Accurate and Efficient Methods for the Scattering Simulation of Dielectric Objects in a Layered Medium
Electromagnetic scattering in a layered medium (LM) is important for many engineering applications, including the hydrocarbon exploration. Various computational methods for tackling well logging simulations are summarized. Given their advantages and limitations, main attention is devoted to the surface integral equation (SIE) and its hybridization with the finite element method (FEM).
The thin dielectric sheet (TDS) based SIE, i.e., TDS-SIE, is introduced to the simulation of fractures. Its accuracy and efficiency are extensively demonstrated by simulating both conductive and resistive fractures. Fractures of variant apertures, conductivities, dipping angles, and extensions are also simulated and analyzed. With the aid of layered medium Green's functions (LMGFs), TDS-SIE is extended into the LM, which results in the solver entitled LM-TDS-SIE.
In order to consider the borehole effect, the well-known loop and tree basis functions are utilized to overcome low-frequency breakdown of the Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) formulation. This leads to the loop-tree (LT) enhanced PMCHWT, which can be hybridized with TDS-SIE to simulate borehole and fracture together. The resultant solver referred to as LT-TDS is further extended into the LM, which leads to the solver entitled LM-LT-TDS.
For inhomogeneous or complex structures, SIE is not suitable for their scattering simulations. It becomes advantageous to hybridize FEM with SIE in the framework of domain decomposition method (DDM), which allows independent treatment of each subdomain and nonconformal meshes between them. This hybridization can be substantially enhanced by the adoption of LMGFs and loop-tree bases, leading to the solver entitled LM-LT-DDM. In comparison with LM-LT-TDS, this solver is more powerful and able to handle more general low-frequency scattering problems in layered media.
Surface Integral Equation
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