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In this work we discuss a numerical model of the forward problem in NDE. The model is based on a volume integral formulation. To treat 3D geometries and complex constitutive relationships, the fully populated matrix arising after discretization has been efficiently compressed, using also parallel algorithms. The method utilizes an effective low-rank approximation of the submatrices representing “far” interactions, obtained through a modified Gram-Schmidt - QR factorization method. Some numerical examples show the advantages of the proposed approach
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