An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states
This work provides a numerical method for simulating ferronematic materials, which is an incremental contribution to computational physics.
The authors developed an energy-decreasing algorithm for finite element approximation of 2D ferronematic equilibrium states, demonstrating its computational performance through numerical experiments.
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of the harmonic energy of two two-dimensional vector fields, both with prescribed length, together with an additional nonlinear relation on the orientation of the two vectors. The finite element setting is based on piecewise continuous finite elements on a weakly acute triangulation. The computational realization of the energy-decreasing algorithm employs a decomposition-coordination framework and a Uzawa-like iteration. Numerical experiments are presented to illustrate the computational performances of the algorithm.