A study of corrosion related electromagnetic signatures of marine vessels using a BEM

摘要

Modelling the corrosion of marine vessels is a semi-infinite domain problem, with a large continuous volume. The BEM is the most suitable numerical method for calculating the electric potential and its normal derivative on the boundary from Laplace's Equation. With these known, it is possible to calculate the electric and magnetic fields due to corrosion, providing an insight into the level of corrosion protection provided and the detectability of the vessel to underwater threats. An innovative method has been developed for integrating the fundamental solution using triangular elements. This consists of performing the integrals by forming polynomials in which the variables are the moments of the element. By extracting the dimensions from the calculations of the moments, they can be calculated using normalised moments which depend solely on a 'shape' parameter. These normalised moments may be expressed as polynomials in this shape parameter where the coefficients are independent of the size or shape of the element. These coefficients can be calculated once and then referred to when required. Hence the integrals can be evaluated by forming polynomials where the coefficients are pre-calculated and the variable is a simple shape parameter. By limiting the polynomials to the order of twenty, the integral calculations have been shown to be accurate to six decimal places. This method has been used to model a ship pf 50,000 tonne displacement. The resulting BEM equations are solved using a point successive over-relaxation method and calculations have been performed to investigate the convergence of this algorithm. Emphasis on realistic polarisation data and comparison to experimental data is subject to further development.