An algorithm for solving three-dimensional harmonic Maxwell equations in ferromagnetic pipes

A numerical method of calculating harmonic three-dimensional electromagnetic field in the metallic pipe with local defects is described. The problem is subdivided onto two stages: calculation of the two-dimensional field in infinite domain for a clean pipe, and calculation of a local three-dimensional field “generated” by a defect. A second-order difference scheme for the four-component equations system of potentials is written out. Several iteration methods of finding the solution of the governing linear equations are investigated. A strategy of the multigrid approach for the considered class of problems is proposed.