  We investigate the solution landscapes of the confined diblock copolymer and
homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki
model. The projected saddle dynamics method is developed to compute the saddle
points with mass conservation and construct the solution landscape by coupling
with downward/upward search algorithms. A variety of novel stationary solutions
are identified and classified in the solution landscape, including Flower
class, Mosaic class, Core-shell class, and Tai-chi class. The relationships
between different stable states are shown by either transition pathways
connected by index-1 saddle points or dynamical pathways connected by a
high-index saddle point. The solution landscapes also demonstrate the
symmetry-breaking phenomena, in which more solutions with high symmetry are
found when the domain size increases.
