Using Finite Element Method to Solve the Load-Balancing Routing Problem for Massively-Dense Wireless Sensor Networks

This paper presents the grid-based directional routing algorithms for massively-dense wireless sensor networks. These algorithms have their theoretical foundation in numerically solving the load-balancing routing problems, which are formulated as partial differential equations via the geographical model. The numerical solutions provide the routing directions at equally spaced grid points in the region of interest, and then the directions can be used as guidance to route information. We investigate the numerical approach, the finite element method (and its derived distributed algorithm, DGSI-FEM), and present the numerical results to demonstrate the quality of the derived routing directions.