  The scaled boundary finite element method (SBFEM) is a semi-analytical
computational scheme, which is based on the characteristics of the finite
element method (FEM) and combines the advantages of the boundary element method
(BEM). This paper integrates the scaled boundary finite element method (SBFEM)
and the polygonal mesh technique into a new approach to solving the
steady-state and transient seepage problems. The proposed method is implemented
in Abaqus using a user-defined element (UEL). The detailed implementations of
the procedure, defining the UEL element, updating the RHS and AMATRX, and
solving the stiffness/mass matrix by the eigenvalue decomposition are
presented. Several benchmark problems from seepage are solved to validate the
proposed implementation. Results show that the polygonal element of PS-SBFEM
has a higher accuracy rate than the standard FEM element in the same element
size. For the transient problems, the results between PS-SBFEM and the FEM are
in excellent agreement. Furthermore, the PS-SBFEM with quadtree meshes shows a
good effect for solving complex geometric in the seepage problem. Hence, the
proposed method is robust accurate for solving the steady-state and transient
seepage problems. The developed UEL source code and the associated input files
can be downloaded from https://github.com/yangyLab/PS-SBFEM.
