skripta za izracun tem valovanja z metodo koncnih elementov
Andrej
commit
d6e7153b84
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r_zila = 0.5;
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r_oklop = 3;
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n_zila = 80;
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n_oklop = 50;
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SetFactory("OpenCASCADE");
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Disk(1) = {1, 0, 0, r_zila, r_zila};
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Disk(2) = {0, 0, 0, r_oklop, r_oklop};
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BooleanDifference{ Surface{2}; Delete; }{ Surface{1}; Delete; }
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Physical Surface("dielektrik", 1) = {2};
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Physical Curve("zila", 2) = {1};
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Physical Curve("oklop", 3) = {2};
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Transfinite Curve {1} = n_zila Using Progression 1;
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Transfinite Curve {2} = n_oklop Using Progression 1;
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r_zila = 0.5;
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r_oklop = 3;
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n_zila = 80;
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n_oklop = 40;
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SetFactory("OpenCASCADE");
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Disk(1) = {0, 0, 0, r_zila, r_zila};
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Disk(2) = {0, 0, 0, r_oklop, r_oklop};
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BooleanDifference{ Surface{2}; Delete; }{ Surface{1}; Delete; }
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Physical Surface("dielektrik", 1) = {2};
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Physical Curve("zila", 2) = {1};
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Physical Curve("oklop", 3) = {2};
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Transfinite Curve {1} = n_zila Using Progression 1;
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Transfinite Curve {2} = n_oklop Using Progression 1;
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@ -0,0 +1,14 @@
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r_zila = 0.5;
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r_oklop = 3;
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n_zila = 80;
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n_oklop = 10;
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SetFactory("OpenCASCADE");
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Disk(1) = {0, 0, 0, r_zila, r_zila};
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Rectangle(2) = {-r_oklop/2, -r_oklop/2, 0, r_oklop, r_oklop, 0};
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BooleanDifference{ Surface{2}; Delete; }{ Surface{1}; Delete; }
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Physical Surface("dielektrik", 1) = {2};
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Physical Curve("zila", 2) = {1};
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Physical Curve("oklop", 3) = {3, 5, 4, 2};
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Transfinite Curve {1} = n_zila Using Progression 1;
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Transfinite Curve {3, 5, 4, 2} = n_oklop Using Progression 1;
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@ -0,0 +1,940 @@
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<?xml version="1.0" encoding="UTF-8"?>
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<dolfin xmlns:dolfin="http://fenicsproject.org">
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<mesh_function type="uint" dim="2" size="935">
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<entity index="0" value="1"/>
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<entity index="791" value="1"/>
|
||||
<entity index="792" value="1"/>
|
||||
<entity index="793" value="1"/>
|
||||
<entity index="794" value="1"/>
|
||||
<entity index="795" value="1"/>
