The Mixed Finite Element Method with Surface Current Boundary Condition for Modeling Geological Fracture

To accelerate the simulation of geological fractures by numerical method, a mixed finite element method (FEM) with surface current boundary condition (SCBC) is proposed. It is the combination of the transverse components of vectorial Helmholtz equation and the Gauss' law in mixed FEM that makes the system matrix good conditioned so as to restrain the low-frequency breakdown phenomenon. In addition, the fracture, through which the electric field distribution is modeled by SCBC, is represented geometrically by a one-dimensional line instead of a thin layer. The method effectively reduces the degrees of freedom and save CPU time, avoiding the local mesh refinement. We demonstrate this method by computing the secondary electric field scattered by a thin layer of hydrocarbon.