One of the principal challenges in the numerical simulation of corrosion phenomena is the development of efficient and robust numerical methods capable of supporting predictive maintenance applications in real-world engineering systems. These systems often involve complex geometries and evolving interfaces, such as in the case of metal pitting corrosion, requiring advanced modeling techniques to predict material degradation over time. In this work, we focus on a phase-field model for metal pitting corrosion [3], which offers a flexible framework for modeling the evolution of corrosion fronts in a way that naturally accommodates the moving boundary problem. The phase field approach simplifies the treatment of the evolving interface between the corroding metal and the surrounding environment, eliminating the need for complicated re-meshing techniques commonly associated with traditional front-tracking methods. However, despite these advantages, the governing equations of the phase-field model, which describe the temporal evolution of the corrosion front, are highly stiff. This stiffness poses significant challenges for time-stepping schemes, as standard explicit time integrators require very small time steps to maintain stability. To overcome this issue, we propose an alternative strategy based on the structure of the discrete Laplacian operator [1]. On the basis of a new matrix-oriented approach that exploits the Kronecker-sum structure resulting from standard finite difference discretizations, we develop highly efficient IMplicit-EXplicit (IMEX) time integrators that do not require the inversion of large matrices. We validate the proposed method through several numerical experiments, comparing its performance with other techniques from the literature [2]. The results demonstrate that the IMEX schemes offer substantial improvements in both computational efficiency and accuracy, making them a promising tool for simulating metal corrosion processes. REFERENCES [1] G. Frasca-Caccia, D. Conte, B. Paternoster. Fast solution of a phase-field model of pitting corrosion. (submitted). [2] H. Gao, L. Ju, R. Duddu, H. Li. An efficient second-order linear scheme for the phase field model of corrosive dissolution. J. Comput. Appl. Math., 367:112472, 2020. [3] W. Mai, S. Soghrati, R. G. Buchheit. A phase field model for simulating the pitting corrosion. Corros. Sci., 110:157–166, 2016.