Upload ex6 and ex7

ex6/ex_6B.py

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+import numpy as np
+import matplotlib.pyplot as plt
+import adaptivity_schemes
+
+np.set_printoptions(precision=2)
+
+
+def lam_func(x):
+    n = len(x)
+    lam_vec = np.zeros(n)
+    for i in range(n):    
+        if (x[i] > 1/np.sqrt(2)):
+            lam_vec[i] = 10
+        else:
+            lam_vec[i] = 1
+    return lam_vec
+    
+
+
+def Solve_6B(mesh):
+    N = len(mesh) - 1   # number of elements
+
+    A = np.zeros((N + 1, N + 1))
+
+    lam_vec = lam_func(mesh)
+
+    for i in range(1, N + 1):
+        h = mesh[i] - mesh[i - 1]
+
+        a_11 = lam_vec[i]/h
+        a_12 = -lam_vec[i]/h
+        a_21 = -lam_vec[i]/h
+        a_22 = lam_vec[i]/h
+                                        
+        A[i - 1, i - 1] += a_11
+        A[i - 1, i] += a_12
+        A[i, i - 1] += a_21
+        A[i, i] += a_22
+
+    #print("A =\n", A)
+    
+    # take dirichlet data into account
+    u_g = np.zeros(N + 1)
+    u_g[0] = 0
+    u_g[N] = 1
+    #print("u_g =\n", u_g)
+
+    # remove first and last row of A
+    A_g = A[1:N, :]
+    #print("A_g =\n", A_g)
+
+    # assemble RHS with dirichlet data
+    f = -A_g.dot(u_g)
+    #print(f)
+
+    # matrix for the inner nodes (excluding nodes with dirichlet bcs)
+    A_0 = A[1:N, 1:N]   
+    #print(A_0)
+
+    # solve for u_0 (free dofs)
+    u_0 = np.linalg.solve(A_0, f)
+
+    # assemble "u = u_0 + u_g"
+    u = np.concatenate([[0], u_0, [1]])
+    #print("u =\n", u)
+
+    return u
+
+
+########## h-adaptivity ##########
+N = 2   # number of elements
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6B(mesh)
+
+plt.plot(mesh, u, '-o')
+plt.grid()
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.title("h-adaptivity")
+
+
+N_vec = ["0 refinements, " + str(N) + " elements"]
+refinements = 5   # number of refinements
+for i in range(refinements):
+    mesh = adaptivity_schemes.adapt_h(mesh, lam_func(mesh)*u, 0.9)
+    u = Solve_6B(mesh)
+    plt.plot(mesh, u, '-o')
+
+    N_vec.append(str(i + 1) + " refinements, " + str(len(mesh) - 1) + " elements")
+
+plt.legend(N_vec)
+plt.show()
+
+
+
+########## r-adaptivity ##########
+N = 5
+mesh = np.linspace(0, 1, N + 1)
+u = Solve_6B(mesh)
+plt.plot(mesh, u, '-o')
+title = "r-adaptivity with " + str(N) + " elements"
+plt.title(title)
+
+adaptations_vec = ["0 adaptations"]
+adaptations = 4   # number of iterations
+for i in range(adaptations):
+    mesh = adaptivity_schemes.adapt_r(mesh, lam_func(mesh)*u)
+    u = Solve_6B(mesh)
+    plt.plot(mesh, u, '-o')
+
+    adaptations_vec.append(str(i + 1) + " adaptations")
+
+
+plt.legend(adaptations_vec)
+plt.xlabel('x')
+plt.ylabel('u_h(x)')
+plt.grid()
+plt.show()
+
+