The Accuracy and Efficiency of a Single-Level Fast Multipole Boundary Element Model for Analyzing Cathodic Protection of Large Pipeline Networks

A single-level fast multipole boundary element method was developed for analyzing cathodic protection systems of large pipeline networks. This method was obtained by embedding far-field approximation within the traditional single-level fast multipole method. The far-field approximation was used for computing the coefficients for far elements within adjacent cells and determining the moments of the elements within far cells. This approximation reduced the difficulty of the procedures and programming leading to a significant decrease in CPU time. The Newton-Raphson method and GMRES were combined based on the proposed method to solve the nonlinear boundary conditions due to the polarization curve. Several cathodic protection problems were considered to verify and evaluate the method. The calculated potentials of this method were in good agreement with the conventional boundary element method, which was achieved by using pipe elements and quadrilateral elements to mesh the surfaces. Finally, the impressed current cathodic protection systems of a large network (more than 100,000 elements) and a complex urban gas network were investigated. The results indicated the capability, efficiency, and precision of the present method for solving large and complicated problems on a common desktop computer.