import numpy as np
[docs]def unit_interval(N):
"""
Computes the coordinates of nodes and elements.
Parameters
- ``N`` (``int``) : Number of nodes
Returns
- ``c4n`` (``float array``) : coordinates of nodes
- ``n4e`` (``int array``) : elements
Example
>>> c4n, n4e = unit_interval(4)
>>> c4n
array([ 0. , 0.33333333, 0.66666667, 1. ])
>>> n4e
array([[0, 1],
[1, 2],
[2, 3]])
"""
c4n = np.linspace(0, 1, N)
n4e = np.array([[item,item+1] for item in range(0,N-1)], dtype=np.int32)
return (c4n, n4e)
[docs]def interval(a, b, M, degree):
"""
Generates mesh information on an interval [a,b].
Parameters
- ``a`` (``float``) : coordinate of left-end point of the interval
- ``b`` (``float``) : coordinate of right-end point of the interval
- ``M`` (``int``) : the number of elements
- ``degree`` (``int``) : polynomial degree for the approximate solution
Returns
- ``c4n`` (``float array``) : coordinates for nodes
- ``n4e`` (``int array``) : nodes for elements
- ``n4db`` (``int array``) : nodes for Dirichlet boundary
- ``ind4e`` (``int array``) : indices for elements
Example
>>> c4n, n4e, n4db, ind4e = interval(0,1,4,2)
>>> c4n
array([ 0. , 0.125, 0.25 , 0.375, 0.5 , 0.625, 0.75 , 0.875, 1. ])
>>> n4e
array([[0, 2],
[2, 4],
[4, 6],
[6, 8]])
>>> n4db
array([0, 8])
>>> ind4e
array([[0, 1, 2],
[2, 3, 4],
[4, 5, 6],
[6, 7, 8]])
"""
nrNodes = M*degree + 1; # the number of nodes on the mesh in terms of M and degree
c4n = np.linspace(a, b, nrNodes)
n4e = np.array([[degree*item, degree*item+degree] for item in range(0,M)], dtype=np.int32)
n4db = np.array([0, nrNodes - 1])
ind4e = np.array([np.arange(degree*item,degree*item+degree+1,1) for item in range(0,M)], dtype=np.int32)
return (c4n, n4e, n4db, ind4e)
def unit_square(h):
print("unit_square is called.")