A Line Model-Based Fast Boundary Element Method for the Cathodic Protection Analysis of Pipelines in Layered Soils

摘要

A line model-based fast boundary element method (BEM) is presented for the large-scale cathodic protection (CP) analysis of three-dimensional pipelines in layered soils. In this approach, pipelines are treated as lines with potentials assumed constant over the cross-section and the boundary integrals happen on the associated cylindrical surfaces. The advantage of this model is that pipelines can be meshed with line elements while the boundary integrals are based on the original shapes. Therefore, the number of unknowns is significantly reduced with accuracy effectively retained. A unified formulation of the multipole moments is developed for the mixed boundary element types in the framework of the fast multipole method in order that large-scale BEM problems by using the line model can be solved on a common desktop computer. An interface boundary integral equation is employed to treat the multi-layered soils with a single-domain formulation. Numerical results demonstrate validity of the proposed method and its potential for large-scale CP analysis of pipelines in multi-domains.