  Current multi-physics Finite Element Method (FEM) solvers are complex systems
in terms of both their mathematical complexity and lines of code. This paper
proposes a skeleton generic FEM solver, named MetaFEM, in total about 5,000
lines of Julia code, which translates generic input Partial Differential
Equation (PDE) weak forms into corresponding GPU-accelerated simulations with a
grammar similar to FEniCS or FreeFEM. Two novel approaches differentiate
MetaFEM from the common solvers: (1) the FEM kernel is based on an original
theory/algorithm which explicitly processes meta-expressions, as the name
suggests, and (2) the symbolic engine is a rule-based Computer Algebra System
(CAS), i.e., the equations are rewritten/derived according to a set of
rewriting rules instead of going through completely fixed routines, supporting
easy customization by developers. Example cases in thermal conduction, linear
elasticity and incompressible flow are presented to demonstrate utility.
