Element Routine¶

Defines element routine for the model.

This file is a part of the coursework module Personal Programming Project (PPP) in M.Sc. Computational Materials Science, Technische Universität Bergakademie Freiberg.
This file is a part of the project Modeling of radiative heat-exchange using finite element method

This file consists of ElementRoutine that computes the element matrices after application of appropriate shape functions, as well as Gaussian Quadrature scheme.

class elementRoutine.ElementRoutine(mesh: Mesh, elem_num: int)¶

Bases: object

Class for element routine computations.

Parameters:

mesh (parser.Mesh) – Mesh object consisting of all information parsed from mesh file.
elem_num (int) – Element number as labeled in the mesh file.

elements¶

Dictionary consisting of all elements

Type:: dict

edgeNodes¶

Dictionary consisting of tags of nodes on the boundaries.

Type:: dict

input_parameters¶

Object consisting of all input parameters.

Type:: inputParams.InputParameters

nodes¶

Nodes of the element in consideration.

Type:: numpy.array

property B: array¶

Value of gradient (B) matrix at a given quadrature point.

Return type:: numpy.array

property J: array¶

Value of Jacobian at a given quadrature point.

Return type:: numpy.array

property N: array¶

Shape function array at a given quadrature point.

Return type:: numpy.array

compute_N(q_points: array) → None¶

Method to compute shape functions.

Parameters:: q_points (numpy.array) – Quadrature point.

compute_boundary_nodes(group_num: int) → array¶

compute_dN(q_points: array) → None¶

Method to compute derivative of shape function with respect to quadrature point.

Parameters:: q_points (numpy.array) – Quadrature point under consideration.

compute_element_routine() → None¶: Method for computation of element contributions.

compute_gradient_matrix() → None¶: Method to compute gradient (B) matrix at a given quadrature point.

compute_jacobian(q_points: array) → None¶

Method to compute jacobian value at a quadrature point.

Parameters:: q_points (numpy.array) – Quadrature point in consideration.

compute_quadrature() → None¶: Method to set quadrature points and weights depending on the dimensions of the mesh.

property dN: array¶

Value of shape function derivative at a quadrature point.

Return type:: numpy.array

property detJ: float¶

Value of determinant of jacobian at a given quadrature point.

Return type:: numpy.array

property element_capacitance¶

Value of the capacitance matrix for the element.

Return type:: numpy.array

property element_stiffness: array¶

Value of the stiffness matrix for the element.

Return type:: numpy.array

property load_vector: array¶

Value of the load vector for the element.

Return type:: numpy.array

property quadrature_points: array¶

Gaussian quadrature points.

Return type:: numpy.array

property quadrature_weights: array¶

Gaussian quadrature weights

Return type:: numpy.array