Algebraic Electromagnetism

This paper introduces the concept of Algebraic Electromagnetism to solve the problem of finding stable spatial discretizations of the electromagnetic field for large scale, ultra-wide-band electromagnetic systems, composed of possibly nonlinear subsystems with memory and/or hysteresis effects. It is a thorough approach to exact discrete electromagnetism, given by an algebraic construction of general material operators that have the property that solving Maxwell's equations with these is exactly equivalent to solving a corresponding system of ordinary differential equations.