Project a scalar field onto an unstructured mesh

This example shows how to generate a correlated random field project it onto an unstructured mesh

import matplotlib.pyplot as plt

import spam.excursions
import spam.mesh

Create the random field

Generate a realisation of the correlated (Gaussian centered) Random Field in a cube of size 1x1x1

covarianceParameters = {
    "var": 1.0,
    "len_scale": 0.5,
}
nNodes = 100  # discretisation of the field
realisation = spam.excursions.simulateRandomField(nNodes=nNodes, covarianceParameters=covarianceParameters, dim=3)
plt.figure()
plt.imshow(realisation[0][nNodes // 2, :, :])
plt.title("2D Slice of the field")
plt.show()

Generating Field_0000... 27.73 seconds

Generate a cylindrical mesh

# Set the geometrical properties of the mesh
centre = [0.5, 0.5]
radius = 0.5
height = 1.0
lcar = 0.1  # average distance between nodes
points, connectivity = spam.mesh.createCylinder(centre, radius, height, lcar, vtkFile="cylinder")
# points, connectivity = spam.mesh.createCuboid([1, 1, 1], lcar, vtkFile="cube")

Projection

Set the geometrical properties of the mesh

field = {
    "origin": [0, 0, 0],
    "lengths": [1, 1, 1],
    "nCells": [nNodes - 1, nNodes - 1, nNodes - 1],
    "values": realisation,
}
thresholds = [0.2]
materials = spam.mesh.projectField(
    {"points": points, "cells": connectivity},
    field,
    thresholds=thresholds,
    writeConnectivity="spam_projection",
    vtkMesh="Hello",
)

Shift connectivity by 1 to start at 1

Returns the connectivity matrix and the material repartition

print(f"Connectivity matrix: {connectivity.shape} -> (node 1, node 2, node 3, node 4)")
print(f"Materials: {materials.shape} -> (phase number, sub volume, orientation x, orientation y, orientation z)")

Connectivity matrix: (4044, 4) -> (node 1, node 2, node 3, node 4)
Materials: (4044, 5) -> (phase number, sub volume, orientation x, orientation y, orientation z)

Notes

One can generate several fields and set them in the list field["values"] line 46. The same number of thresholds have to be set on line 48.