-
Notifications
You must be signed in to change notification settings - Fork 0
/
VM15D.py
161 lines (142 loc) · 8.35 KB
/
VM15D.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
#
# BSD 2-Clause License
#
# Copyright (c) 2021, Cristel Chandre
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import numpy as xp
from scipy.fft import rfft, irfft, rfftfreq
from scipy.integrate import simpson
from VM15D_modules import integrate
from VM15D_dict import dict
def main():
integrate(VM15D(dict))
class VM15D:
def __repr__(self):
return '{self.__class__.__name__}({self.DictParams})'.format(self=self)
def __str__(self):
return '1.5D Vlasov-Maxwell equation ({self.__class__.__name__})'.format(self=self)
def __init__(self, dict):
for key in dict:
setattr(self, key, dict[key])
self.DictParams = dict
self.z = xp.linspace(-self.Lz, self.Lz, self.Nz, endpoint=False, dtype=xp.float64)
self.vx = xp.linspace(-self.Lvx, self.Lvx, self.Nvx, endpoint=False, dtype=xp.float64)
self.vz = xp.linspace(-self.Lvz, self.Lvz, self.Nvz, endpoint=False, dtype=xp.float64)
self.z_ = xp.linspace(-self.Lz, self.Lz, self.Nz+1, dtype=xp.float64)
self.vx_ = xp.linspace(-self.Lvx, self.Lvx, self.Nvx+1, dtype=xp.float64)
self.vz_ = xp.linspace(-self.Lvz, self.Lvz, self.Nvz+1, dtype=xp.float64)
self.kz = xp.pi / self.Lz * rfftfreq(self.Nz, d=1/self.Nz)
self.div = xp.divide(1, 1j * self.kz, where=self.kz!=0)
self.div[0] = 0
self.kvx = xp.pi / self.Lvx * rfftfreq(self.Nvx, d=1/self.Nvx)
self.kvz = xp.pi / self.Lvz * rfftfreq(self.Nvz, d=1/self.Nvz)
self.tail_indx = [(xp.s_[3*self.Nz//8:], xp.s_[:], xp.s_[:],), (xp.s_[:], xp.s_[3*self.Nvx//8:], xp.s_[:],), (xp.s_[:], xp.s_[:], xp.s_[3*self.Nvz//8:])]
f_ = self.f_init(self.z_[:, None, None], self.vx_[None, :, None], self.vz_[None, None, :])
self.f = f_[:-1, :-1, :-1]
self.f0 = simpson(simpson(simpson(f_, self.vz_, axis=2), self.vx_, axis=1), self.z_)
self.Ez = lambda rho: irfft(self.div * self.rfft_(rho))
if self.integrator_kinetic == 'position-Verlet':
self.integr2_coeff = [0.5, 1, 0.5]
self.integr2_type = [1, 2, 1]
self.integr5_coeff = [0.25, 0.5, 0.25, 0.25, 0.5, 0.25, 1, 0.25, 0.5, 0.25, 0.25, 0.5, 0.25]
self.integr5_type = [1, 2, 1, 3, 4, 3, 5, 3, 4, 3, 1, 2, 1]
def Hpx(self, f, Ex, Ez, By, dt):
ft = irfft(xp.exp(-1j * self.kvz[None, None, :] * self.vx[None, :, None] * By[:, None, None] * dt) * self.rfft_(f, axis=2), axis=2)
f_ = xp.pad(f, ((0, 1),), mode='wrap')
Etx = Ex - simpson(simpson(self.vx_[None, :, None] * f_, self.vz_, axis=2), self.vx_, axis=1)[:-1] * dt
return ft, Etx, Ez, By
def Hpz(self, f, Ex, Ez, By, dt):
ft = f.copy()
for coeff, type in zip(self.integr2_coeff, self.integr2_type):
if type == 1:
ft = irfft(xp.exp(-1j * self.vz[None, None, :] * self.kz[:, None, None] * coeff * dt) * self.rfft_(ft, axis=0), axis=0)
elif type == 2:
ft = irfft(xp.exp(1j * self.vz[None, None, :] * By[:, None, None] * self.kvx[None, :, None] * coeff * dt) * self.rfft_(ft, axis=1), axis=1)
Etz = self.Ez(simpson(simpson(xp.pad(ft, ((0, 1),), mode='wrap'), self.vz_, axis=2), self.vx_, axis=1)[:-1])
return ft, Ex, Etz, By
def Hcz(self, f, Ex, Ez, By, dt):
ft = irfft(xp.exp(-1j * Ez[:, None, None] * self.kvz[None, None, :] * dt) * self.rfft_(f, axis=2), axis=2)
return ft, Ex, Ez, By
def Hcx(self, f, Ex, Ez, By, dt):
ft = irfft(xp.exp(-1j * Ex[:, None, None] * self.kvx[None, :, None] * dt) * self.rfft_(f, axis=1), axis=1)
Bty = By - irfft(1j * self.kz * self.rfft_(Ex)) * dt
return ft, Ex, Ez, Bty
def Hcy(self, f, Ex, Ez, By, dt):
Etx = Ex - irfft(1j * self.kz * self.rfft_(By)) * dt
return f, Etx, Ez, By
def closure(self, f):
rho, Px, Pz, S20, S11, S02, Ex, By = xp.split(f, 8)
