1. A computer-implemented method of electronically simulating a physical system simultaneously for a plurality of excitations, the method comprising: (a) storing, in computer memory, a model of the physical system based on a system matrix; and (b) computationally simulating, using the computer, the physical system by: (1) initiating approximations of physical quantities associated with the physical system for the plurality of excitations; and (2) iteratively improving the approximations based, at least in part, on the model by: (i) computing a plurality of residual errors, each residual error being based on a residual vector corresponding to a different one of the plurality of excitations; (ii) selecting an excitation from the plurality of excitations corresponding to a maximum one of the plurality of residual errors; (iii) performing a single conjugate gradient residual (CGR) iteration based on the excitation corresponding to the maximum residual error; (iv) updating the approximations for all of the excitations based, at least in part, on the selected excitation; and (v) repeating substeps (i) through (iv) until a termination condition is satisfied.