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Abstract: In this paper, an adaptive trust region filter algorithm for unconstrained optimization is presented. The global convergence results of the algorithm are established and the numerical results show that the new algorithm is efficient in practical computation. [Copyright &y& Elsevier]

• We propose a two-scale iterative scheme to solve a phase-field model for precipitation and dissolution in porous media. • We combine the two-scale iterative scheme with a robust non-linear solver at the micro scale. • We prove the boundedness of the micro-scale and macro-scale solution under certain choice of parameters. • We prove the convergence of the two-scale iterative scheme on a simplified setting. • We enrich the two-scale iterative scheme with an adaptive strategy to make it more efficient at both scales. Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an apriori unknown manner. To deal with such aspects, we here adopt a two-scale phase-field model, and propose a robust scheme for the numerical approximation of the solution. The scheme takes into account both the scale separation in the model, as well as the non-linear character of the model. After proving the convergence of the scheme, an adaptive two-scale strategy is incorporated, which improves the efficiency of the simulations. Numerical tests are presented, showing the efficiency and accuracy of the scheme in the presence of anisotropies and heterogeneities. [ABSTRACT FROM AUTHOR]