Mikhail S. Litsarev

Ilias I. Giannakopoulos, Mikhail S. Litsarev, Athanasios G. Polimeridis

We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations. The arising Green's function tensors have low multilinear rank, which allows Tucker decomposition to be employed for their compression, thereby greatly reducing the required memory storage for numerical simulations. Consequently, the compressed components are able to fit inside a graphical processing unit (GPU) on which highly parallelized computations can vastly accelerate the iterative solution of the arising linear system. In addition, the element-wise products throughout the iterative solver's process require additional flops, thus, we provide a variety of novel and efficient methods that maintain the linear complexity of the classic element-wise product with an additional multiplicative small constant. We demonstrate the utility of our approach via its application to VIE simulations for the Magnetic Resonance Imaging (MRI) of a human head. For these simulations we report an order of magnitude acceleration over standard techniques.

Ioannis P. Georgakis, Ilias I. Giannakopoulos, Mikhail S. Litsarev et al.

A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic scattering from highly inhomogeneous and high contrast objects.We employ the Galerkin Method of Moments to discretize the formulation with discontinuous piecewise linear basis functions on uniform voxelized grids, allowing for the acceleration of the associated matrix-vector products in an iterative solver, with the help of FFT. Numerical results illustrate the superior accuracy and more stable convergence properties of the proposed framework, when compared against standard low order (piecewise constant) discretization schemes and a more conventional VIE formulation based on electric flux densities. Finally, the developed solver is applied to analyze complex geometries, including realistic human body models, typically used in modeling the interactions between electromagnetic waves and biological tissue.