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AMReX-Microelectronics / FerroX

FerroX is a massively parallel, 3D phase-field simulation framework for modeling ferroelectric materials based scalable logic devices.
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Implement Newton's method for iterative scheme for Poisson solve in MFIS #17

Closed prkkumar closed 2 years ago

prkkumar commented 2 years ago

Motivated by issue https://github.com/AMReX-Microelectronics/FerroX/issues/9. This PR implements a new iterative algorithm for the solution of Poisson's equation for MFIS stack. It's based on the Newton's method described in the attached pdf and is more robust than our current "iterate in place" approach. Newton_accelerated_Poisson_Solve_FerroX_v1.pdf

Input file to test

n_cell = 64 64 32

max_grid_size = 32

prob_type = 2 

P_BC_flag_lo = 0 # Polarization BC at FE-DE interface
P_BC_flag_hi = 1 # Polarization BC at FE-Metal interface

Phi_Bc_lo = 0.0  # Dirichlet BC for Poisson solve at bottom metal contact
Phi_Bc_hi = 1.2   # Dirichlet BC for Poisson solve at top metal contact

TimeIntegratorOrder = 1 

nsteps = 1500
plot_int = 500 

dt = 2.0e-13

delta = 1.e-6 #To calculate Jacobian in Newton's method for Poisson solve

prob_lo = -16.e-9 -16.e-9 0.e-9
prob_hi =  16.e-9  16.e-9 16.e-9

epsilon_0 = 8.85e-12
epsilonX_fe = 24.0
epsilonZ_fe = 24.0
epsilon_de = 3.9 
epsilon_si = 11.7
alpha = -2.5e9
beta = 6.0e10
gamma = 1.5e11
BigGamma = 100 
g11 = 1.0e-9
g44 = 1.0e-9

SC_lo = 0.0 
SC_hi = 10.0e-9
DE_lo = 10.0e-9
DE_hi = 11.0e-9
FE_lo = 11.0e-9
FE_hi = 16.0e-9

lambda = 3.0e-9