Title: Memory footprint reduction for the FFT-based volume integral equation method via tensor decompositions,
Abstract: 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.