A type of efficient multigrid method for semilinear parabolic interface problems

This paper proposes and analyzes a type of efficient multigrid method, which is called multilevel correction method, for solving semilinear parabolic interface problems. The core idea of this method is that, at each time step, the semilinear elliptic interface problem’s solution is transformed into the same-scale linear elliptic interface problem’s solution in each level of multilevel space sequence and the semilinear elliptic interface problem’s solution on a newly defined low dimensional augmented subspace. Through analyzing the algebraic error estimate of the method, we design the method to iterate only one step in the intermediate grid layer, which makes our method more efficient than the work of Xu et al. (2022a) without losing accuracy. In addition, in the aspect of theoretical analysis, we present a new technique of analysis to derive the convergence order estimates. Numerical experiments are conducted to validate the precision and effectiveness of our proposed method.