Testing differential operators (Div, Grad, Curl)

SimPEG/tests/test_curl.py

@@ -0,0 +1,48 @@
+import numpy as np
+
+import sys
+sys.path.append('../')
+from TensorMesh import TensorMesh
+from getDiffop import getCurlMatrix
+
+
+err=0.
+print '>> Test Curl operator'
+for i in range(4):
+    icount=i+1
+    nc = 2**icount
+    # Define the mesh    
+    h1 = np.ones((1,nc))/nc
+    h2 = np.ones((1,nc))/nc
+    h3 = np.ones((1,nc))/nc
+    h = [h1, h2, h3]
+    x0 = np.zeros((3, 1))
+    M = TensorMesh(h, x0)
+    #n = M.plotGrid()
+
+    # Generate DIV matrix
+    CURL = getCurlMatrix(h)
+    #Test function
+    fun = lambda x: np.cos(x)  # i (cos(y)) + j (cos(z)) + k (cos(x))
+    sol = lambda x: np.sin(x)  # i (sin(z)) + j (sin(x)) + k (sin(y))
+    
+    Ex = fun(M.gridEx[:,1])
+    Ey = fun(M.gridEy[:,2])
+    Ez = fun(M.gridEz[:,0])
+    E = np.concatenate((Ex,Ey,Ez))     
+
+    Fx = sol(M.gridFx[:,2])
+    Fy = sol(M.gridFy[:,0])
+    Fz = sol(M.gridFz[:,1])
+    curlE_anal = np.concatenate((Fx,Fy,Fz))     
+
+    curlE = CURL*E    
+    err = np.linalg.norm((curlE-curlE_anal), np.inf)
+
+    if icount == 1:
+        print 'h       |   inf norm   | error ratio'        
+        print '---------------------------------------'                
+        print '%6.4f  |  %8.2e  |'% (h1[0,0], err)
+    else:
+        print '%6.4f  |  %8.2e  |  %6.4f' % (h1[0,0], err, err_old/err)
+    err_old = err            

SimPEG/tests/test_div.py

@@ -5,16 +5,18 @@ sys.path.append('../')
 from TensorMesh import TensorMesh
 from getDIV import getDivMatrix, getarea, getvol
 
-# Define the mesh
+
 err=0.
+print '>> Test face Divergence operator'
 for i in range(4):
-    icount=i+1;
-    nc = 2*icount;
-    h1 = np.pi/nc*np.ones((1,nc))
-    h2 = np.pi/nc*np.ones((1,nc))
-    h3 = np.pi/nc*np.ones((1,nc))
+    icount=i+1
+    nc = 2**icount
+    # Define the mesh        
+    h1 = np.ones((1,nc))/nc
+    h2 = np.ones((1,nc))/nc
+    h3 = np.ones((1,nc))/nc
     h = [h1, h2, h3]
-    x0 = -np.pi/2*np.ones((3, 1))
+    x0 = np.zeros((3, 1))
     M = TensorMesh(h, x0)
     #n = M.plotGrid()
 
@@ -34,12 +36,13 @@ for i in range(4):
      
     area = getarea(h)
     vol = getvol(h)
-    err = np.linalg.norm((divF-divF_anal)*np.sqrt(vol), 2)
+    #err = np.linalg.norm((divF-divF_anal)*np.sqrt(vol), 2)
+    err = np.linalg.norm((divF-divF_anal), np.inf)
+
     if icount == 1:
-        err1 = err
-        print 'h       |   2 norm   | error ratio'        
+        print 'h       |   inf norm   | error ratio'        
         print '---------------------------------------'                
         print '%6.4f  |  %8.2e  |'% (h1[0,0], err)
     else:
-        print '%6.4f  |  %8.2e  |  %6.4f' % (h1[0,0], err, err1/err)
-        
+        print '%6.4f  |  %8.2e  |  %6.4f' % (h1[0,0], err, err_old/err)
+    err_old = err    

SimPEG/tests/test_grad.py

@@ -0,0 +1,46 @@
+import numpy as np
+
+import sys
+sys.path.append('../')
+from TensorMesh import TensorMesh
+from getDiffop import getGradMatrix
+
+
+err=0.
+print '>> Test nodal Gradient operator'    
+for i in range(4):
+    icount=i+1
+    nc = 2**icount
+    # Define the mesh    
+    h1 = np.ones((1,nc))/nc
+    h2 = np.ones((1,nc))/nc
+    h3 = np.ones((1,nc))/nc
+    h = [h1, h2, h3]
+    x0 = np.zeros((3, 1))
+    M = TensorMesh(h, x0)
+    #n = M.plotGrid()
+
+    # Generate DIV matrix
+    GRAD = getGradMatrix(h)
+    #Test function
+    fun = lambda x, y, z: (np.cos(x)+np.cos(y)+np.cos(z))    
+    sol = lambda x: -np.sin(x) # i (sin(x)) + j (sin(y)) + k (sin(z))
+    
+    phi = fun(M.gridN[:,0], M.gridN[:,1], M.gridN[:,2])
+    gradE = GRAD*phi
+
+    Ex = sol(M.gridEx[:,0])
+    Ey = sol(M.gridEy[:,1])
+    Ez = sol(M.gridEz[:,2])
+
+    gradE_anal = np.concatenate((Ex,Ey,Ez))     
+    err = np.linalg.norm((gradE-gradE_anal), np.inf)
+
+    if icount == 1:
+        print 'h       |   inf norm   | error ratio'        
+        print '---------------------------------------'                
+        print '%6.4f  |  %8.2e  |'% (h1[0,0], err)
+    else:
+        print '%6.4f  |  %8.2e  |  %6.4f' % (h1[0,0], err, err_old/err)
+    err_old = err    
+