mimetic_basis_polynomials_2d.py¶
Node, edge and face polynomials in the 2d reference domain .
grid2d¶
Let A=(a1, a2)
, B=(b1,b2,b3)
. Then
grid2d (A
, B
) refers to a sequence of coordinates,
(a1, b1)
, (a2, b1)
, (a1, b2)
, (a2, b2)
,
(a1, b3)
, (a2, b3)
. Namely, we
first do a meshgrid
(A
, B
), then put the coordinates
into a sequence one by one picking along A
direction firstly, B
direction secondly and finally C
direction. Also see grid2d()
.
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[mimetic_basis_polynomials_2d.py]
.
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- class mimetic_basis_polynomials_2d.MimeticBasisPolynomials2D(nodes_rho, nodes_tau)[source]¶
A wrapper of basis node, edge, face polynomials in the 2d reference domain .
- Parameters:
nodes_rho (1d np.array) – The nodes on which the 1D mimetic polynomials are built along the first axis ().
nodes_tau (1d np.array) – The nodes on which the 1D mimetic polynomials are built along the second axis ().
- Example:
>>> bf = MimeticBasisPolynomials2D('Lobatto-3', 'Lobatto-3') >>> bf.degree # N = nodes_rho = nodes_tau = 3 [3, 3] >>> rho = np.linspace(-1, 1, 5) >>> tau = np.linspace(-1, 1, 6) >>> NP = bf.node_polynomials(rho, tau) >>> NP.shape # 4^2=16 node polynomials evaluated at 5*6=30 points (16, 30) >>> EP_rho, EP_tau = bf.edge_polynomials(rho, tau) >>> EP_rho.shape # 3*4=12 edge polynomials (12, 30) >>> FP = bf.face_polynomials(rho, tau) >>> FP.shape # 3*3=9 face polynomials (9, 30)
- mimetic_basis_polynomials_2d.grid2d(A, B)[source]¶
The function to compute the grid of two sets of nodes.
- Parameters:
A (1d data object) – The first (along ) set of nodes.
B (1d data object) – The second (along ) set of nodes.
- Returns:
A tuple of three outputs:
(1d np.array) The grided coordinates.
(1d np.array) The grided coordinates.
- Example:
>>> A = np.array([1, 2]) >>> B = np.array([3, 4, 5]) >>> x, y = grid2d(A, B) >>> D = np.vstack((x,y)).T >>> D array([[1, 3], [2, 3], [1, 4], [2, 4], [1, 5], [2, 5]])
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