Adaptive Cross Approximation Algorithm for Accelerating BEM in Eddy Current Nondestructive Evaluation

This paper presents the adaptive cross approximation (ACA) algorithm to accelerate boundary element method (BEM) for eddy current nondestructive evaluation (NDE) problem. The eddy current problem is formulated by boundary integral equation and discretized into matrix equations by BEM. Stratton–Chu formulation is selected and implemented for the conductive medium which does not has low frequency breakdown issue. The ACA algorithm has the advantage of purely algebraic and kernel independent. It starts with hierarchically partitioning the object to get diagonal blocks, near blocks and far blocks. The far-block interactions which are rank deficient can be compressed by ACA algorithm meanwhile the elements for diagonal-block interactions and near-block interactions are stored and computed by BEM. We apply modified ACA (MACA) for more memory saving while keeping almost same accuracy compared with original ACA. For numerical testing, several practical NDE examples such as coil above a half space conductor, tube in a fast reactor and Testing Electromagnetic Analysis Methods (TEAM) workshop benchmark problem are presented to show the robust and efficiency of our method. With the aid of ACA, for electrically small problems, the complexity of both the memory requirement and CPU time for BEM are reduced to $$ O\left( {N\log N} \right). $$