A two-step algorithm for finite-element solution of electromagnetic-testing problems: Electric-capacitance testing

A procedure for numerical solution of 3D electromagnetic-testing problems is described. This procedure is intended for problems where approximation of the systems of differential equations through standard finite-element schemes requires significant computer resources. Such a situation is mainly typical of the problems where effects of 3D flaws are not significant relative to the value of the main (usually 2D) field but nevertheless have to be calculated with a sufficiently high accuracy. At the first stage of the finite-element simulation algorithm, a 2D problem is numerically solved for a “flaw-free” field. At the second stage, the field of the flaw’s effect is calculated, the sources of this field being localized in the vicinity of the flaw. Owing to such an approach, the computer resources needed to solve the problems of this type may be significantly reduced so that the problems become solvable by means of PCs. The proposed procedure has been implemented in the MagNum3D package [1, 2] and the procedure’s efficiency has been confirmed via solution of a model problem of electric-capacitance testing.