
Nonlinear Preconditioning Techniques for Efficient Phase-Field Fracture Modeling
Please login to view abstract download link
The phase-field approach has emerged as a powerful framework for modeling complex fracture phenomena, such as crack initiation, propagation, branching, and merging. However, solving the resulting nonlinear systems poses significant challenges due to the non-convexity, non-smoothness, and high computational cost associated with the energy functional. To address these issues, we explore nonlinear preconditioning strategies that enhance solver robustness and efficiency. Our focus includes the development and analysis of advanced preconditioning techniques, such as field-split-based additive and multiplicative Schwarz preconditioners integrated within Newton’s method. These strategies exploit the structure of the coupled displacement and phase-field equations to improve convergence rates and solution stability. Through numerical benchmarks and comparative studies against traditional methods like alternate minimization, we demonstrate the efficacy of the proposed strategies in tackling challenging phase-field fracture problems. The results highlight the potential of nonlinear preconditioning to significantly reduce computational costs while maintaining accuracy in modeling intricate fracture processes.