# Testing script for 2 dimensional mesh import import functions2D import numpy import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm #Order of points NPoints=40 #Order of polynomials Ni=1 Nj=5 #Calculation #Create Mesh [x,y]=functions2D.Nodes2D(NPoints) [r,s]=functions2D.xytors(x,y) #Create Polynomials [a,b]=functions2D.rstoab(r,s) P=functions2D.Simplex2DP(a,b,Ni,Nj) #Check Vandermonde NVander=10 Vander=functions2D.Vandermonde2D(NVander, r, s) gradVander=functions2D.GradVandermonde2D(NVander,r,s) print Vander.shape print gradVander[0].shape print gradVander[1].shape #Plot plt.figure(1) plt.scatter(x,y,c=P,cmap=cm.jet)
# Testing script for 2 dimensional mesh import import functions2D import numpy import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm #Order of points NPoints = 40 #Order of polynomials Ni = 1 Nj = 5 #Calculation #Create Mesh [x, y] = functions2D.Nodes2D(NPoints) [r, s] = functions2D.xytors(x, y) #Create Polynomials [a, b] = functions2D.rstoab(r, s) P = functions2D.Simplex2DP(a, b, Ni, Nj) #Check Vandermonde NVander = 10 Vander = functions2D.Vandermonde2D(NVander, r, s) gradVander = functions2D.GradVandermonde2D(NVander, r, s) print Vander.shape print gradVander[0].shape print gradVander[1].shape #Plot plt.figure(1) plt.scatter(x, y, c=P, cmap=cm.jet)
# Purpose : Setup script, building operators, grid, metric, and connectivity tables. import globalVar2D as glb import functions2D import numpy # Definition of constants glb.Nfp = glb.N+1 glb.Np = (glb.N+1)*(glb.N+2)/2 glb.Nfaces=3 glb.NODETOL = 1e-12 # Compute nodal set [glb.x,glb.y] = functions2D.Nodes2D(glb.N) [glb.r,glb.s] = functions2D.xytors(glb.x,glb.y) # Build reference element matrices glb.V = functions2D.Vandermonde2D(glb.N,glb.r,glb.s) glb.invV = numpy.linalg.inv(glb.V) glb.MassMatrix = glb.invV.transpose().dot(glb.invV) [glb.Dr,glb.Ds] = functions2D.Dmatrices2D(glb.N, glb.r, glb.s, glb.V) # build coordinates of all the nodes va = glb.EToV[:,0] vb = glb.EToV[:,1] vc = glb.EToV[:,2] glb.x = 0.5*(-numpy.array([(glb.r+glb.s)]).transpose().dot(numpy.array([glb.VX[va]]))+numpy.array([(1+glb.r)]).transpose().dot(numpy.array([glb.VX[vb]]))+numpy.array([(1+glb.s)]).transpose().dot(numpy.array([glb.VX[vc]]))) glb.y = 0.5*(-numpy.array([(glb.r+glb.s)]).transpose().dot(numpy.array([glb.VY[va]]))+numpy.array([(1+glb.r)]).transpose().dot(numpy.array([glb.VY[vb]]))+numpy.array([(1+glb.s)]).transpose().dot(numpy.array([glb.VY[vc]]))) # find all the nodes that lie on each edge
# Purpose : Setup script, building operators, grid, metric, and connectivity tables.
import globalVar2D as glb
import functions2D
import numpy
# Definition of constants
glb.Nfp = glb.N + 1
glb.Np = (glb.N + 1) * (glb.N + 2) / 2
glb.Nfaces = 3
glb.NODETOL = 1e-12
# Compute nodal set
[glb.x, glb.y] = functions2D.Nodes2D(glb.N)
[glb.r, glb.s] = functions2D.xytors(glb.x, glb.y)
# Build reference element matrices
glb.V = functions2D.Vandermonde2D(glb.N, glb.r, glb.s)
glb.invV = numpy.linalg.inv(glb.V)
glb.MassMatrix = glb.invV.transpose().dot(glb.invV)
[glb.Dr, glb.Ds] = functions2D.Dmatrices2D(glb.N, glb.r, glb.s, glb.V)
# build coordinates of all the nodes
va = glb.EToV[:, 0]
vb = glb.EToV[:, 1]
vc = glb.EToV[:, 2]
glb.x = 0.5 * (
-numpy.array([(glb.r + glb.s)]).transpose().dot(numpy.array([glb.VX[va]]))
+ numpy.array([(1 + glb.r)]).transpose().dot(numpy.array([glb.VX[vb]])) +
numpy.array([(1 + glb.s)]).transpose().dot(numpy.array([glb.VX[vc]])))