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Mesh Analysis

sigmaepsilon.mesh provides some useful classes and algorithms for mesh management and operations related to the geometry or the topology of polygonal meshes.

import pyvista as pv
import numpy as np
from sigmaepsilon.mesh import PolyData

d, h, a = 6.0, 15.0, 15.0
cyl = pv.CylinderStructured(
    center=(0.0, 0.0, 0.0),
    direction=(0.0, 0.0, 1.0),
    radius=np.linspace(d / 2, a / 2, 15),
    height=h,
    theta_resolution=100,
    z_resolution=40,
)
mesh: PolyData = PolyData.from_pv(cyl)

Nodal Distribution Factors

mesh.nodal_distribution_factors()

array([[1.        , 0.47580645, 0.23790323, ..., 0.23790323, 0.11895161,
        0.25      ],
       [0.52419355, 0.47794118, 0.23897059, ..., 0.23897059, 0.11948529,
        0.13104839],
       [0.52205882, 0.47972973, 0.23986486, ..., 0.23986486, 0.11993243,
        0.13051471],
       ...,
       [0.12807377, 0.12207031, 0.24414062, ..., 0.24414062, 0.48828125,
        0.51229508],
       [0.12792969, 0.12220149, 0.24440299, ..., 0.24440299, 0.48880597,
        0.51171875],
       [0.12779851, 0.25      , 0.5       , ..., 0.5       , 1.        ,
        0.51119403]])

Nodal Adjacency

To access the nodal adjacency matrix as a scipy sparse matrix:

mesh.nodal_adjacency(frmt="scipy-csr")

<60600x60600 sparse array of type '<class 'numpy.intc'>'
        with 1527274 stored elements in Compressed Sparse Row format>

mesh.nodal_adjacency(frmt="nx")

<networkx.classes.graph.Graph at 0x20a5d6d3820>

as an Awkward array:

mesh.nodal_adjacency(frmt="jagged")

[[0, 1, 15, 16, 1515, 1516, 1530, 1531],
 [0, 1, 2, 15, 16, 17, 1515, 1516, 1517, 1530, 1531, 1532],
 [1, 2, 3, 16, 17, 18, 1516, 1517, 1518, 1531, 1532, 1533],
 [2, 3, 4, 17, 18, 19, 1517, 1518, 1519, 1532, 1533, 1534],
 [3, 4, 5, 18, 19, 20, 1518, 1519, 1520, 1533, 1534, 1535],
 [4, 5, 6, 19, 20, 21, 1519, 1520, 1521, 1534, 1535, 1536],
 [5, 6, 7, 20, 21, 22, 1520, 1521, 1522, 1535, 1536, 1537],
 [6, 7, 8, 21, 22, 23, 1521, 1522, 1523, 1536, 1537, 1538],
 [7, 8, 9, 22, 23, 24, 1522, 1523, 1524, 1537, 1538, 1539],
 [8, 9, 10, 23, 24, 25, 1523, 1524, 1525, 1538, 1539, 1540],
 ...,
 [59060, 59061, 59062, 59075, 59076, ..., 60576, 60577, 60590, 60591, 60592],
 [59061, 59062, 59063, 59076, 59077, ..., 60577, 60578, 60591, 60592, 60593],
 [59062, 59063, 59064, 59077, 59078, ..., 60578, 60579, 60592, 60593, 60594],
 [59063, 59064, 59065, 59078, 59079, ..., 60579, 60580, 60593, 60594, 60595],
 [59064, 59065, 59066, 59079, 59080, ..., 60580, 60581, 60594, 60595, 60596],
 [59065, 59066, 59067, 59080, 59081, ..., 60581, 60582, 60595, 60596, 60597],
 [59066, 59067, 59068, 59081, 59082, ..., 60582, 60583, 60596, 60597, 60598],
 [59067, 59068, 59069, 59082, 59083, ..., 60583, 60584, 60597, 60598, 60599],
 [59068, 59069, 59083, 59084, 60583, 60584, 60598, 60599]]
-----------------------------------------------------------------------------
type: 60600 * var * int64

or as a Numba-jittable CSR matrix from sigmaepsilon.math:

mesh.nodal_adjacency(frmt="csr")

60600x60600 CSR matrix of 1527274 values.

Pseudo Peripheral Nodes

from sigmaepsilon.math.topology.graph import pseudo_peripheral_nodes

csr = mesh.nodal_adjacency(frmt="csr")
ppn = pseudo_peripheral_nodes(csr)

Rooted Level Structure

from sigmaepsilon.math.topology.graph import rooted_level_structure

rls = rooted_level_structure(csr)

K-Nearest-Neighbours with Scipy or SkLearn

from sigmaepsilon.mesh import grid, PolyData, PointData
from sigmaepsilon.mesh.cells import H8

size = 80, 60, 20
shape = 10, 8, 4
coords, topo = grid(size=size, shape=shape, eshape="H8")
pd = PointData(coords=coords)
cd = H8(topo=topo)
mesh = PolyData(pd, cd)
mesh.k_nearest_cell_neighbours(k=3, knn_options=dict(max_distance=10.0))[:5]

array([[0, 1, 4],
       [1, 2, 0],
       [2, 1, 3],
       [3, 2, 7],
       [4, 5, 0]], dtype=int64)