Field-Split Preconditioning via Schur Complement for Phase-Field Fracture Mechanics with Finite Element Method M. A. Badri1,∗, G. Rastiello2 1 Université Paris-Saclay, CEA, Service de Génie Logiciel pour la Simulation (SGLS), 91191 Gifsur-Yvette cedex. France 2 Université Paris-Saclay, CEA, Service d’études mécaniques et thermiques (SEMT), 91191 Gifsur-Yvette cedex. France ∗ mohd-afeef.badri@cea.fr Keywords: phase-field method, HPC, field-split preconditioning The phase-field method is a useful tool for simulating fractures, crack propagation, and studying complex fracture phenomena. However, solving certain phase-field fracture problems numerically with FEM involves tackling large systems of linear equations, which can be computationally demanding. To address this issue, parallel computing through the domain decomposition method can be employed. However, to achieve scalable parallel simulations, an optimal preconditioner is required. In this work, we explore the application of field-split preconditioning via the Schur complement [1] to enhance the efficiency of solving phase-field fracture problems in parallel. We utilize vectorial finite elements [2], which facilitate an overall monolithic approach. The field-split preconditioning technique aims to decompose the original monolithic linear system into smaller sub-problems that can be solved more efficiently. By exploiting the underlying physics, the linear system is split based on two involved fields: displacement and phase-field variables. The Schur complement matrix is derived from the original system matrix by eliminating the unknowns associated with the displacement field, providing a smaller and more favorable precondition. 118
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