Pix = Px + irfft(self.div * self.rfft_(By)) - self.alpha
S21 = - S11 * Pix + S20 * S11 / Pix
S12 = - S02 * Pix + S11**2 / Pix
S03 = - S11 / S20 * (3 * S02 - 2 * S11**2 / S20) * Pix + S11**3 / S20 / Pix + self.lam * (S02 - S11**2 / S20)**(4/3)
return S21, S12, S03
def eqn_3f(self, t, f):
rho, Px, Pz, S20, S11, S02, Ex, By = xp.split(f, 8)
S21, S12, S03 = self.closure(f)
Ez = self.Ez(rho)
rho_dot = - irfft(1j * self.kz * self.rfft_(rho * Pz))
Px_dot = - Pz * irfft(1j * self.kz * self.rfft_(Px)) + Ex - Pz * By - irfft(1j * self.kz * self.rfft_(rho**2 * S11)) / rho
Pz_dot = - Pz * irfft(1j * self.kz * self.rfft_(Pz)) + Ez + Px * By - irfft(1j * self.kz * self.rfft_(rho**3 * S02)) / rho
S20_dot = - Pz * irfft(1j * self.kz * self.rfft_(S20)) - 2 * rho * S11 * (By + irfft(1j * self.kz * self.rfft_(Px))) - irfft(1j * self.kz * self.rfft_(rho**2 * S21)) / rho
S11_dot = - Pz * irfft(1j * self.kz * self.rfft_(S11)) + By * S20 / rho - rho * S02 * (By + irfft(1j * self.kz * self.rfft_(Px))) - irfft(1j * self.kz * self.rfft_(rho**3 * S12)) / rho**2
S02_dot = - Pz * irfft(1j * self.kz * self.rfft_(S02)) + 2 * By * S11 / rho - irfft(1j * self.kz * self.rfft_(rho**4 * S03)) / rho**3
Ex_dot = -irfft(1j * self.kz * self.rfft_(By)) - rho * Px
By_dot = -irfft(1j * self.kz * self.rfft_(Ex))
return xp.hstack((rho_dot, Px_dot, Pz_dot, S20_dot, S11_dot, S02_dot, Ex_dot, By_dot))
def compute_moments(self, f):
f_ = xp.pad(f, ((0, 1),), mode='wrap')
rho = simpson(simpson(f_, self.vz_, axis=2), self.vx_, axis=1)
Px = simpson(simpson(self.vx_[None, :, None] * f_, self.vz_, axis=2), self.vx_, axis=1) / rho
Pz = simpson(simpson(self.vz_[None, None, :] * f_, self.vz_, axis=2), self.vx_, axis=1) / rho
S20 = simpson(simpson((self.vx_[None, :, None] - Px[:, None, None])**2 * f_, self.vz_, axis=2), self.vx_, axis=1) / rho
S11 = simpson(simpson((self.vx_[None, :, None] - Px[:, None, None]) * (self.vz_[None, None, :] - Pz[:, None, None]) * f_, self.vz_, axis=2), self.vx_, axis=1) / rho**2
S02 = simpson(simpson((self.vz_[None, None, :] - Pz[:, None, None])**2 * f_, self.vz_, axis=2), self.vx_, axis=1) / rho**3
return xp.hstack((rho[:-1], Px[:-1], Pz[:-1], S20[:-1], S11[:-1], S02[:-1]))
def rfft_(self, f, axis=0):
fft_f = rfft(f, axis=axis)
fft_f[xp.abs(fft_f) <= self.precision] = 0
fft_f[self.tail_indx[axis][:f.ndim]] = 0
return fft_f
def energy_fluid(self, f):
rho, Px, Pz, S20, S11, S02, Ex, By = [xp.pad(_, (0, 1), mode='wrap') for _ in xp.split(f, 8)]
Ez = xp.pad(self.Ez(rho), (0, 1), mode='wrap')
return simpson(rho * (Px**2 + Pz**2) + rho * S20 + rho**3 * S02 + Ex**2 + Ez**2 + By**2, self.z_) / 2
def energy_kinetic(self, f, Ex, Ez, By):
f_ = xp.pad(f, ((0, 1),), mode='wrap')
Ex_ = xp.pad(Ex, (0, 1), mode='wrap')
Ez_ = xp.pad(Ez, (0, 1), mode='wrap')
By_ = xp.pad(By, (0, 1), mode='wrap')
return (simpson(simpson(simpson((self.vx_[None, :, None]**2 + self.vz_[None, None, :]**2) * f_, self.vz_, axis=2), self.vx_, axis=1), self.z_) + simpson(Ex_**2 + Ez_**2 + By_**2, self.z_)) / 2
def casimirs_kinetic(self, f, n):
f_ = xp.pad(f, ((0, 1),), mode='wrap')
return [simpson(simpson(simpson(f_**m, self.vz_, axis=2), self.vx_, axis=1), self.z_) for m in range(1, n+1)]
def casimirs_fluid(self, f, n):
rho, Px, Pz, S20, S11, S02, Ex, By = [xp.pad(_, (0, 1), mode='wrap') for _ in xp.split(f, 8)]
Pix = xp.pad(Px[:-1] + irfft(self.div * self.rfft_(By[:-1])) - self.alpha, (0, 1), mode='wrap')
Cl = simpson(rho * (S02 - S11**2 / S20)**(1/3), self.z_)
Ct = [simpson(rho * (Pix**2 + S20) * (Pix / (Pix**2 + S20))**m, self.z_) for m in range(n-1)]
return xp.hstack((Cl, Ct))
if __name__ == "__main__":
main()