Application of Poisson and Helmholtz operators#
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from vampyr import vampyr3d as vp
from plotter import grid_plotter
MRA = vp.MultiResolutionAnalysis(box=[-16, 16], order=6)
prec = 1.0e-5
P_eps = vp.ScalingProjector(MRA, prec)
mu = 1.0
H = vp.HelmholtzOperator(MRA, mu, prec)
P = vp.PoissonOperator(MRA, prec)
def slater_function(x):
center = np.array([0.1, 0.2, 0.3])
r = np.linalg.norm(np.array(x) - center) # Calculate the distance from center
return np.exp(- 50.0 * np.abs(r)) # Return the Slater function value
def unit_charge_gaussian(x,b):
a = (b/np.pi)**(3./2.)
center = np.array([0.1, 0.2, 0.3])
r = np.linalg.norm(np.array(x) - center)
val = a * np.exp(-b * r**2)
return val
wide_charge = lambda x: unit_charge_gaussian(x,10)
narrow_charge = lambda x: unit_charge_gaussian(x,50)
center = [0.1, 0.2, 0.3]
power = [0, 0, 0]
b = 10.0
a = (b/np.pi)**(3./2.)
wideG = vp.GaussFunc(b, a, center, power)
b = 10.0
a = (b/np.pi)**(3./2.)
narrowG = vp.GaussFunc(b, a, center, power)
wide_charge_tree = P_eps(wideG)
narrow_charge_tree = P_eps(narrowG)
#slater_tree = P_eps(slater_function)
P_wide_tree = 4 * np.pi * P(wide_charge_tree)
P_narrow_tree = 4 * np.pi * P(narrow_charge_tree)
#H_slater_tree = 4 * np.pi * H(slater_tree)
print(wide_charge_tree.integrate()) # check if the total chatge integrates to 1
print(narrow_charge_tree.integrate()) # check if the total chatge integrates to 1
0.9999999999997281
0.9999999999997281
from plotter import grid_plotter
print("Narrow Gaussian")
grid_plotter(narrow_charge_tree)
grid_plotter(P_narrow_tree)
print("Wide Gaussian")
grid_plotter(wide_charge_tree)
grid_plotter(P_wide_tree)
Narrow Gaussian
Wide Gaussian
(<Figure size 900x900 with 1 Axes>, <Axes3DSubplot:>)
![../../_images/27f05f0358da630338e43b71226739af5ec4a999729763be9f77662167caf09b.png](../../_images/27f05f0358da630338e43b71226739af5ec4a999729763be9f77662167caf09b.png)
![../../_images/2107f4a08c79047a768de5dd9c650e383dfaec43762a359d59024d4d5b3050b6.png](../../_images/2107f4a08c79047a768de5dd9c650e383dfaec43762a359d59024d4d5b3050b6.png)
![../../_images/27f05f0358da630338e43b71226739af5ec4a999729763be9f77662167caf09b.png](../../_images/27f05f0358da630338e43b71226739af5ec4a999729763be9f77662167caf09b.png)
![../../_images/2107f4a08c79047a768de5dd9c650e383dfaec43762a359d59024d4d5b3050b6.png](../../_images/2107f4a08c79047a768de5dd9c650e383dfaec43762a359d59024d4d5b3050b6.png)
import matplotlib.pyplot as plt
def pot_point_charge(x):
center = np.array([0.1, 0.2, 0.3])
r = np.linalg.norm(np.array(x) - center)
val = 1 / r
return val
x_vec = np.linspace(-5,5,1001)
y1_vec = np.array([P_narrow_tree([x,0.2,0.3]) for x in x_vec ])
y2_vec = np.array([P_wide_tree([x,0.2,0.3]) for x in x_vec ])
y3_vec = np.array([pot_point_charge([x,0.2,0.3]) for x in x_vec ])
plt.plot(x_vec, y1_vec, "tab:red") # potential from narrow Gaussian
plt.plot(x_vec, y2_vec, "tab:blue") # potential from wide Gaussian
plt.plot(x_vec, y3_vec, "tab:green") # point charge potential
plt.ylim(0.0,12.0)
plt.show()
![../../_images/a10da0417b52902617dc4235d21c1f4b638993d2d2d1ec0f0951c31c819bda02.png](../../_images/a10da0417b52902617dc4235d21c1f4b638993d2d2d1ec0f0951c31c819bda02.png)
help(vp.Gaussian)
Help on class Gaussian in module vampyr._vampyr.vampyr3d:
class Gaussian(RepresentableFunction)
| Method resolution order:
| Gaussian
| RepresentableFunction
| pybind11_builtins.pybind11_object
| builtins.object
|
| Methods defined here:
|
| __init__(...)
| __init__(self: vampyr._vampyr.vampyr3d.Gaussian, arg0: float, arg1: float, arg2: List[float[3]], arg3: List[int[3]]) -> None
|
| __str__(...)
| __str__(self: vampyr._vampyr.vampyr3d.Gaussian) -> str
|
| coef(...)
| coef(self: vampyr._vampyr.vampyr3d.Gaussian) -> float
|
| exp(...)
| exp(self: vampyr._vampyr.vampyr3d.Gaussian, dim: int = 0) -> float
|
| overlap(...)
| overlap(self: vampyr._vampyr.vampyr3d.Gaussian, inp: vampyr._vampyr.vampyr3d.Gaussian) -> float
|
| periodify(...)
| periodify(self: vampyr._vampyr.vampyr3d.Gaussian, period: List[float[3]], std_dev: float = 4.0) -> mrcpp::GaussExp<3>
|
| pos(...)
| pos(self: vampyr._vampyr.vampyr3d.Gaussian) -> List[float[3]]
|
| pow(...)
| pow(self: vampyr._vampyr.vampyr3d.Gaussian, dim: int) -> int
|
| ----------------------------------------------------------------------
| Methods inherited from RepresentableFunction:
|
| __call__(...)
| __call__(self: vampyr._vampyr.vampyr3d.RepresentableFunction, arg0: List[float[3]]) -> float
|
| ----------------------------------------------------------------------
| Static methods inherited from pybind11_builtins.pybind11_object:
|
| __new__(*args, **kwargs) from pybind11_builtins.pybind11_type
| Create and return a new object. See help(type) for accurate signature.