-- 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 = 100001                           -- num of iterations
sim.gmsh_model = "resonator.geo"                -- gmsh model filename
sim.use_gpu = 0                                 -- 0: cpu, 1: gpu
sim.approx_order = 1                            -- approximation order
sim.time_integrator = "euler"
postpro.silo_output_rate = 100
postpro.cycle_print_rate = 100                  -- console print rate

postpro["E"].silo_mode = "zonal"
postpro["H"].silo_mode = "zonal"
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
debug.dump_cell_ranks = true