Adaptive Finite Element Method For Self-consistent Field Theory On General Curved Surfaces

Self-consistent field theory is a coarse-grained model based on average field approximation to describe polymer systems,it is a powerful tool to study the micro-phase separation of heterogeneous polymers and related soft matter systems,its outstanding advantage is that it can describe the detailed characteristics of various topological configurations of polymer chains more accurately.In this thesis,we design a high-order adaptive surface finite element method based on the self-consistent field theory of block copolymers on general surfaces,this method combines the spectral delay correction method in the direction of the contour variable to achieve higher accuracy with fewer discrete points in the contour.At the same time,in the process of adaptation,we propose a new marking strategy,compared with the traditional marking strategy,this strategy can obtain the information of the number of times of refinement or coarsening of the marking cell,which improves the efficiency of mesh adaptation.In order to verify the effectiveness of the numerical method,we applied it to the calculation of the diblock copolymer system and the strong condensation system on the general surface,the ordered structure obtained by the numerical results verified that our method is effective.