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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.timesteps = 501 -- num of iterations
sim.gmsh_model = "resonator.geo" -- gmsh model filename
sim.use_gpu = 0 -- 0: cpu, 1: gpu
sim.approx_order = 3 -- approximation order
postpro.silo_output_rate = 100
postpro.cycle_print_rate = 100 -- console print rate
postpro["E"].silo_mode = "nodal"
postpro["H"].silo_mode = "nodal"
local epsr = 1.0
local mur = 1.0
materials.epsilon = function(tag, x, y, z)
return epsr;
end
materials.mu = function(tag, x, y, z)
return mur;
end
materials.sigma = function(tag, x, y, z)
return 0.0;
end
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 = {}
-- determine if we should do I/O
local do_IO = (not parallel) or (parallel and parallel.comm_rank == 0)
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 omega = c0*math.sqrt(u*u + v*v + w*w)/math.sqrt(epsr*mur)
local resonance_f = omega/(2*math.pi)
local resonance_MHz = resonance_f/1e6
local cycle_timesteps = 1/(resonance_f*sim.dt)
local eps = epsr * const.eps0
local mu = mur * const.mu0
local k_sq = (omega*mu)*(omega*eps)
local kc_sq = u*u + v*v
local beta = math.sqrt(k_sq - kc_sq)
local Zte = omega*mu/beta
local We = eps*a*b*d/16
if ( do_IO ) then
print("\x1b[1mANALYTICAL SOLUTION DATA:")
print(" Resonance frequency: " .. resonance_MHz .. " Mhz")
print(" Cavity impedance: " .. Zte .. " Ohm")
print(" Timesteps for 1 cycle: " .. cycle_timesteps)
print(" Expected energy " .. 2*We .. " J \x1b[0m")
end
function ansol(tag, x, y, z, t)
local Ex = 0.0
local Ey = math.cos(omega*t)*math.sin(math.pi*x)*math.sin(math.pi*z)
local Hx = math.sin(omega*t)*math.sin(math.pi*x)*math.cos(math.pi*z)/Zte
local Hz = -math.sin(omega*t)*math.cos(math.pi*x)*math.sin(math.pi*z)/Zte
debug.analytical_solution = ansol
--debug.dump_cell_ranks = true
--if ( do_IO ) then
-- fh = io.open("energy.txt", "w")
--end
--function on_timestep(ts)
--local e = compute_energy()
--local err = compute_error()
--if ( do_IO ) then
-- local tot_energy = e.Ex + e.Ey + e.Ez + e.Hx + e.Hy + e.Hz
-- local energy_err = 100*(tot_energy - 2*We)/(2*We)
-- fh:write(energy_err, " ", tot_energy, " ", e.Ey, " ", e.Hx, " ", e.Hz, "\n")
--end
--end
--function on_exit()
-- if ( do_IO ) then
-- fh:close()
-- end
--end