Finite Element Bases¶
Interval Element Basis Functions¶
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class
FEMpy.FEBasis.IntervalBasis1D(basis_type)[source]¶ Defines a finite element basis function set on a one-dimensional interval.
Creates a complete set of finite element basis functions for a one-dimensional domain of either linear or quadratic basis types.
Parameters: basis_type ({101, ‘linear’, 102, ‘quadratic’}) – Finite element basis type. Can either be called as a integer code or a string identifier to indicate the type of basis function we are using.
- 101, ‘linear’ : 1-dimensional, linear basis.
- 102, ‘quadratic’ : 1-dimensional, quadratic basis.
Raises: TypeError– If the basis type is not a string identifier or an integer code.-
basis_type Basis type standardized to an integer code.
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fe_local_basis(x, vertices, basis_idx, derivative_order)[source]¶ Defines the finite element local basis functions.
Parameters: - x (float or array_like) – A value or array of points to evaluate the function on.
- vertices (array_like) – Global node coordinates for the mesh element En.
- basis_idx (int) – Local basis index value.
- derivative_order (int) – The derivative order to take the basis function to.
Returns: The local basis function (or derivative of funtion) evaluated at the points in x.
Return type:
2D Triangular Element Basis Functions¶
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class
FEMpy.FEBasis.TriangularBasis2D(basis_type)[source]¶ Defines a finite element basis function set on a two-dimensional domian with triangular elements.
Creates a complete set of finite element basis functions for a two-dimensional domain with triangular elements of either linear or quadratic basis types.
Parameters: - basis_type ({201, ‘linear’, ‘linear2D_tri’, 202, ‘quadratic’, ‘quadratic2D_tri’})
- Finite element basis type. Can either be called as a integer code or a string identifier to indicate the
- type of basis function we are using.
- - 201, ‘linear’, ‘linear2D_tri (1-dimensional, linear basis on triangular elements.)
- - 202, ‘quadratic’, ‘quadratic2D_tri (1-dimensional, quadratic basis on triangular elements.)
Raises: TypeError– If the basis type is not a string identifier or an integer code.-
fe_local_basis(coords, vertices, basis_idx, derivative_order)[source]¶ Defines the finite element local basis functions.
Parameters: - coords (array_like) – The x and y coordinate values to evaluate the function on. e.g.,
(`x`, `y`). - vertices (array_like) – Global node coordinates for all vertices of triangular mesh nodes on the mesh element En.
- basis_idx (int) – Local basis index value.
- derivative_order (tuple of int) – The derivative orders to take the basis function to. Should be specified as a tuple with the
orders corresponding to the coordinate axes in the basis functions. e.g.,
(`x_order`, `y_order`).
Returns: The local basis function (or derivative of function) evaluated at the points in coords.
Return type: - coords (array_like) – The x and y coordinate values to evaluate the function on. e.g.,