A Hybrid FEM-BEM Unified Boundary Condition with Sub-Cycling for Electromagnetic Radiation

This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either an inhomogenous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a unified boundary condition (UBC), for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements or by sub-cycling the boundary element portion of the formulation. This sub-cycling, for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique