Updated Jupyter Book folder to include wave1D_prog and vib_undamped.

Author: rbanerjee20

fdm-jupyter-book/_build/.doctrees/index.doctree

@@ -79,6 +79,58 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
   </a>
  </li>
 </ul>
+<p class="caption">
+ <span class="caption-text">
+  Vibration ODEs
+ </span>
+</p>
+<ul class="nav sidenav_l1">
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html">
+   Finite difference discretization
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#implementation">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#visualization-of-long-time-simulations">
+   Visualization of long time simulations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#analysis-of-the-numerical-scheme">
+   Analysis of the numerical scheme
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#alternative-schemes-based-on-1st-order-equations">
+   Alternative schemes based on 1st-order equations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#energy-considerations">
+   Energy considerations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#the-euler-cromer-method">
+   The Euler-Cromer method
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#staggered-mesh">
+   Staggered mesh
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#exercises-and-problems">
+   Exercises and Problems
+  </a>
+ </li>
+</ul>
 <p class="caption">
  <span class="caption-text">
   Wave equations
@@ -95,6 +147,16 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
    Verification
   </a>
  </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html#exercises">
+   Exercises
+  </a>
+ </li>
 </ul>
 
 </nav>

fdm-jupyter-book/_build/html/genindex.html

@@ -39,7 +39,7 @@
     <script async="async" src="_static/sphinx-thebe.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
-    <link rel="next" title="Simulation of waves on a string" href="notebooks/wave/wave1D_fd1.html" />
+    <link rel="next" title="Finite difference discretization" href="notebooks/vib/vib_undamped.html" />
 
     <meta name="viewport" content="width=device-width, initial-scale=1">
     <meta name="docsearch:language" content="en">
@@ -79,6 +79,58 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
   </a>
  </li>
 </ul>
+<p class="caption">
+ <span class="caption-text">
+  Vibration ODEs
+ </span>
+</p>
+<ul class="nav sidenav_l1">
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html">
+   Finite difference discretization
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#implementation">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#visualization-of-long-time-simulations">
+   Visualization of long time simulations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#analysis-of-the-numerical-scheme">
+   Analysis of the numerical scheme
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#alternative-schemes-based-on-1st-order-equations">
+   Alternative schemes based on 1st-order equations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#energy-considerations">
+   Energy considerations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#the-euler-cromer-method">
+   The Euler-Cromer method
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#staggered-mesh">
+   Staggered mesh
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#exercises-and-problems">
+   Exercises and Problems
+  </a>
+ </li>
+</ul>
 <p class="caption">
  <span class="caption-text">
   Wave equations
@@ -95,6 +147,16 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
    Verification
   </a>
  </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html#exercises">
+   Exercises
+  </a>
+ </li>
 </ul>
 
 </nav>
@@ -188,6 +250,8 @@ <h1>Welcome to the Devito Book!<a class="headerlink" href="#welcome-to-the-devit
 <p>We would like to say a special thank you to H. P. Langtangen and S. Linge, the authors of the <a class="reference external" href="https://github.com/hplgit/fdm-book">book</a> that these tutorials were based upon (“Finite Difference Computing with PDEs - A Modern Software Approach”).</p>
 <div class="toctree-wrapper compound">
 </div>
+<div class="toctree-wrapper compound">
+</div>
 </div>
 
     <script type="text/x-thebe-config">
@@ -218,7 +282,7 @@ <h1>Welcome to the Devito Book!<a class="headerlink" href="#welcome-to-the-devit
 
     <div class='prev-next-bottom'>
 
-    <a class='right-next' id="next-link" href="notebooks/wave/wave1D_fd1.html" title="next page">Simulation of waves on a string</a>
+    <a class='right-next' id="next-link" href="notebooks/vib/vib_undamped.html" title="next page">Finite difference discretization</a>
 
     </div>
     <footer class="footer mt-5 mt-md-0">

fdm-jupyter-book/_build/html/index.html

@@ -83,6 +83,58 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
   </a>
  </li>
 </ul>
+<p class="caption">
+ <span class="caption-text">
+  Vibration ODEs
+ </span>
+</p>
+<ul class="nav sidenav_l1">
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html">
+   Finite difference discretization
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#implementation">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#visualization-of-long-time-simulations">
+   Visualization of long time simulations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#analysis-of-the-numerical-scheme">
+   Analysis of the numerical scheme
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#alternative-schemes-based-on-1st-order-equations">
+   Alternative schemes based on 1st-order equations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#energy-considerations">
+   Energy considerations
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#the-euler-cromer-method">
+   The Euler-Cromer method
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#staggered-mesh">
+   Staggered mesh
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/vib/vib_undamped.html#exercises-and-problems">
+   Exercises and Problems
+  </a>
+ </li>
+</ul>
 <p class="caption">
  <span class="caption-text">
   Wave equations
@@ -99,6 +151,16 @@ <h1 class="site-logo" id="site-title">The Devito Book</h1>
    Verification
   </a>
  </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html">
+   Implementation
+  </a>
+ </li>
+ <li class="toctree-l1">
+  <a class="reference internal" href="notebooks/wave/wave1D_prog.html#exercises">
+   Exercises
+  </a>
+ </li>
 </ul>
 
