the given reference coordinates.
- Return type:
tuple