Added normalization of M magnitude at each iteration of 2nd order algorithm

[jackieyao0114]

Added normalization of M magnitude at each iteration for MacroscopicEvolveM_2nd.

As there are potential problems with the coupling between LLG and Maxwell, which is going to be fixed by future PR, ** to run the demo, make sure to turn off the coupling between LLG equation and Maxwell equations by changing

Real Hx_eff = Hx_xface + Hx_bias_xface;
Real Hy_eff = Hy_xface + Hy_bias_xface;
Real Hz_eff = Hz_xface + Hz_bias_xface;

into

Real Hx_eff = Hx_bias_xface;
Real Hy_eff = Hy_bias_xface;
Real Hz_eff = Hz_bias_xface;

for x, y, and z faces. **

Input file for the demo case:

################################
####### GENERAL PARAMETERS ######
#################################
max_step = 1000
amr.n_cell = 8 8 8 # number of cells spanning the domain in each coordinate direction at level 0
amr.max_grid_size = 512 # maximum size of each AMReX box, used to decompose the domain
amr.blocking_factor = 8
geometry.coord_sys = 0
geometry.is_periodic = 1 1 1
geometry.prob_lo = -1.5e-6 -1.5e-6 -1.5e-6
geometry.prob_hi = 1.5e-6 1.5e-6 1.5e-6
amr.max_level = 0

#################################
############ NUMERICS ###########
#################################
warpx.verbose = 0
warpx.use_filter = 0
warpx.cfl = 4000
warpx.do_pml = 0
warpx.mag_time_scheme_order = 2 # default 1
#algo.em_solver_medium = vacuum # vacuum/macroscopic
algo.em_solver_medium = macroscopic # vacuum/macroscopic
algo.macroscopic_sigma_method = laxwendroff # laxwendroff or backwardeuler
macroscopic.sigma_init_style = "parse_sigma_function" # parse or "constant"
macroscopic.sigma_function(x,y,z) = "0.0"
#macroscopic.sigma = 0.0
macroscopic.epsilon_init_style = "parse_epsilon_function" # parse or "constant"
macroscopic.epsilon_function(x,y,z) = "8.8541878128e-12"
#macroscopic.epsilon = 8.8541878128e-12
macroscopic.mu_init_style = "parse_mu_function" # parse or "constant"
macroscopic.mu_function(x,y,z) = "1.25663706212e-06"
#macroscopic.mu = 1.25663706212e-06
macroscopic.mag_Ms_init_style = "parse_mag_Ms_function" # parse or "constant"
macroscopic.mag_Ms_function(x,y,z) = "1.4e5"
#macroscopic.mag_Ms = 1.4e5 # in unit A/m, equal to 1750 Gauss
#unit conversion: 1 Gauss = (1000/4pi) A/m
macroscopic.mag_alpha_init_style = "parse_mag_alpha_function"
macroscopic.mag_alpha_function(x,y,z) = "5e-01"
#macroscopic.mag_alpha = 5e-01 # alpha is unitless, typical values range from 1e-3 ~ 1e-5
macroscopic.mag_gamma_init_style = "parse_mag_gamma_function"
macroscopic.mag_gamma_function(x,y,z) = "-1.759e11"
#macroscopic.mag_gamma = 1.759e11 # gyromagnetic ratio is constant for electrons in all materials
macroscopic.mag_max_iter = 100 # maximum number of M iteration in each time step
macroscopic.mag_tol = 0.00001 # M magnitude relative error tolerance compared to previous iteration
macroscopic.mag_normalized_error = 0.1 # if M magnitude relatively changes more than this value, raise a red flag
particles.nspecies = 0

#################################
############ FIELDS #############
#################################
my_constants.pi = 3.14159265359
my_constants.L = 141.4213562373095e-6
my_constants.c = 299792458.
my_constants.wavelength = 1.2e-1
warpx.E_ext_grid_init_style = parse_E_ext_grid_function
warpx.Ez_external_grid_function(x,y,z) = 0.
warpx.Ex_external_grid_function(x,y,z) = 0.
warpx.Ey_external_grid_function(x,y,z) = 0.
#warpx.Ey_external_grid_function(x,y,z) = "1.e5exp(-z2/L2)cos(2piz/wavelength)"
warpx.B_ext_grid_init_style = parse_B_ext_grid_function
#warpx.Bx_external_grid_function(x,y,z)= "-1.e5exp(-z2/L2)cos(2piz/wavelength)/c"
warpx.Bx_external_grid_function(x,y,z)= 0.1759
#warpx.Bx_external_grid_function(x,y,z)= 0.
warpx.By_external_grid_function(x,y,z)= 0.
warpx.Bz_external_grid_function(x,y,z) = 0.
warpx.H_bias_ext_grid_init_style = parse_H_bias_ext_grid_function
warpx.Hx_bias_external_grid_function(x,y,z)= 0.
warpx.Hy_bias_external_grid_function(x,y,z)= 0.
warpx.Hz_bias_external_grid_function(x,y,z)= 3e4 # in A/m, equal to 382 Oersted
#warpx.Hz_bias_external_grid_function(x,y,z)= 0. # in A/m, equal to 382 Oersted
#unit conversion: 1 Gauss = 1 Oersted = (1000/4pi) A/m
#calculation of H_bias: H_bias (oe) = frequency / 2.8e6
#warpx.H_bias_ext_grid_init_style = constant
#warpx.Hx_bias_external_grid = 0
#warpx.Hy_bias_external_grid = 0
#warpx.Hz_bias_external_grid = 0
#warpx.M_ext_grid_init_style = parse_M_ext_grid_function
#warpx.Mx_external_grid_function(x,y,z)= "-1.e5exp(-z2/L2)cos(2piz/wavelength)/c"
#warpx.My_external_grid_function(x,y,z)= 0.
#warpx.Mz_external_grid_function(x,y,z) = 0.
warpx.M_ext_grid_init_style = constant
warpx.M_external_grid = 140000. 0. 0.

#Diagnostics
diagnostics.diags_names = plt
plt.period = 10
plt.diag_type = Full
#plt.fields_to_plot = Mx_xface My_xface Mz_xface Mx_yface My_yface Mz_yface Mx_zface My_zface Mz_zface
plt.fields_to_plot = Mx_xface My_xface Mz_xface
plt.plot_raw_fields = 0

[ajnonaka]

PR looks good!

[RevathiJambunathan]

Thank you @jackieyao0114