Most efficient way to plot finite element mesh using matplotlib?

Question

My question is fairly simple but for those who need more context see the wikipedia page on finite element methods.

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))

Carlos · Accepted Answer · 2020-01-29T16:47:06.540

First, use matplotlib.tri.Triangulation(x, y, triangles) to create an unstructured triangular grid, where:

x is a 1D list containing the x-coordinate of each node;
y is a 1D list containing the y-coordinate of each node;
triangles is a "2D list" containing the nodes of each triangle (0 based index);

Second, use matplotlib.pyplot.triplot(triangulation, linespec) to plot just the mesh (lines only), where:

triangulation is the instance created by matplotlib.tri.Triangulation(x, y, triangles);
linespec is the line specification;

Third, use matplotlib.pyplot.tricontourf(triangulation, scalars) to plot the scalar field contours , where:

triangulation is the instance created by matplotlib.tri.Triangulation(x, y, triangles);
scalars a 1D list containing the nodal scalar data;

Finally, use matplotlib.pyplot.colorbar() and matplotlib.pyplot.show().

Full code:

import matplotlib.pyplot as plt
import matplotlib.tri as tri

nodes_x = [0.000, 1.000, 2.000, 0.000, 1.000, 1.750, 1.000]
nodes_y = [0.000, 0.000, 0.500, 1.000, 1.000, 1.300, 1.700]
scalars = [1.000, 2.000, 1.000, 2.000, 7.000, 4.000, 5.000]
elements = [
    [0, 1, 4],
    [4, 3, 0],
    [1, 2, 5],
    [5, 4, 1],
    [3, 4, 6],
    [4, 5, 6]
    ]

triangulation = tri.Triangulation(nodes_x, nodes_y, elements)
plt.triplot(triangulation, '-k')
plt.tricontourf(triangulation, scalars)
plt.colorbar()
plt.show()

Output:

If you want to visualize other types of 2D-elements (quadrangles or higher-order elements), you must first "split" these into triangles. However, if you want to visualize 3D-elements, or if you want to make your life easier and your code more efficient/faster for large meshes, you must abandon matplotlib and use something like VTK.

EDIT

Check my answer on the following question to plot FEM meshes that contain quadrangles:

How can I plot 2d FEM results using matplotlib?

Most efficient way to plot finite element mesh using matplotlib?

1 Answers1