Solution of boundary integral equations for eddy current nondestructive evaluation in three dimensions
Eddy current nondestructive evaluation (NDE) of airframe structures involves the detection of electromagnetic field irregularities due to non‐conducting inhomogeneities in an electrically conducting material, which often treats with complicated geometrical features such as cracks, fasteners, sharp corners∕edges, multi‐layered structures, etc. The eddy‐current problem can be formulated by the boundary integral equations (BIE) and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). This paper introduces the implementation of Stratton‐Chu formulation for the conductive medium, in which the induced electric and magnetic surface currents are expanded in terms of Rao‐Wilton‐Glisson (RWG) vector basis function and the normal component of magnetic field is expanded in terms of pulse basis function. Also, a low frequency approximation is applied in the external medium, that is, free space in our case. Computational tests are presented to demonstrate the accuracy and capability of the BIE method with a complex wave number for three‐dimensional objects described by a number of triangular patches. This work prepares the BIE solution procedure that will be embedded with the Fast Multipole Method (FMM), which is a well‐established and effective method for accelerating numerical solutions of the matrix equations. When accelerated by the FMM, the BIE method will have the capability of solving large‐scale electromagnetic wave propagation and eddy‐current problems.
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This article appeared in AIP Conference Proceedings, 1096 (2009): 303–310 and may be found at: http://dx.doi.org/10.1063/1.3114219.