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-- Resonant cavity test. See Pozar, section 6.3 for theory.
-----------------------
--[[ Problem setup ]]--
sim.name = "test_maxwell_resonator" -- simulation name
sim.dt = 1e-12 -- timestep size
sim.gmsh_model = "resonator.geo" -- gmsh model filename
sim.approx_order = 1 -- approximation order
sim.time_integrator = "euler"
postpro.silo_output_rate = 100
postpro.cycle_print_rate = 100 -- console print rate
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postpro["J"].silo_mode = "none"
local epsr = 1
local mur = 1
materials[1] = {}
materials[1].epsilon = epsr
materials[1].mu = mur
materials[1].sigma = 0
function electric_initial_condition(x, y, z)
local Ex = 0
local Ey = math.sin(math.pi*x) * math.sin(math.pi*z)
local Ez = 0
return Ex, Ey, Ez
end
--------------------------
--[[ Validation stuff ]]--
debug = {}
local c0 = 1/math.sqrt(const.eps0*const.mu0)
-- Mode
local m = 1 -- along x
local n = 0 -- along y
local l = 1 -- along z
-- Cavity dimensions (must match sim.gmsh_model)
local a = 1 -- along x
local b = 0.1 -- along y
local d = 1 -- along z
local u = m*math.pi/a
local v = n*math.pi/b
local w = l*math.pi/d
-- Compute resonant frequency
local omega0 = c0*math.sqrt(u*u + v*v + w*w)/math.sqrt(epsr*mur)
-- Compute impedance
local eps = materials[1].epsilon * const.eps0
local mu = materials[1].mu * const.mu0
local Y = math.sqrt(eps/mu)
function ansol(tag, x, y, z, t)
local Ex = 0.0
local Ey = math.cos(omega0*t)*math.sin(math.pi*x)*math.sin(math.pi*z)
local Ez = 0.0
local Hx = -Y*math.sin(omega0*t)*math.sin(math.pi*x)*math.cos(math.pi*z)
local Hy = 0.0
local Hz = Y*math.sin(omega0*t)*math.cos(math.pi*x)*math.sin(math.pi*z)
return Ex, Ey, Ez, Hx, Hy, Hz
end
--debug.analytical_solution = ansol