A Novel Implicit–Explicit Hybrid Iterative Solver for Efficient Simulation of Thermo-Mechanical Processes in Advanced Ceramics

This paper introduces a novel hybrid implicit–explicit iterative solver, termed ImEx-GS, for the  efficient numerical solution of strongly coupled thermo-mechanical equations governing ceramic sintering processes. The method decouples the thermal and mechanical field equations through a Gauss–Seidel-type iteration, solving the thermal equation implicitly for stability and the 
mechanical equation explicitly for efficiency. Theoretical analysis demonstrates that ImEx-GS permits time steps comparable to fully implicit schemes while reducing computational cost by 40–60%. Convergence analysis shows a spectral radius approaching unity faster than classical Jacobi and Gauss–Seidel methods, leading to accelerated iterative convergence. Validation across 
multiple ceramic systems (Al₂O₃, Si₃N₄, ZrO₂, SiC, AlN) confirms robust performance under varying thermo-mechanical coupling strengths. The solver achieves O(N¹·⁸) computational scaling versus O(N²) for conventional block-iterative approaches, making it particularly suitable for large-scale, high-resolution simulations of industrial sintering cycles. This work provides a practical 
computational framework for optimizing thermal processing parameters to minimize residual 
stresses and micro-cracking in technical ceramics.