 </nav>

fdm-jupyter-book/_build/html/objects.inv

@@ -1,6 +1,11 @@
 - file: index.md
   numbered: true
 
+- chapter: Vibration ODEs
+  sections:
+  - file: notebooks/vib/vib_undamped.ipynb
+
 - chapter: Wave equations
   sections:
   - file: notebooks/wave/wave1D_fd1.ipynb
+  - file: notebooks/wave/wave1D_prog.ipynb

fdm-jupyter-book/_build/html/search.html

@@ -0,0 +1,80 @@
+#import matplotlib.pyplot as plt
+import scitools.std as plt
+import odespy
+import numpy as np
+
+def solver(alpha, ic, T, dt=0.05):
+    def f(u, t):
+        x_A, vx_A, y_A, vy_A, x_B, vx_B, y_B, vy_B = u
+        distance3 = np.sqrt((x_B-x_A)**2 + (y_B-y_A)**2)**3
+        system = [
+            vx_A,
+            1/(1.0 + alpha)*(x_B - x_A)/distance3,
+            vy_A,
+            1/(1.0 + alpha)*(y_B - y_A)/distance3,
+            vx_B,
+            -1/(1.0 + alpha**(-1))*(x_B - x_A)/distance3,
+            vy_B,
+            -1/(1.0 + alpha**(-1))*(y_B - y_A)/distance3,
+            ]
+        return system
+
+    Nt = int(round(T/dt))
+    t_mesh = np.linspace(0, Nt*dt, Nt+1)
+
+    solver = odespy.RK4(f)
+    solver.set_initial_condition(ic)
+    u, t = solver.solve(t_mesh)
+    x_A = u[:,0]
+    x_B = u[:,2]
+    y_A = u[:,4]
+    y_B = u[:,6]
+    return x_A, x_B, y_A, y_B, t
+
+def demo_circular():
+    # Mass B is at rest at the origin,
+    # mass A is at (1, 0) with vel. (0, 1)
+    ic = [1, 0, 0, 1, 0, 0, 0, 0]
+    x_A, x_B, y_A, y_B, t = solver(
+        alpha=0.001, ic=ic, T=2*np.pi, dt=0.01)
+    plt.plot(x_A, x_B, 'r2-', y_A, y_B, 'b2-',
+             legend=['A', 'B'],
+             daspectmode='equal') # x and y axis have same scaling
+    plt.savefig('tmp_circular.png')
+    plt.savefig('tmp_circular.pdf')
+    plt.show()
+
+def demo_two_stars(animate=True):
+    # Initial condition
+    ic = [0.6, 0, 0, 1,   # star A: velocity (0,1)
+          0, 0, 0, -0.5]  # star B: velocity (0,-0.5)
+    # Solve ODEs
+    x_A, x_B, y_A, y_B, t = solver(
+        alpha=0.5, ic=ic, T=4*np.pi, dt=0.05)
+    if animate:
+        # Animate motion and draw the objects' paths in time
+        for i in range(len(x_A)):
+            plt.plot(x_A[:i+1], x_B[:i+1], 'r-',
+                     y_A[:i+1], y_B[:i+1], 'b-',
+                     [x_A[0], x_A[i]], [x_B[0], x_B[i]], 'r2o',
+                     [y_A[0], y_A[i]], [y_B[0], y_B[i]], 'b4o',
+                     daspectmode='equal',  # axes aspect
+                     legend=['A', 'B', 'A', 'B'],
+                     axis=[-1, 1, -1, 1],
+                     savefig='tmp_%04d.png' % i,
+                     title='t=%.2f' % t[i])
+    else:
+        # Make a simple static plot of the solution
+        plt.plot(x_A, x_B, 'r-', y_A, y_B, 'b-',
+                 daspectmode='equal', legend=['A', 'B'],
+                 axis=[-1, 1, -1, 1], savefig='tmp_two_stars.png')
+    #plt.axes().set_aspect('equal')  # mpl
+    plt.show()
+
+if __name__ == '__main__':
+    import sys
+    if sys.argv[1] == 'circular':
+        demo_circular()
+    else:
+        demo_two_stars(True)
+    raw_input()