Optimization of cathodic protection for complicated structures using fast multipole boundary element method and equivalent boundary condition

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This research consists of three parts.In the first part, boundary element methods (BEM) to analyze the cathodic protection for complicated structures were reviewed. At first an experimental verification of BEM solusion was shown for an actual seawater pump with zinc sacrificial anodes. where the dependence of polarization curves on flow rate and time must be taken into account. Then, an effective BEM based on a concept "macroscopic polarization curve" was presented, and a heat exchanger having thousands of stainless steel tubes and naval brass tube-holder plates with zinc sacrificial anodes was analyzed using this method. Optimization of the impressed current and location of electrodes in impressed current cathodic protection was performed using the BEM for an underground long pipeline. An inverse and optimization problems in impressed current cathodic protection for a large ship were also solved.In the second part, application of the fast multipole boundary element method (FMBEM) to c … More orrosion problems was studied. It was found that this method can be successfully applied to corrosion analysis by employing the previous research results on the potential problems together with the following procedures ; (1) use of M^O_O of the root cell (which is obtained in the process of multipole expansion) for the infinite region problems, and (2) modification of the residual calculation formula in the Bi-CGSTAB iterative method to cope with the nonlinearity caused by polarization curves. A pipe element which is suitable to the FMBEM was also developed to increase the efficiency of calculation for pipelines. A few examples were shown to demonstrate the applicability of the FMBEM to corrosion problems.In the third part, an effective optimization technique for cathodic protection design was developed. To cope with the large amount of memory and calculation, FMBEM is applied. To achieve an effective optimization, the initial values of the design variables, i.e., the location and current of each electrode, are determined by solving an inverse problem. In the inverse problem both of the potential and the current density on the metal surfaces to be protected are given as the ideal values, i.e., the protection potential and its corresponding current density. The inverse problem is solved effectively by using FMBEM.Using thus obtained initial values, the optimization problem is solved by the symplex method. A couple of example problems were solved to demonstrate the effectiveness and usefulness of the present method. Less