Preconditioning for finite element methods with strain smoothing

Strain smoothing methods such as the smoothed finite element (S-FEMs) and strain-smoothed element~(SSE) method have successfully improved performance of elements, there been numerous applications them in analysis. For sake efficient to large-scale problems, it is important develop a mathematically numerically well-elaborated iterative solver for strain methods. In this paper, inspired by spectral properties methods, we propose ways preconditioning First, analyze spectrums stiffness matrices edge-based S-FEM SSE method. Then, an two-level additive Schwarz preconditioner modifying local solvers appropriately. convenience implementation, alternative form also proposed defining coarse-scale operation terms standard FEM. We verify our theoretical results through numerical experiments.