Novel high precision UFFT methodology for fast analysis of 3D Planar circuits embedded in shielded layered media

Unified-FFT (UFFT) is a novel 3D-Planar Method of Moments (MoM) solver of the Electric Field Integral Equation (EFIE). UFFT is the resultant algorithm of combining the FFT-enhanced Matrix Solve Operations (MSO) currently utilized in Sonnet Suites with FFT-enhanced Matrix Fill Operations (MFO). It has been shown, in conjunction with iterative MSO based on GMRES, to solve matrix vector products scaling with O(NlogN) operations and O(N) memory for planar, single-plane geometries (B. J. Rautio, V. I. Okhmatovski, J.K. Lee, IMS 2013). Previous UFFT implementations have achieved O(NlogN) scaling through acceleration of iterative matrix-vector products within GMRES by separating near and far interactions and calculating far interactions implicitly as in PFFT. In this work, the same uniform grid used with MFO is extended for use with MSO, negating the need to treat near and far interactions independently and allowing the entire matrix to be stored implicitly with no significant loss of precision. The resulting algorithm, UFFT-Grid Totalizing (UFFT-GT), achieves O(NlogN) operations and O(N) memory scaling with minimal loss in precision vs. full matrix inverse beyond numerical noise.