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The Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) is a widely used integral equation for simulating radiation and scattering from penetrable objects. This formulation, however, is plagued from mesh refinement and low-frequency ill-conditioning. Existing techniques for handling these problems, however, suffer from very low-frequency numerical cancellations or they require the detection of global loops...
We present an analysis of the application of (general) hierarchical basis preconditioners developed for preconditioning the electric field integral equation (EFIE) to the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation on simply and multiply-connected geometries. First, we discuss the correct choice of the rescaling factors for the solenoidal and non-solenoidal hierarchical bases...
The time domain PMCHWT equation models transient scattering by piecewise homogeneous dielectrics. After discretization, it can be solved using the marching-on-in-time algorithm. Unfortunately, the PMCHWT equation suffers from DC instability: it supports constant in time regime solutions. Upon discretization, the corresponding poles of the system response function shift into the unstable region of...
The time domain electric field integral equation (TD-EFIE) models transient scattering by perfect electric conductors. Upon discretization, this equation yields an ill-conditioned system matrix when the time step is large (low frequency breakdown), or the mesh is dense (dense discretization breakdown). Furthermore, its solution suffers from spurious static loop currents (DC instability). The quasi-Helmholtz...
In time domain boundary integral equations, scattered fields are computed from a priori unknown electric current and charge densities. In many implementations, the charge density is eliminated from the integral equation prior to discretization, using the charge-current continuity equation. In this contribution, the charge density is explicitly discretized, and the continuity equation is weakly enforced...
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