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We derive thermodynamically consistent models for diblock copolymer solutionscoupled with the electric and magnetic field, respectively. These modelssatisfy the second law of thermodynamics and therefore are thereforethermodynamically consistent. We then design a set of 2nd order, linear,semi-discrete schemes for the models using the energy quadratization method andthe supplementary variable method, respectively, which preserve energydissipation rates of the models. The spatial discretization is carried outsubsequently using 2nd order finite difference methods, leading to fullydiscrete algorithms that preserve discrete energy-dissipation-rates of themodels so that the resulting fully discrete models are thermodynamicallyconsistent. Convergence rates are numerically confirmed through mesh refinementtests and several numerical examples are given to demonstrate the role of themobility in pattern formation, defect removing effect of both electric andmagnetic fields as well as the hysteresis effect for applied external fields incopolymer solutions.

Thermodynamically Consistent Algorithms for Models of Diblock Copolymer Solutions Interacting with Electric and Magnetic Fields