Potential-based volume integral equations

Electromagnetic potential-based volume integral equations (VIEs) for the efficient analysis of large-scale problems are presented. Different from the conventional VIEs the proposed approach is based on scalar and vector potential unknowns. A VIE and the Lorentz gauge equations constitute a complete required set. The introduced potential VIEs (PVIEs) allow using scalar interpolatory nodal basis functions, do not require any surface integrals (both for homogeneous or inhomogeneous domains), and do not involve any hyper-singular integrals. This method works from very low- to high-frequency regimes, does not have high-density mesh breakdowns, requires a significantly reduced number of quadrature nodes as compared to methods based on vector basis functions, and is easy to implement for low- and high-order basis functions. The method is coupled with fast interpolation based techniques implemented on Graphics Processing Units (GPUs) to allow for the rapid analysis of complex structures.