To Improve the Convergence and Parallelism of Gauss-Seidel Routing Algorithm with Finite Element Method for Wireless Sensor Networks

The scalability challenge of many problems in massively -dense wireless sensor networks may be mitigated from a macroscopic perspective. One example is the weak formulation of the load-balancing routing problem, which solution can be used to route information. Hence, a routing algorithm, the distributed Gauss-Seidel iteration (DGSI), was proposed to coordinate sensors to solve the weak formulation iteratively. In this paper, we propose the atomic red-black distributed Gauss-Seidel iteration with finite element method (ARB-DGSI-FEM) to eliminate the early termination problem of DGSI due to the presence of holes, and thus improve the accuracy of numerical solutions. In addition, ARB-DGSI-FEM allows the values of unknowns to be updated in the red-black order to achieve the maximum degree of parallelism and reduce the convergence time. Our simulation results reveal that ARB-DGSI-FEM significantly improves the parallelism without too much sacrifice of accuracy.