First commit

tests/analytical_solutions.py

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+import numpy as np
+
+from gprMax.constants import c, e0
+from gprMax.utilities import rvalue
+from gprMax.waveforms import Waveform
+
+
+def hertzian_dipole_fs(timewindow, dt, dxdydz, rx):
+    """Analytical solution of a z-directed Hertzian dipole in free space with a Gaussian current waveform (http://dx.doi.org/10.1016/0021-9991(83)90103-1).
+    
+    Args:
+        timewindow (float): Length of time window (seconds).
+        dt (float): Time step (seconds).
+        dxdydz (float): Tuple of spatial resolution (metres).
+        rx (float): Tuple of coordinates of receiver position relative to transmitter position (metres).
+        
+    Returns:
+        fields (float): Array contain electric and magnetic field components.
+    """
+
+    # Waveform
+    w = Waveform()
+    w.type = 'gaussiandot'
+    w.amp = 1
+    w.freq = 1e9
+    
+    # Waveform integral
+    wint = Waveform()
+    wint.type = 'gaussian'
+    wint.amp = w.amp
+    wint.freq = w.freq
+
+    # Waveform first derivative
+    wdot = Waveform()
+    wdot.type = 'gaussiandotdot'
+    wdot.amp = w.amp
+    wdot.freq = w.freq
+
+    # Time
+    iterations = rvalue(timewindow / dt)
+    time = np.linspace(0, timewindow, iterations)
+
+    # Spatial resolution
+    dx = dxdydz[0]
+    dy = dxdydz[1]
+    dz = dxdydz[2]
+
+    # Coordinates of Rx relative to Tx
+    x = rx[0]
+    y = rx[1]
+    z = rx[2]
+    if z == 0:
+        sign_z = 1
+    else:
+        sign_z = np.sign(z)
+
+    # Coordinates of Rx for Ex FDTD component
+    Ex_x = x + 0.5 * dx
+    Ex_y = y
+    Ex_z = z - 0.5 * dz
+    Er_x = np.sqrt((Ex_x**2 + Ex_y**2 + Ex_z**2))
+    tau_Ex = Er_x / c
+
+    # Coordinates of Rx for Ey FDTD component
+    Ey_x = x
+    Ey_y = y + 0.5 * dy
+    Ey_z = z - 0.5 * dz
+    Er_y = np.sqrt((Ey_x**2 + Ey_y**2 + Ey_z**2))
+    tau_Ey = Er_y / c
+
+    # Coordinates of Rx for Ez FDTD component
+    Ez_x = x
+    Ez_y = y
+    Ez_z = z
+    Er_z = np.sqrt((Ez_x**2 + Ez_y**2 + Ez_z**2))
+    tau_Ez = Er_z / c
+
+    # Coordinates of Rx for Hx FDTD component
+    Hx_x = x
+    Hx_y = y + 0.5 * dy
+    Hx_z = z
+    Hr_x = np.sqrt((Hx_x**2 + Hx_y**2 + Hx_z**2))
+    tau_Hx = Hr_x / c
+
+    # Coordinates of Rx for Hy FDTD component
+    Hy_x = x + 0.5 * dx
+    Hy_y = y
+    Hy_z = z
+    Hr_y = np.sqrt((Hy_x**2 + Hy_y**2 + Hy_z**2))
+    tau_Hy = Hr_y / c
+
+    # Coordinates of Rx for Hz FDTD component
+    Hz_x = x + 0.5 * dx
+    Hz_y = y + 0.5 * dy
+    Hz_z = z - 0.5 * dz
+    Hr_z = np.sqrt((Hz_x**2 + Hz_y**2 + Hz_z**2))
+    tau_Hz = Hr_z / c
+
+    # Initialise fields
+    fields = np.zeros((iterations, 6))
+
+    # Calculate fields
+    for timestep in range(iterations):
+        
+        # Calculate values for waveform
+        fint_Ex = wint.calculate_value((timestep * dt) - tau_Ex, dt) * dx
+        f_Ex = w.calculate_value((timestep * dt) - tau_Ex, dt) * dx
+        fdot_Ex = wdot.calculate_value((timestep * dt) - tau_Ex, dt) * dx
+        
+        fint_Ey = wint.calculate_value((timestep * dt) - tau_Ey, dt) * dy
+        f_Ey= w.calculate_value((timestep * dt) - tau_Ey, dt) * dy
+        fdot_Ey = wdot.calculate_value((timestep * dt) - tau_Ey, dt) * dy
+        
+        fint_Ez = wint.calculate_value((timestep * dt) - tau_Ez, dt) * dz
+        f_Ez = w.calculate_value((timestep * dt) - tau_Ez, dt) * dz
+        fdot_Ez = wdot.calculate_value((timestep * dt) - tau_Ez, dt) * dz
+        
+        fint_Hx = wint.calculate_value((timestep * dt) - tau_Hx, dt) * dx
+        f_Hx = w.calculate_value((timestep * dt) - tau_Hx, dt) * dx
+        fdot_Hx = wdot.calculate_value((timestep * dt) - tau_Hx, dt) * dx
+        
+        fint_Hy = wint.calculate_value((timestep * dt) - tau_Hy, dt) * dy
+        f_Hy= w.calculate_value((timestep * dt) - tau_Hy, dt) * dy
+        fdot_Hy = wdot.calculate_value((timestep * dt) - tau_Hy, dt) * dy
+        
+        fint_Hz = wint.calculate_value((timestep * dt) - tau_Hz, dt) * dz
+        f_Hz = w.calculate_value((timestep * dt) - tau_Hz, dt) * dz
+        fdot_Hz = wdot.calculate_value((timestep * dt) - tau_Hz, dt) * dz
+        
+        # Ex
+        fields[timestep, 0] = ((Ex_x * Ex_z) / (4 * np.pi * e0 * Er_x**5)) * (3 * (fint_Ex + (tau_Ex * f_Ex)) + (tau_Ex**2 * fdot_Ex))
+        
+        # Ey
+        try:
+            tmp = Ey_y / Ey_x
+        except ZeroDivisionError:
+            tmp = 0
+        fields[timestep, 1] = tmp * ((Ey_x * Ey_z) / (4 * np.pi * e0 * Er_y**5)) * (3 * (fint_Ey + (tau_Ey * f_Ey)) + (tau_Ey**2 * fdot_Ey))
+
+        # Ez
+        fields[timestep, 2] = (1 / (4 * np.pi * e0 * Er_z**5)) * ((2 * Ez_z**2 - (Ez_x**2 + Ez_y**2)) * (fint_Ez + (tau_Ez * f_Ez)) - (Ez_x**2 + Ez_y**2) * tau_Ez**2 * fdot_Ez)
+
+        # Hx
+        fields[timestep, 3] = - (Hx_y / (4 * np.pi * Hr_x**3)) * (f_Hx + (tau_Hx * fdot_Hx))
+
+        # Hy
+        try:
+            tmp = Hy_x / Hy_y
+        except ZeroDivisionError:
+            tmp = 0
+        fields[timestep, 4] = - tmp * (- (Hy_y / (4 * np.pi * Hr_y**3)) * (f_Hy + (tau_Hy * fdot_Hy)))
+
+        # Hz
+        fields[timestep, 5] = 0
+
+    return fields
+