The effectiveness of the field-split preconditioning with Schur complement for phase-field fracture is demonstrated via numerical experiments. As an example, a heterogeneous problem with thirty randomly place polygonal-shaped materials is used. The accompanying figure clearly depicts rapid convergence achieved by field-split preconditioning, with convergence attained in less than five Krylov iterations. This represents a substantial reduction in the number of iterations and CPU time compared to other well-known preconditioners. References [1] Y. Saad, (2007). Schur complement preconditioners for distributed general sparse linear systems. Domain Decomposition Methods in Science and Engineering XVI, pp. 127-138 [2] M. A. Badri and G. Rastiello and E. Foerster. (2021). Preconditioning strategies for vectorial finite element linear systems arising from phase-field models for fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 373, pp. 113472 119
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