Package hedge :: Module element :: Class Element

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Class Element

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Instance Methods

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basis_functions(self)
Get a sequence of functions that form a basis of the approximation space.

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grad_basis_functions(self)
Get the gradient functions of the basis_functions(), in the same order.

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vandermonde(self)

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inverse_mass_matrix(self)
Return the inverse of the mass matrix of the unit element with respect to the nodal coefficients.

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mass_matrix(self)
Return the mass matrix of the unit element with respect to the nodal coefficients.

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grad_vandermonde(self)
Compute the Vandermonde matrices of the grad_basis_functions().

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differentiation_matrices(self)
Return matrices that map the nodal values of a function to the nodal values of its derivative in each of the unit coordinate directions.

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multi_face_mass_matrix(self)
Return a matrix that combines the effect of multiple face mass matrices applied to a vector of the shape:

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lifting_matrix(self)
Return a matrix that combines the effect of the inverse mass matrix applied after the multi-face mass matrix to a vector of the shape:

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find_diff_mat_permutation(self, target_idx)
Find a permuation p such that: source code

Inherited from object: __delattr__, __getattribute__, __hash__, __init__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __str__

Properties

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Inherited from object: __class__

Method Details

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vandermonde(self)

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Decorators:

@memoize_method

inverse_mass_matrix(self)

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Return the inverse of the mass matrix of the unit element with respect to the nodal coefficients. Divide by the Jacobian to obtain the global mass matrix.

Decorators:

@memoize_method

mass_matrix(self)

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Return the mass matrix of the unit element with respect to the nodal coefficients. Multiply by the Jacobian to obtain the global mass matrix.

Decorators:

@memoize_method

grad_vandermonde(self)

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Compute the Vandermonde matrices of the grad_basis_functions(). Return a list of these matrices.

Decorators:

@memoize_method

differentiation_matrices(self)

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Return matrices that map the nodal values of a function to the nodal values of its derivative in each of the unit coordinate directions.

Decorators:

@memoize_method

multi_face_mass_matrix(self)

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Return a matrix that combines the effect of multiple face mass matrices applied to a vector of the shape:

   [face_1_dofs]+[face_2_dofs]+...+[face_n_dofs]

Observe that this automatically maps this vector to a volume contribution.

Decorators:

@memoize_method

lifting_matrix(self)

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Return a matrix that combines the effect of the inverse mass matrix applied after the multi-face mass matrix to a vector of the shape:

   [face_1_dofs]+[face_2_dofs]+...+[face_n_dofs]

Observe that this automatically maps this vector to a volume contribution.

Decorators:

@memoize_method

find_diff_mat_permutation(self, target_idx)

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Find a permuation p such that:

   diff_mats = self.differentiation_matrices()
   diff_mats[0][p][:,p] == diff_mats[target_idx]

The permutation is returned as a numpy array of type intp.