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quadratureformulas

Abstract Base Class for Numerical Quadrature Formulas.

This module provides the base interface for implementing various numerical quadrature schemes. It defines the common structure and required methods that all quadrature implementations must follow.

Key functionalities
  • Abstract interface for quadrature rule implementations
  • Standard methods for accessing quadrature points and weights
  • Flexible framework for different element types and dimensions
The module serves as a foundation for
  • Multiple quadrature rule implementations
  • Different element type integrations
  • Various quadrature orders and types
  • Custom quadrature scheme implementations
Key classes
  • Quadratureformulas: Abstract base class for all quadrature implementations
Dependencies
  • abc: For abstract base class functionality
Authors

Thivin Anandh D (https://thivinanandh.github.io)

Version Info

27/Dec/2024: Initial version - Thivin Anandh D

Quadratureformulas

Abstract base class for numerical quadrature formulas.

This class defines the interface that all quadrature implementations must follow. It provides the basic structure for implementing various quadrature rules while ensuring consistent access to quadrature data.

Attributes:

Name Type Description
quad_order

Order of the quadrature rule
quad_type

Type of quadrature (e.g., 'gauss-legendre', 'gauss-jacobi')
num_quad_points

Total number of quadrature points
Example

class MyQuadrature(Quadratureformulas): ... def init(self): ... super().init(quad_order=3, ... quad_type='custom', ... num_quad_points=9) ... def get_quad_values(self): ... # Implementation ... pass ... def get_num_quad_points(self): ... return self.num_quad_points

Note

This is an abstract base class. Concrete implementations must override: - get_quad_values() - get_num_quad_points()

The implementation should ensure proper initialization of: - Quadrature points - Quadrature weights - Number of quadrature points

Source code in scirex/core/sciml/fe/quadratureformulas.py 
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class Quadratureformulas:
    """Abstract base class for numerical quadrature formulas.

    This class defines the interface that all quadrature implementations must
    follow. It provides the basic structure for implementing various quadrature
    rules while ensuring consistent access to quadrature data.

    Attributes:
        quad_order: Order of the quadrature rule
        quad_type: Type of quadrature (e.g., 'gauss-legendre', 'gauss-jacobi')
        num_quad_points: Total number of quadrature points

    Example:
        >>> class MyQuadrature(Quadratureformulas):
        ...     def __init__(self):
        ...         super().__init__(quad_order=3,
        ...                         quad_type='custom',
        ...                         num_quad_points=9)
        ...     def get_quad_values(self):
        ...         # Implementation
        ...         pass
        ...     def get_num_quad_points(self):
        ...         return self.num_quad_points

    Note:
        This is an abstract base class. Concrete implementations must override:
        - get_quad_values()
        - get_num_quad_points()

        The implementation should ensure proper initialization of:
        - Quadrature points
        - Quadrature weights
        - Number of quadrature points
    """

    def __init__(self, quad_order: int, quad_type: str, num_quad_points: int):
        """
        Constructor for the Quadratureformulas_Quad2D class.

        Args:
            quad_order: Order of quadrature rule
            quad_type: Type of quadrature ('gauss-legendre' or 'gauss-jacobi')
            num_quad_points: Total number of quadrature points

        Returns:
            None
        """
        self.quad_order = quad_order
        self.quad_type = quad_type
        self.num_quad_points = num_quad_points

    @abstractmethod
    def get_quad_values(self):
        """
        Returns the quadrature weights, xi and eta values.

        Args:
            None

        Returns:
            weights: Weights for each quadrature point
            xi: x-coordinates of quadrature points in reference element
            eta: y-coordinates of quadrature points in reference element
        """

    @abstractmethod
    def get_num_quad_points(self):
        """
        Returns the number of quadrature points.

        Args:
            None

        Returns:
            num_quad_points: Total number of quadrature points
        """

__init__(quad_order, quad_type, num_quad_points)

Constructor for the Quadratureformulas_Quad2D class.

Parameters:

Name Type Description Default
quad_order int

Order of quadrature rule

 required
quad_type str

Type of quadrature ('gauss-legendre' or 'gauss-jacobi')

 required
num_quad_points int

Total number of quadrature points

 required

Returns:

Type Description

None
Source code in scirex/core/sciml/fe/quadratureformulas.py 
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def __init__(self, quad_order: int, quad_type: str, num_quad_points: int):
    """
    Constructor for the Quadratureformulas_Quad2D class.

    Args:
        quad_order: Order of quadrature rule
        quad_type: Type of quadrature ('gauss-legendre' or 'gauss-jacobi')
        num_quad_points: Total number of quadrature points

    Returns:
        None
    """
    self.quad_order = quad_order
    self.quad_type = quad_type
    self.num_quad_points = num_quad_points

get_num_quad_points() abstractmethod

Returns the number of quadrature points.

Returns:

Name Type Description
num_quad_points

Total number of quadrature points
Source code in scirex/core/sciml/fe/quadratureformulas.py 
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@abstractmethod
def get_num_quad_points(self):
    """
    Returns the number of quadrature points.

    Args:
        None

    Returns:
        num_quad_points: Total number of quadrature points
    """

get_quad_values() abstractmethod

Returns the quadrature weights, xi and eta values.

Returns:

Name Type Description
weights

Weights for each quadrature point
xi

x-coordinates of quadrature points in reference element
eta

y-coordinates of quadrature points in reference element
Source code in scirex/core/sciml/fe/quadratureformulas.py 
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@abstractmethod
def get_quad_values(self):
    """
    Returns the quadrature weights, xi and eta values.

    Args:
        None

    Returns:
        weights: Weights for each quadrature point
        xi: x-coordinates of quadrature points in reference element
        eta: y-coordinates of quadrature points in reference element
    """