Directed Transmission Method, A Fully Asynchronous approach to Solve Sparse Linear Systems in Parallel

TL;DR

This paper introduces the Directed Transmission Method, a fully asynchronous, architecture-aware algorithm for solving sparse symmetric positive definite linear systems efficiently on heterogeneous parallel computers.

Contribution

The paper presents a novel fully asynchronous distributed algorithm, DTM, with proven convergence and demonstrated stability and efficiency through numerical experiments.

Findings

DTM is stable and efficient in numerical tests.

DTM converges for SPD sparse linear systems.

Works on heterogeneous parallel architectures.

Abstract

In this paper, we propose a new distributed algorithm, called Directed Transmission Method (DTM). DTM is a fully asynchronous and continuous-time iterative algorithm to solve SPD sparse linear system. As an architecture-aware algorithm, DTM could be freely running on all kinds of heterogeneous parallel computer. We proved that DTM is convergent by making use of the final-value theorem of Laplacian Transformation. Numerical experiments show that DTM is stable and efficient.