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#Magnetostatic equation that solves for magnetic vector potential, | ||
#where the reluctivity matrix can be defined as inverse of permeability matrix.. | ||
#https://fenicsproject.discourse.group/t/anisotropic-material-definition-and-results-issue/1051 | ||
from dolfin import * | ||
from mshr import * | ||
from scipy import constants | ||
from vtkplotter.dolfin import plot | ||
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domain = Rectangle(Point(-10, -10), Point(10, 10)) | ||
mesh = generate_mesh(domain, 64) | ||
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# function space | ||
V = FunctionSpace(mesh, "P", 1) | ||
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# boundary conditions | ||
walls = "on_boundary && (near(abs(x[0]), 10.0) || near(abs(x[1]), 10.0))" | ||
bc = DirichletBC(V, Constant(0.0), walls) | ||
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tol = 1e-6 | ||
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# Wire | ||
class Omega_0(SubDomain): | ||
def inside(self, x, on_boundary): | ||
return x[0] ** 2 + x[1] ** 2 <= 4 - tol | ||
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# Space | ||
class Omega_1(SubDomain): | ||
def inside(self, x, on_boundary): | ||
return x[0] ** 2 + x[1] ** 2 > 4 + tol | ||
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def curl2D(v): | ||
return as_vector((v.dx(1), -v.dx(0))) | ||
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materials = MeshFunction("size_t", mesh, mesh.topology().dim()) | ||
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subdomain_0 = Omega_0() | ||
subdomain_1 = Omega_1() | ||
subdomain_0.mark(materials, 0) | ||
subdomain_1.mark(materials, 1) | ||
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dx = Measure("dx", domain=mesh, subdomain_data=materials) | ||
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A_z = Function(V) # magnetic vector potential | ||
v = TestFunction(V) | ||
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J = 5.0e6 | ||
# anisotropic material parameters, reluctivity = 1/constants.mu_0 | ||
reluctivity = as_matrix( | ||
((1 / (constants.mu_0 * 1000), 0), | ||
(0, 1 / (constants.mu_0 * 1))) | ||
) | ||
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F = inner(reluctivity * curl2D(A_z), curl2D(v)) * dx - J * v * dx(0) | ||
solve(F == 0, A_z, bc) | ||
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W = VectorFunctionSpace(mesh, "P", 1) | ||
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Bx = A_z.dx(1) | ||
By = -A_z.dx(0) | ||
B = project(as_vector((Bx, By)), W) | ||
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plot(B, mode='mesh and arrows', | ||
style=2, | ||
scale=0.01, | ||
lw=0, | ||
warpZfactor=-0.01, | ||
) |
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