interpolation functions verification

modules/shape.py

@@ -162,8 +162,10 @@ def test_interpolation_functions(x1,x2,xI,L,shape_type):
  import numpy as np
  import matplotlib.pyplot as plt
 
+ # particle position 
  x = np.linspace(x1,x2,num=500);
 
+ # interpolation function values and its gradients
  ni = np.zeros_like(x)
  dni = np.zeros_like(x)
 
@@ -186,4 +188,45 @@ def test_interpolation_functions(x1,x2,xI,L,shape_type):
  plt.legend()
  plt.ylabel(r"$N_I$, $dN_I/dx$")
  plt.xlabel(r"x")
- plt.show()
+ plt.show()
+
+def get_interpolation_functions(x1,x2,xI,L,shape_type):
+ """
+ Returns the interpolation functions Ni and its gradients dNi
+
+ Arguments
+ ---------
+ x1 : float
+ initial particle position
+ x2 : float
+ final particle position
+ xI : float
+ fixed node position
+ L : float
+ element length
+ shape_type: string
+ interpolation function type, may be 'linear' or 'cpGIMP'
+ """
+ import numpy as np
+ import matplotlib.pyplot as plt
+
+ # particle position 
+ x = np.linspace(x1,x2,num=500);
+
+ # interpolation function values and its gradients
+ ni = np.zeros_like(x)
+ dni = np.zeros_like(x)
+
+ # linear shape function
+ if (shape_type=='linear'):
+ for i in range(len(x)):
+ ni[i] = NiLinear(x[i],xI,L)
+ dni[i] = dNiLinear(x[i],xI,L)
+
+ # cpGIMP shape function
+ elif (shape_type=='cpGIMP'):
+ for i in range(len(x)):
+ ni[i] = NicpGIMP(L,L/4,x[i],xI)
+ dni[i] = dNicpGIMP(L,L/4,x[i],xI)
+
+ return [x, ni, dni]

tests/interpolation_functions_test.py

@@ -0,0 +1,55 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Mar 17 08:52:30 2021
+
+Author
+------
+Fabricio Fernandez (<[email protected]>)
+
+Purpose
+-------
+
+This examples tests the interpolation functions and its derivative.
+
+"""
+
+import matplotlib.pyplot as plt
+
+# include the modules' path to the current path
+import sys
+sys.path.append("..") 
+
+# local modules
+from modules import shape as shape# for interpolation
+
+# domain
+L = 2
+
+# elements
+nelem = 2
+
+# cell dimension
+le = L/nelem 
+
+# get linear interpolation functions values in nodes
+[x1,n1_linear,dn1_linear] = shape.get_interpolation_functions(x1=0,x2=L,xI=0,L=L/nelem,shape_type="linear")
+[x2,n2_linear,dn2_linear] = shape.get_interpolation_functions(x1=0,x2=L,xI=L/2,L=L/nelem,shape_type="linear")
+[x3,n3_linear,dn3_linear] = shape.get_interpolation_functions(x1=0,x2=L,xI=L,L=L/nelem,shape_type="linear")
+
+plt.plot(x1,n1_linear,"--",label="n1-linear")
+plt.plot(x2,n2_linear,"--",label="n2-linear")
+plt.plot(x3,n3_linear,"--",label="n3-linear")
+plt.plot(x1,n1_linear+n2_linear+n3_linear,"--",label="n1+n2+n3-linear")
+plt.legend()
+
+# get cpgimp interpolation functions values
+[x1,n1_cpgimp,dn1_cpgimp] = shape.get_interpolation_functions(x1=0,x2=L,xI=0,L=L/nelem,shape_type="cpGIMP")
+[x2,n2_cpgimp,dn2_cpgimp] = shape.get_interpolation_functions(x1=0,x2=L,xI=L/2,L=L/nelem,shape_type="cpGIMP")
+[x3,n3_cpgimp,dn3_cpgimp] = shape.get_interpolation_functions(x1=0,x2=L,xI=L,L=L/nelem,shape_type="cpGIMP")
+
+plt.plot(x1,n1_cpgimp, label="n1-cpGIMP")
+plt.plot(x2,n2_cpgimp, label="n2-cpGIMP")
+plt.plot(x3,n3_cpgimp, label="n3-cpGIMP")
+plt.plot(x1,n1_cpgimp+n2_cpgimp+n3_cpgimp, label="n1+n2+n3-cpGIMP")
+plt.legend()