Joy of Computing with Volume-Integrals

摘要

As an alternative to the finite-difference time-domain (FDTD), the finite-element method (FEM), and the Method of Moments (MoM) based on the surface integral equation (SIE), a volume-integral equation (VIE) approach using MoM 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 inhomogenous regions in multilayered media. Since volume element discretization is limited to local inhomogenous regions, numerical solutions for many complex problems can be achieved more efficiently than FDTD, FEM, and MoM/SIE. A challenge-problem in the field of nondestructive evaluation is the inspection of fastener sites for fatigue cracks in multilayer structures, ferromagnetic fastener sites, gaps between materials interfaces, and the presence of fatigue cracks are accurately modeled. Simulated studies are presented with VIC-3D, a proprietary volume- integral code, and comparisons are made with FEM highlighting performance advantages of the VIE approach.