|
||||
<entity index="796" value="1"/>
|
||||
<entity index="797" value="1"/>
|
||||
<entity index="798" value="1"/>
|
||||
<entity index="799" value="1"/>
|
||||
<entity index="800" value="1"/>
|
||||
<entity index="801" value="1"/>
|
||||
<entity index="802" value="1"/>
|
||||
<entity index="803" value="1"/>
|
||||
<entity index="804" value="1"/>
|
||||
<entity index="805" value="1"/>
|
||||
<entity index="806" value="1"/>
|
||||
<entity index="807" value="1"/>
|
||||
<entity index="808" value="1"/>
|
||||
<entity index="809" value="1"/>
|
||||
<entity index="810" value="1"/>
|
||||
<entity index="811" value="1"/>
|
||||
<entity index="812" value="1"/>
|
||||
<entity index="813" value="1"/>
|
||||
<entity index="814" value="1"/>
|
||||
<entity index="815" value="1"/>
|
||||
<entity index="816" value="1"/>
|
||||
<entity index="817" value="1"/>
|
||||
<entity index="818" value="1"/>
|
||||
<entity index="819" value="1"/>
|
||||
<entity index="820" value="1"/>
|
||||
<entity index="821" value="1"/>
|
||||
<entity index="822" value="1"/>
|
||||
<entity index="823" value="1"/>
|
||||
<entity index="824" value="1"/>
|
||||
<entity index="825" value="1"/>
|
||||
<entity index="826" value="1"/>
|
||||
<entity index="827" value="1"/>
|
||||
<entity index="828" value="1"/>
|
||||
<entity index="829" value="1"/>
|
||||
<entity index="830" value="1"/>
|
||||
<entity index="831" value="1"/>
|
||||
<entity index="832" value="1"/>
|
||||
<entity index="833" value="1"/>
|
||||
<entity index="834" value="1"/>
|
||||
<entity index="835" value="1"/>
|
||||
<entity index="836" value="1"/>
|
||||
<entity index="837" value="1"/>
|
||||
<entity index="838" value="1"/>
|
||||
<entity index="839" value="1"/>
|
||||
<entity index="840" value="1"/>
|
||||
<entity index="841" value="1"/>
|
||||
<entity index="842" value="1"/>
|
||||
<entity index="843" value="1"/>
|
||||
<entity index="844" value="1"/>
|
||||
<entity index="845" value="1"/>
|
||||
<entity index="846" value="1"/>
|
||||
<entity index="847" value="1"/>
|
||||
<entity index="848" value="1"/>
|
||||
<entity index="849" value="1"/>
|
||||
<entity index="850" value="1"/>
|
||||
<entity index="851" value="1"/>
|
||||
<entity index="852" value="1"/>
|
||||
<entity index="853" value="1"/>
|
||||
<entity index="854" value="1"/>
|
||||
<entity index="855" value="1"/>
|
||||
<entity index="856" value="1"/>
|
||||
<entity index="857" value="1"/>
|
||||
<entity index="858" value="1"/>
|
||||
<entity index="859" value="1"/>
|
||||
<entity index="860" value="1"/>
|
||||
<entity index="861" value="1"/>
|
||||
<entity index="862" value="1"/>
|
||||
<entity index="863" value="1"/>
|
||||
<entity index="864" value="1"/>
|
||||
<entity index="865" value="1"/>
|
||||
<entity index="866" value="1"/>
|
||||
<entity index="867" value="1"/>
|
||||
<entity index="868" value="1"/>
|
||||
<entity index="869" value="1"/>
|
||||
<entity index="870" value="1"/>
|
||||
<entity index="871" value="1"/>
|
||||
<entity index="872" value="1"/>
|
||||
<entity index="873" value="1"/>
|
||||
<entity index="874" value="1"/>
|
||||
<entity index="875" value="1"/>
|
||||
<entity index="876" value="1"/>
|
||||
<entity index="877" value="1"/>
|
||||
<entity index="878" value="1"/>
|
||||
<entity index="879" value="1"/>
|
||||
<entity index="880" value="1"/>
|
||||
<entity index="881" value="1"/>
|
||||
<entity index="882" value="1"/>
|
||||
<entity index="883" value="1"/>
|
||||
<entity index="884" value="1"/>
|
||||
<entity index="885" value="1"/>
|
||||
<entity index="886" value="1"/>
|
||||
<entity index="887" value="1"/>
|
||||
<entity index="888" value="1"/>
|
||||
<entity index="889" value="1"/>
|
||||
<entity index="890" value="1"/>
|
||||
<entity index="891" value="1"/>
|
||||
<entity index="892" value="1"/>
|
||||
<entity index="893" value="1"/>
|
||||
<entity index="894" value="1"/>
|
||||
<entity index="895" value="1"/>
|
||||
<entity index="896" value="1"/>
|
||||
<entity index="897" value="1"/>
|
||||
<entity index="898" value="1"/>
|
||||
<entity index="899" value="1"/>
|
||||
<entity index="900" value="1"/>
|
||||
<entity index="901" value="1"/>
|
||||
<entity index="902" value="1"/>
|
||||
<entity index="903" value="1"/>
|
||||
