Analysis and computer implementation of the mathematical model of $180^{^\circ}$ domain structures formation in ferroelectrics

The study is devoted to the theoretical analysis and numerical implementation of the 2D mathematical model of $180^{^\circ}$ ferroelectric domain structures formation within the framework of the Landau – Ginzburg – Devonshire thermodynamic approach supplemented by the Landau – Khalatnikov equation to express the polarization dynamics. The mathematical problem statement is formalized as an initial-boundary value problem for semilinear parabolic partial differential equation. A finite element implementation of the model is performed with the use of COMSOL Multiphysics platform. A series of computational experiments were conducted to visualize various configurations of ferroelectric domain structures.