A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations

Abstract

This paper is concerned with a hybrid method for three-dimensional semilinear elliptic equations, constructed by combining the ideas presented in [Huang et al., J. Comput. Phys. 419 (2020)] and [Zhang et al., Comput. Math. Appl. 80 (2020)]. The convergence rate analysis indicates that the method converges rapidly. Numerical examples support the theoretical results and show that the method proposed outperforms the purely deep learning-based and traditional iterative methods.