Using the Gaussian function to simulate constant potential anodes in multiobjective optimization of cathodic protection systems

The purpose of this work is to numerically find the optimum location of constant potential anodes to ensure complete structure surface protection using a cathodic protection technique. The existence of sacrificial anodes is originally introduced through the boundary conditions of the corresponding boundary value problem (BVP). However, if constant potential galvanic regions are introduced through its boundaries, then finding their optimal location is not an easy task due to the necessity of redefining boundary geometric nodes and the arrangement of virtual sources for the standard method of fundamental solutions (MFS) formulation. Therefore, in this work, the galvanic anodes are introduced as source terms using a Gaussian function. Hence, the boundary remains the same for different anode positions. The optimization process includes the identification of the following parameters characterizing the Gaussian function: the optimum coordinates of the centre of the anode, a factor that involves the inherent potential of the electrode and a proportionality factor for the electrode diameter. The MFS methodology coupled with a genetic algorithm presented good results for this multiobjective optimization procedure. This fact can be seen in the several results of applications that are discussed in this paper, considering numerical simulations in finite regions in R2.