<entity index="904" value="1"/>
|
||||
<entity index="905" value="1"/>
|
||||
<entity index="906" value="1"/>
|
||||
<entity index="907" value="1"/>
|
||||
<entity index="908" value="1"/>
|
||||
<entity index="909" value="1"/>
|
||||
<entity index="910" value="1"/>
|
||||
<entity index="911" value="1"/>
|
||||
<entity index="912" value="1"/>
|
||||
<entity index="913" value="1"/>
|
||||
<entity index="914" value="1"/>
|
||||
<entity index="915" value="1"/>
|
||||
<entity index="916" value="1"/>
|
||||
<entity index="917" value="1"/>
|
||||
<entity index="918" value="1"/>
|
||||
<entity index="919" value="1"/>
|
||||
<entity index="920" value="1"/>
|
||||
<entity index="921" value="1"/>
|
||||
<entity index="922" value="1"/>
|
||||
<entity index="923" value="1"/>
|
||||
<entity index="924" value="1"/>
|
||||
<entity index="925" value="1"/>
|
||||
<entity index="926" value="1"/>
|
||||
<entity index="927" value="1"/>
|
||||
<entity index="928" value="1"/>
|
||||
<entity index="929" value="1"/>
|
||||
<entity index="930" value="1"/>
|
||||
<entity index="931" value="1"/>
|
||||
<entity index="932" value="1"/>
|
||||
<entity index="933" value="1"/>
|
||||
<entity index="934" value="1"/>
|
||||
</mesh_function>
|
||||
</dolfin>
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
r_zila = 0.5;
|
||||
r_oklop = 3;
|
||||
n_zila = 80;
|
||||
n_oklop = 50;
|
||||
|
||||
SetFactory("OpenCASCADE");
|
||||
Disk(1) = {0, 0, 0, r_zila, r_zila};
|
||||
Disk(2) = {0, 0, 0, r_oklop, 0.5*r_oklop};
|
||||
BooleanDifference{ Surface{2}; Delete; }{ Surface{1}; Delete; }
|
||||
Physical Surface("dielektrik", 1) = {2};
|
||||
Physical Curve("zila", 2) = {1};
|
||||
Physical Curve("oklop", 3) = {2};
|
||||
Transfinite Curve {1} = n_zila Using Progression 1;
|
||||
Transfinite Curve {2} = n_oklop Using Progression 1;
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,17 @@
|
|||
w = 0.8e-3;
|
||||
d = 32e-6;
|
||||
h = 1.6e-3;
|
||||
W = 5*w;
|
||||
|
||||
SetFactory("OpenCASCADE");
|
||||
Rectangle(1) = {-w/2, 0, 0, w, d, 0};
|
||||
Rectangle(2) = {-W/2, -h/2, 0, W, h, 0};
|
||||
BooleanDifference{ Surface{2}; Delete; }{ Surface{1}; Delete; }
|
||||
Physical Surface("dielektrik", 1) = {2};
|
||||
Physical Curve("signal", 2) = {4, 3, 2, 1};
|
||||
Physical Curve("gnd", 3) = {8, 5};
|
||||
Physical Curve("strani", 4) = {6, 7};
|
||||
Transfinite Curve {4, 2} = 5 Using Progression 1;
|
||||
Transfinite Curve {3, 1} = 30 Using Progression 1;
|
||||
Transfinite Curve {8, 5} = 50 Using Progression 1;
|
||||
Transfinite Curve {6, 7} = 15 Using Progression 1;
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,4 @@
|
|||
$I$,1.587683737682743,A
|
||||
$Z_0$,62.984836102152215,\ohm
|
||||
$C$,85.01743830691181,pF\per\metre
|
||||
$L$,337.2717935248947,nH\per\metre
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
velicina,FEM,analično,enote,napaka
|
||||
$I$,1.4799117786125573,1.4864136437608977,A,-0.43741963588880184
|
||||
$Z_0$,67.5715954458797,67.27602401911606,\ohm,0.439341401447334
|
||||
$C$,79.25265419345939,79.1751819962321,pF\per\metre,0.0978490927005213
|
||||
$L$,361.8613193411615,358.35189404068905,nH\per\metre,0.9793237761076143
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
$I$,2.25507989038385,A
|
||||
$Z_0$,44.34432696882345,\ohm
|
||||
$C$,120.7478854118662,pF\per\metre
|
||||
$L$,237.44097645189865,nH\per\metre
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
$I$,2.0541699124167185,A
|
||||
$Z_0$,48.681464661484895,\ohm
|
||||
$C$,109.99576988969797,pF\per\metre
|
||||
$L$,260.67732529965474,nH\per\metre
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
$I$,1.6176838349767209,A
|
||||
$Z_0$,61.816776453996674,\ohm
|
||||
$C$,88.9077872061038,pF\per\metre
|
||||
$L$,339.7445587269718,nH\per\metre
|
||||
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|
|
@ -0,0 +1,178 @@
|
|||
#!/usr/bin/python3
|
||||
|
||||
from fenics import *
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from sys import argv
|
||||
|
||||
from scipy.constants import epsilon_0, mu_0
|
||||
|
||||
primeri = ('koax','izmaknjen','potlacen','kvadratni','stripline')
|
||||
|
||||
if argv[1] in primeri:
|
||||
problem = argv[1]
|
||||
else:
|
||||
print('Neznan primer. Nadaljujem s koax.')
