Mesh¶

mozart.mesh.rectangle.interval(a, b, M, degree)[source]¶

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]])

mozart.mesh.rectangle.unit_interval(N)[source]¶

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]])