A reformulation of porous electrode theory is presented which allows efficient simulation of numerous battery systems. An efficient finite-difference rectangular grid system is revealed which for 1D systems eliminates banded matrices and reduces all relevant implicit solutions to much simpler tridiagonal systems. Use of Greens function methods to decouple the liquid phase diffusion from the electrode potentials, and a similar decoupling of potentials from the solid phase diffusion are described. The so called hot loop in most full physics simulations of porous electrode batteries results from solving the spherical diffusion equation for concentration of active species in cathode and anode particles. A non linear grid is described which results in very accurate results for the solid phase surface concentrations, from a surprisingly small number of grid points. (C) 2013 The Electrochemical Society. All rights reserved.