A Minimization Method for The Double-Well Energy Functional
This work provides a theoretically grounded minimization approach for a known problem in phase-field modeling, but the method is incremental as it relates to existing schemes like Invariant Energy Quadratization.
The paper proposes an iterative minimization method for approximating the minimizer of the double-well energy functional in phase-field theory, proving unconditional energy stability and deriving a variant of the first-order scheme for the Allen-Cahn equation.
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed convex set and is shown to be unconditionally energy stable. By the minimization approach, we also derive an variant of the first-order scheme for the Allen-Cahn equation, which has been constructed in the context of Invariant Energy Quadratization, and prove its unconditional energy stability.