# Efficiently plot a finite element mesh solution with Matplotlib

I am looking for the most efficient way to plot a mesh using Matplotlib given the following information, coordinates of each node, what nodes belong to each element, and the value each node has. Below I have some example data and image showing what the mesh looks like

nodeinfo=[[0.000,0.000],[1.000,0.000],[2.000,0.500],[0.000,1.000],
[1.000,1.000],[1.750,1.300],[1.000,1.700]]
elementInfo=[[1,2,5],[5,4,1],[2,3,6],[6,5,2],[4,5,7],[5,6,7]]
nodevalues=[1,2,1,2,7,4,5]


nodeinfo is the coordinates of each nodes(e.g. node 7 has coordinates (1,1.7)), elementInfo gives what nodes each element is composed of (e.g. element 3 has nodes 2,3,6), nodevalues gives the value of each node(e.g. node 5 has value 7).

Using this info how can I plot meshes with matplotlib with a colour gradient showing the different values of the nodes(if possible it would be great if there was a colour gradient between nodes as each element is linear).

Note If you want to use it have created a bit of code that organizes the information into node objects.

class node:
# Initializer / Instance Attributes
def __init__(self, number, xCord, yCord):
self.number=number
self.value=1
self.isOnBoundary=False
self.xCord=xCord
self.yCord=yCord
self.boundaryType=None
self.element=[]

#makes all class variables callable
def __call__(self):
return self

def checkIfOnBoundary(self,boundarylist):
# Checks if the node is on the boundary when it is invoked
# If the node is not on the boundary then it is set to false

if self.number in boundarylist:
self.isOnBoundary=True
self.boundaryType=boundarylist[self.number][0]
if self.boundaryType == "Dirchlet":
self.value=boundarylist[self.number][1]
else:
self.isOnBoundary=False

def setElement(self,elementInfo):
#given a list in the form [element1,element2,...,elementn]
#where element1 is a list that contains all the nodes that are on that element
for element in elementInfo:
if self.number in element:
self.element.append(elementInfo.index(element)+1)

def setValue(self,value):
# changes the value of the node
self.value=value

def description(self):
return "Node Number: {}, Node Value: {}, Element Node Belongs to: {}, Is Node On the Boundary: {}".format(self.number, self.value, self.element, self.isOnBoundary)

nodeinfo=[[0.000,0.000],[1.000,0.000],[2.000,0.500],[0.000,1.000],
[1.000,1.000],[1.750,1.300],[1.000,1.700]]
elementInfo=[[1,2,5],[5,4,1],[2,3,6],[6,5,2],[4,5,7],[5,6,7]]
nodevalues=[1,2,1,2,7,4,5]

#create list of node objects which we will call on often
nodes=[]
for i in range(len(nodeinfo)):
print(i)
nodes.append(node(i+1,nodeinfo[i][0],nodeinfo[i][1]))
nodes[i].setElement(elementInfo)

#print information related to each object
for phi in nodes:
print(vars(phi))


You might be interested in trying other visualization tools such as ParaView, Mayavi or PyVista.

But, since the question is about Matplotlib, I would suggest that you use tricontour, tricontourf or tripcolor. They already accept the data in your format. Keep in mind that the enumeration of nodes starts from 0 in Python.

The following snippet show your data visualized.

import numpy as np
import matplotlib.pyplot as plt

nodes= np.array([
[0.000, 0.000],
[1.000, 0.000],
[2.000, 0.500],
[0.000, 1.000],
[1.000, 1.000],
[1.750, 1.300],
[1.000, 1.700]])
eles = np.array([
[1, 2, 5],
[5, 4, 1],
[2, 3, 6],
[6, 5, 2],
[4, 5, 7],
[5, 6, 7]])
node_vals = [1, 2, 1, 2, 7, 4, 5]

x, y = nodes.T
plt.tricontourf(x, y, eles - 1, node_vals, 12)
plt.colorbar()
plt.show()


• Thanks for the answer I didn't know what functions / packages were available to me in python as I usually use Mathematica for plotting. I'll make sure to experiment with the other options. Just two small questions. What is the '.T' for? And how do I add a legend showing what the color values mean?
– AzJ
Apr 19 '19 at 3:06
• The .T is the transpose of the array, to get the columns with the x and y coordinates. Apr 19 '19 at 4:36