A Tensor Train Compression Scheme for Remote Volume-surface Integral Equation Interactions

Abstract

We propose a memory compression scheme for the coupling matrices appearing in volume-surface integral equation formulations. When there is some distance between the surface and the volumetric scatterers, the low-rank properties of the coupling matrix, allow us to reshape it into a set of four-dimensional tensors, which can be heavily compressed with the tensor train decomposition. The associated matrix-vector products can be rapidly performed with the aid of a graphical processing unit. We achieved a compression of more than 8 thousand times with a relative error around 1e – 5, for the calculation of the electromagnetic field generated by a radiofrequency coil inside an object at 1 mm voxel isotropic resolution. In this case, the matrix-vector product could be executed in less than a second.