A Discontinuous Galerkin Integral Equation Method for Multiscale Surface-Wire Structures

The surface-wire integral equation method is an efficient and well-established approach in microwave engineering, as it simplifies mesh generation and improves efficiency without sacrificing accuracy. However, it faces significant challenges when applied to multiscale structures with densely distributed wire-surface junctions, such as vias or interconnections. This difficulty arises because junction points must align with surface mesh vertices, imposing additional constraints on mesh generation. To address this limitation and enhance the flexibility of mesh generation for complex structures, in this work, we extend the discontinuous Galerkin integral equation (DGIE) method to surface-wire structures, so that the mesh for wire and surface can be discretized independently. The non-overlapping subdomain partitioning scheme and the simple basis function definitions for surface-wire junctions are provided. Similar to the surface DGIE method, the numerical discretization procedure is derived to guarantee the current continuity and zero charge accumulation on the DG contour lines, to ensure the correctness of electromagnetic analysis. Different numerical examples are provided to demonstrate the correctness, accuracy, and flexibility of the proposed method, and to exhibit its superior performance over conventional methods in challenging multiscale problems.