|
||||
problem = 'koax'
|
||||
shrani = True #spravi vse rezultate v fajle?
|
||||
|
||||
mreza = Mesh('geometrija/{}.xml'.format(problem))
|
||||
domena = MeshFunction('size_t', mreza,
|
||||
'geometrija/{}_physical_region.xml'.format(problem))
|
||||
rob = MeshFunction('size_t', mreza,
|
||||
'geometrija/{}_facet_region.xml'.format(problem))
|
||||
|
||||
dx = Measure('dx', domain=mreza, subdomain_data=domena)
|
||||
ds = Measure('ds', domain=mreza, subdomain_data=rob)
|
||||
|
||||
V = FunctionSpace(mreza, 'P', 2)
|
||||
|
||||
napetost = 100
|
||||
zila = DirichletBC(V, Constant(napetost), rob, 2)
|
||||
oklop = DirichletBC(V, Constant(0), rob, 3)
|
||||
r_pogoji = [zila, oklop]
|
||||
eps_r = 2.55
|
||||
|
||||
u = TrialFunction(V)
|
||||
v = TestFunction(V)
|
||||
a = dot(grad(u), grad(v))*dx
|
||||
L = Constant(0)*v*dx
|
||||
u = Function(V)
|
||||
solve(a == L, u, r_pogoji)
|
||||
|
||||
plot(mreza, linewidth=0.5)
|
||||
p = plot(u)
|
||||
cp = plt.colorbar(p)
|
||||
cp.set_label('Elektricni potencial V (V)')
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-V.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
E = -grad(u)
|
||||
plot(mreza, linewidth=0.5)
|
||||
p = plot(E, zorder=3)
|
||||
cp = plt.colorbar(p)
|
||||
cp.set_label('Elektricno polje E (V/m)')
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-E.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
Z_w = np.sqrt(mu_0/epsilon_0/eps_r)
|
||||
cross_z = lambda w: as_vector((-w[1],+w[0]))
|
||||
H = cross_z(E)/Z_w
|
||||
|
||||
plot(mreza, linewidth=0.5)
|
||||
p = plot(H, zorder=3)
|
||||
cp = plt.colorbar(p)
|
||||
cp.set_label('Magnetno polje H (A/m)')
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-H.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
nhat = FacetNormal(mreza)
|
||||
cross_t = lambda w,x: w[0]*x[1]-w[1]*x[0]
|
||||
k = cross_t(nhat, H)
|
||||
tok = assemble(-k*ds(2))
|
||||
Z0 = napetost/tok
|
||||
|
||||
C = epsilon_0*eps_r/napetost**2 * assemble(E**2 * dx(1))
|
||||
L = mu_0/tok**2 * assemble(H**2 * dx(1))
|
||||
|
||||
print(tok, Z0, C, L)
|
||||
if shrani:
|
||||
with open('izracuni/{}-out.txt'.format(problem), 'w') as out:
|
||||
out.write('$I$,{},A\n'.format(tok))
|
||||
out.write('$Z_0$,{},\\ohm\n'.format(Z0))
|
||||
out.write('$C$,{},pF\\per\\metre\n'.format(C*1e12))
|
||||
out.write('$L$,{},nH\\per\\metre'.format(L*1e9))
|
||||
|
||||
# nadaljni del kode relevanten samo za koaksilani vod
|
||||
# izračuna analitske vrednosti in jih za primer polj
|
||||
# primerja z analitsko resitvijo
|
||||
if problem == 'koax':
|
||||
b = 3
|
||||
a = 0.5
|
||||
lg = np.log(b/a)
|
||||
u_anal = lambda r: napetost/lg*np.log(r/a)
|
||||
E_anal = lambda r: napetost/lg/r
|
||||
H_anal = lambda r: E_anal(r)/Z_w
|
||||
tok_anal = 2*np.pi*napetost/lg/Z_w
