Abstract-Several methods are presented for highly efficient calculation of substrate noise transport in integrated circuits. A three-dimensional Green's function-based boundary element method, accelerated through use of the fast Fourier transform, allows the computation of sensitivities with respect to all substrate parameters at a considerably higher speed than any methods reported in the literature. Substrate sensitivities are used in a number of physical optimization tools, such as placement and trend analysis. The aim is a fast and accurate estimation of the impact of technology migration and/or layout redesign on substrate noise and, ultimately, on the circuit's overall performance. The suitability of the approach is shown through industrial-strength mixed-mode integrated circuits fabricated on a standard CMOS process.Index Terms-Boundary element methods, convergence of numerical methods, discrete Fourier transients, integrated circuit noise, noise, noise generators, noise measurement, numerical analysis, numerical stability, optimization methods, phase noise, sensitivity, semiconductor device noise, switching circuits, switching transients.