SCALAR AUXILIARY VARIABLE APPROACH IN ITERATIVE MINIMIZATION FORMULATION FOR SADDLE POINT SEARCH

Saddle points have been extensively investigated in the study of activated process in gradient flow driven by free energy. This paper aims to use the iterative minimization formulation processes in the H-1 gradient flow, i.e., index-1 saddle points of the corresponding energy in H-1 metric. In each cycle of the IMF, we introduce the SAV approach to minimize the auxiliary functional. A general principle of constructing linear, efficient and robust energy stable schemes for this approach is presented. This new SAV based IMF method improves the efficiency of saddle point search and can be implemented easily for different free energies. By conducting some numerical experiments for the Ginzburg-Landau and the Landau-Brazovskii free energies, the efficient performance of the proposed method is validated.