|
||||
Z0_anal = 1/2/np.pi*Z_w*lg
|
||||
C_anal = 2*np.pi*eps_r*epsilon_0/lg
|
||||
L_anal = mu_0/2/np.pi*lg
|
||||
|
||||
print(tok_anal, tok)
|
||||
print(Z0_anal, Z0)
|
||||
print(C_anal, C)
|
||||
print(L_anal, L)
|
||||
if shrani:
|
||||
with open('izracuni/{}-out.txt'.format(problem), 'w') as out:
|
||||
out.write('velicina,FEM,analično,enote,napaka\n')
|
||||
out.write('$I$,{},{},A,'.format(tok,tok_anal))
|
||||
out.write('{}\n'.format((tok-tok_anal)/tok_anal*100))
|
||||
out.write('$Z_0$,{},{},\\ohm,'.format(Z0,Z0_anal))
|
||||
out.write('{}\n'.format((Z0-Z0_anal)/Z0_anal*100))
|
||||
out.write('$C$,{},{},pF\\per\\metre,'.format(C*1e12,C_anal*1e12))
|
||||
out.write('{}\n'.format((C-C_anal)/C_anal*100))
|
||||
out.write('$L$,{},{},nH\\per\\metre,'.format(L*1e9,L_anal*1e9))
|
||||
out.write('{}'.format((L-L_anal)/L_anal*100))
|
||||
|
||||
x = np.linspace(a, b, 100)
|
||||
y = np.zeros(len(x))
|
||||
|
||||
primer_ana_e = E_anal(x)
|
||||
primer_fem_e = np.array(list(map(project(E),zip(x,y))))[:,0]
|
||||
plt.plot(x, primer_ana_e, label='Analitsko')
|
||||
plt.plot(x, primer_fem_e, '--', label='FEniCS')
|
||||
plt.xlabel('Polmer (m)')
|
||||
plt.ylabel('Elektricno polje E (V/m)')
|
||||
plt.grid()
|
||||
plt.legend()
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-anal-e.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
plt.plot(x, (primer_ana_e-primer_fem_e)/primer_ana_e*100)
|
||||
plt.xlabel('Polmer (m)')
|
||||
plt.ylabel('Relativna napaka %')
|
||||
plt.grid()
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-napaka-e.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
primer_ana_h = H_anal(x)
|
||||
primer_fem_h = np.array(list(map(project(H),zip(x,y))))[:,1]
|
||||
plt.plot(x, primer_ana_h, label='Analitsko')
|
||||
plt.plot(x, primer_fem_h, '--', label='FEniCS')
|
||||
plt.xlabel('Polmer (m)')
|
||||
plt.ylabel('Magnetno polje H (V/m)')
|
||||
plt.grid()
|
||||
plt.legend()
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-anal-h.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
plt.plot(x, (primer_ana_h-primer_fem_h)/primer_ana_h*100)
|
||||
plt.xlabel('Polmer (m)')
|
||||
plt.ylabel('Relativna napaka %')
|
||||
plt.grid()
|
||||
if shrani:
|
||||
plt.savefig('slike/{}-napaka-h.pdf'.format(problem),bbox_inches='tight')
|
||||
plt.show()
|
||||
|
||||
if problem == 'stripline':
|
||||
def We(W, b):
|
||||
if W/b > 0.35:
|
||||
return W
|
||||
else:
|
||||
We_b = W/b-(0.35-W/b)**2
|
||||
return We_b*b
|
||||
|
||||
W = 0.8e-3
|
||||
b = 1.6e-3
|
||||
tmp = b/(We(W,b)+0.441*b)
|
||||
Z0strip = 30*np.pi/np.sqrt(eps_r)*tmp
|
||||
print(Z0strip)
|
||||
print(Z0)
|
||||
napaka = (Z0strip-Z0)/Z0*100
|
||||
print(napaka)
|
||||
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Reference in New Issue