Transmission line inspires a new distributed algorithm to solve the nonlinear dynamical system of physical circuit

As known, physical circuits, e.g. integrated circuits or power system, work in a distributed manner, but these circuits could not be easily simulated in a distributed way. This is mainly because that, the dynamical system of physical circuits is nonlinear, and the linearized system of physical circuits is nonsymmetrical. This paper proposes a simple and natural strategy to mimic the distributed behavior of the physical circuit by mimicking the distributed behavior of the internal wires inside this circuit. Mimic Transmission Method (MTM) is a new distributed algorithm to solve the nonlinear ordinary differential equations extracted from physical circuits. It is a black-box algorithm. By mimicking the transmission lines, MTM seals the nonlinear dynamical system within the subcircuits and each subcircuit could be solved by SPICE on one processor. As the result, we do not need to pay attention on how to solve the nonlinear dynamic system or nonsymmetrical linear system in parallel. As a distributed algorithm, MTM is not iterative but direct, and it does only one distributed computation at each time window to obtain accurate result, so unconvergence problems do not need to be worried about.