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.

💡 Research Summary

The paper introduces the Virtual Transmission Method (VTM), a novel distributed stationary iterative algorithm designed to solve the large sparse linear systems that arise from circuit analysis. The central idea is to insert “virtual transmission lines” (VTLs) at chosen cut‑sets of a circuit, thereby “tearing” the circuit into several sub‑circuits that can be processed in parallel. Each VTL is modeled by the telegrapher equation (V = Z I + V_{\text{delay}}), where (Z) is a characteristic impedance and (V_{\text{delay}}) accounts for propagation delay. By augmenting each sub‑circuit’s local matrix with the impedance of the attached VTLs, the global system can be rewritten in a fixed‑point form

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