Multilevel Green’s Function Interpolation Method for Low-Frequency Layered Magnetic Problems

Fast and memory-efficient computation of magnetic signature of the geometrically complex ferromagnetic objects submerged in the layered marine environment (LME) is challenging because of the z-directional translation-variant Dyadic layered Green’s functions (DLGFs). In this paper, the kernel-independent multilevel Green’s Function Interpolation Method (MLGFIM) is implemented to compute the low frequency magnetic signature of ferromagnetic object submerged in LME, for the first time. In the implementation, the z-directional translation-variant DLGFs are interpolated via the peer-level and lower-to-upper level interpolation techniques. The closed-formed approximation formulas instead of time-consuming Sommerfeld Integrals (SI) are used to generate the interpolation table of the DLGF used in MLGFIM. The magnetic signature of an underwater vessel with 171,948 unknowns is calculated using a 7-level MLGFIM. The Lagrange interpolation points for each cube is set to K=27. A total of 7.3 GB memory storage is used despite the z-directional translation-variant DLGFs and 6.3 second CPU time for one matrix-vector-multiplication in GMRES. To validate, the numerical results of the proposed method are compared with FEKO reference solution. The estimation of the magnetic signature is important for underwater detection and remote sensing application.