Transmission line inspires a new distributed algorithm to solve linear system of circuit

Transmission line, or wire, is always troublesome to integrated circuits designers, but it could be helpful to parallel computing researchers. This paper proposes the Virtual Transmission Method (VTM), which is a new distributed and stationary iterative algorithm to solve the linear system extracted from circuit. It tears the circuit by virtual transmission lines to achieve distributed computing. For the symmetric positive definite (SPD) linear system, VTM is proved to be convergent. For the unsymmetrical linear system, numerical experiments show that VTM is possible to achieve better convergence property than the traditional stationary algorithms. VTM could be accelerated by some preconditioning techniques, and the convergence speed of VTM is fast when its preconditioner is properly chosen.