commit d6e7153b8481e01b28e1e13ffb574e10ddb441b3 Author: Andrej Date: Mon Aug 30 10:35:33 2021 +0200 skripta za izracun tem valovanja z metodo koncnih elementov diff --git a/geometrija/izmaknjen.geo b/geometrija/izmaknjen.geo new file mode 100644 index 0000000..29743e5 --- /dev/null +++ b/geometrija/izmaknjen.geo @@ -0,0 +1,14 @@ +r_zila = 0.5; +r_oklop = 3; +n_zila = 80; +n_oklop = 50; + +SetFactory("OpenCASCADE"); +Disk(1) = {1, 0, 0, r_zila, r_zila}; +Disk(2) = {0, 0, 0, r_oklop, 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; diff --git a/geometrija/izmaknjen.msh b/geometrija/izmaknjen.msh new file mode 100644 index 0000000..ed78d50 --- /dev/null +++ b/geometrija/izmaknjen.msh @@ -0,0 +1,2970 @@ +$MeshFormat +2.2 0 8 +$EndMeshFormat 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+++ b/geometrija/potlacen.geo @@ -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; diff --git a/geometrija/potlacen.msh b/geometrija/potlacen.msh new file mode 100644 index 0000000..0e397df --- /dev/null +++ b/geometrija/potlacen.msh @@ -0,0 +1,2244 @@ +$MeshFormat +2.2 0 8 +$EndMeshFormat +$PhysicalNames +3 +1 2 "zila" +1 3 "oklop" +2 1 "dielektrik" +$EndPhysicalNames +$Nodes +743 +1 0.5 0 0 +2 3 0 0 +3 0.4984194195073479 0.03972508348585724 0 +4 0.4936876709681667 0.07919901220360759 0 +5 0.485834670020205 0.1181722192664526 0 +6 0.4749100658638913 0.1563983035111138 0 +7 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/izracuni/izmaknjen-out.txt b/izracuni/izmaknjen-out.txt new file mode 100644 index 0000000..e783bdf --- /dev/null +++ b/izracuni/izmaknjen-out.txt @@ -0,0 +1,4 @@ +$I$,1.587683737682743,A +$Z_0$,62.984836102152215,\ohm +$C$,85.01743830691181,pF\per\metre +$L$,337.2717935248947,nH\per\metre \ No newline at end of file diff --git a/izracuni/koax-out.txt b/izracuni/koax-out.txt new file mode 100644 index 0000000..7a6a68c --- /dev/null +++ b/izracuni/koax-out.txt @@ -0,0 +1,5 @@ +velicina,FEM,analično,enote,napaka +$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$,361.8613193411615,358.35189404068905,nH\per\metre,0.9793237761076143 \ No newline at end of file diff --git a/izracuni/kvadratni-out.txt b/izracuni/kvadratni-out.txt new file mode 100644 index 0000000..6161b39 --- /dev/null +++ b/izracuni/kvadratni-out.txt @@ -0,0 +1,4 @@ +$I$,2.25507989038385,A +$Z_0$,44.34432696882345,\ohm +$C$,120.7478854118662,pF\per\metre +$L$,237.44097645189865,nH\per\metre \ No newline at end of file diff --git a/izracuni/potlacen-out.txt b/izracuni/potlacen-out.txt new file mode 100644 index 0000000..7fac558 --- /dev/null +++ b/izracuni/potlacen-out.txt @@ -0,0 +1,4 @@ +$I$,2.0541699124167185,A +$Z_0$,48.681464661484895,\ohm +$C$,109.99576988969797,pF\per\metre +$L$,260.67732529965474,nH\per\metre \ No newline at end of file diff --git a/izracuni/stripline-out.txt b/izracuni/stripline-out.txt new file mode 100644 index 0000000..ef36957 --- /dev/null +++ b/izracuni/stripline-out.txt @@ -0,0 +1,4 @@ +$I$,1.6176838349767209,A +$Z_0$,61.816776453996674,\ohm +$C$,88.9077872061038,pF\per\metre +$L$,339.7445587269718,nH\per\metre \ No newline at end of file diff --git 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b/slike/stripline-V.pdf differ diff --git a/tem.py b/tem.py new file mode 100644 index 0000000..13064b2 --- /dev/null +++ b/tem.py @@ -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)