The Joy of Computing with Volume Integrals: Foundations for Nondestructive Evaluation of Planar Layered Media

─ As an alternative to the finitedifference time-domain (FDTD), the finiteelement method (FEM), and the method of moments (MoM) based on the surface integral equation (SIE), a volume-integral equation (VIE) approach using the method of moments and conjugate-gradient methods is presented to address a wide variety of complex problems in computational electromagnetics. A formulation of the volume integral method is presented to efficiently address inhomogeneous regions in multi-layered media. Since volume element discretization is limited to local inhomogeneous regions, numerical solutions for many complex problems can be achieved more efficiently than FDTD, FEM, and MoM/SIE. This is the first of a series of papers dealing with volume-integral equations; in subsequent papers of this series we will apply volume-integrals to problems in the field on nondestructive evaluation. Index Terms ─ Aircraft structures, computational electromagnetics, electromagnetic nondestructive evaluation, volume-integral equations.

[1]  Roger F. Harrington,et al.  A VOLUME INTEGRAL CODE FOR EDDY-CURRENT NONDESTRUCTIVE EVALUATION , 1989 .

[2]  M. Cátedra,et al.  A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform , 1989 .

[3]  H. Sabbagh.  A model of eddy-current probes with ferrite cores , 1987 .

[4]  V. Petrovic,et al.  Comparison of MoM/SIE, MoM/VIE and FEM based on topological analysis of two canonical problems , 1998, IEEE Antennas and Propagation Society International Symposium. 1998 Digest. Antennas: Gateways to the Global Network. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.98CH36.

[5]  Harold A. Sabbagh,et al.  Advances in Modeling Eddy‐Current NDE of Ferromagnetic Bodies , 2003 .

[6]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[7]  Harold A. Sabbagh,et al.  Reconstruction of semielliptical and epicyclic cracks by eddy-current inversion , 2002 .

[8]  M. Cátedra.  The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics , 1995 .

[9]  Harold A. Sabbagh,et al.  Assessing thermal barrier coatings by eddy current inversion , 2001 .

[10]  R. Mittra.  A look at some challenging problems in computational electromagnetics , 2004, IEEE Antennas and Propagation Magazine.

[11]  R. Harrington.  Time-Harmonic Electromagnetic Fields , 1961 .

[12]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[13]  P. M. Berg,et al.  The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems , 1992 .

[14]  Harold A. Sabbagh,et al.  A theoretical and computational model of eddy-current probes incorporating volume integral and conjugate gradient methods , 1989 .

[15]  H. A. Sabbagh,et al.  Splines and their reciprocal-bases in volume-integral equations , 1992 .

[16]  Harold A. Sabbagh,et al.  Recent advances in modeling eddy-current probes , 2002 .

[17]  Harold A. Sabbagh,et al.  Validation of a volume-integral eddy-current code by bench-mark experiments , 2002 .

[18]  H. Sabbagh,et al.  Verification of an eddy-current flaw inversion algorithm , 1986 .

[19]  Harold A. Sabbagh,et al.  Eddy-current probe impedance due to a surface slot in a conductor , 1990 .

[20]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[21]  John C. Aldrin,et al.  Efficient Solution of Electromagnetic Scattering Problems Using Spatial Decomposition Algorithms , 2006 .

[22]  B. Kolundzija,et al.  Solution of large complex problems in computational electromagnetics using higher-order basis in MoM with out-of-core solvers , 2006, IEEE Antennas and Propagation Magazine.

[23]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[24]  W. Marsden.  I and J , 2012 .

[25]  Magnus R. Hestenes,et al.  Conjugate Direction Methods in Optimization , 1980 .

[26]  H. Sabbagh,et al.  An eddy-current model for three-dimensional inversion , 1986 .

[27]  J. Richmond.  Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .