  A realistic material may possess defects, which often bring the material new
properties that have practical applications. The boundary defects of a
two-dimensional topologically ordered system are thought of as an alternative
way of realizing topological quantum computation. To facilitate the study of
such boundary defects, in this paper, we construct an exactly solvable
Hamiltonian model of topological orders with gapped boundary junctions, where
the boundary defects reside, by placing the Levin-Wen model on a disk, whose
gapped boundary is separated into multiple segments by junctions. We find that
the Hamiltonian of a gapped boundary junction is characterized by either a
morphism between or a common Frobenius subalgebra of the two Frobenius algebras
(in the input fusion category) characetrizing the two boundary segments joint
by the junction. We derive a formula of the ground state degeneracy and an
explicit ground-state basis of our model. We propose the notion of mobile and
immobile charges on the boundary and find that they are quantum observables and
label the ground-state basis. Our model is computation friendly.
