'''
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:
1. set_cell() - To set the physical coordinates of the cell. These coordinates are essential for subsequent computations involving Jacobians and transformations.
2. get_original_from_ref(xi, eta) - Given reference coordinates (xi, eta), this method returns the corresponding coordinates in the physical domain.
3. 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
'''
from abc import abstractmethod
[docs]
class FETransforamtion2D:
"""
This class represents a 2D finite element transformation.
"""
def __init__(self):
"""
Constructor for the FETransforamtion2D class.
"""
[docs]
@abstractmethod
def set_cell(self):
"""
Set the cell coordinates, which will be used to calculate the Jacobian and actual values.
:return: None
"""
@abstractmethod
def get_original_from_ref(self, xi, eta):
"""
This method returns the original coordinates from the reference coordinates.
:param xi: The xi coordinate in the reference space.
:type xi: float
:param eta: The eta coordinate in the reference space.
:type eta: float
:return: The original coordinates (x, y) corresponding to the given reference coordinates.
:rtype: tuple
"""
[docs]
@abstractmethod
def get_original_from_ref(self, xi, eta):
"""
This method returns the original coordinates from the reference coordinates.
:param xi: The xi value of the reference coordinates.
:type xi: float
:param eta: The eta value of the reference coordinates.
:type eta: float
:return: The original coordinates corresponding to the given reference coordinates.
:rtype: tuple
"""
[docs]
@abstractmethod
def get_jacobian(self, xi, eta):
"""
This method returns the Jacobian of the transformation.
:param xi: The xi coordinate.
:type xi: float
:param eta: The eta coordinate.
:type eta: float
:return: The Jacobian matrix.
:rtype: numpy.ndarray
"""
## Mandatory, Import all the basis functions here (Quad element Transformations)
from .quad_affine import *
from .quad_bilinear import *