Accelerated domain decomposition FEM-BEM solver for magnetic resonance imaging (MRI) via discrete empirical interpolation method

Abstract

A finite element and combined field integral equation domain decomposition approach is presented for electromagnetic scattering from multiple domains. The main computational bottleneck is the construction of the dense coupling impedance matrix blocks capturing the interactions between different domains. In order to accelerate such coupling computation, A. Hochman et al. in [1] proposed the combination of the randomized singular value decomposition (rSVD) and of the discrete empirical interpolation method (DEIM). The computation of the incident fields due to equivalent currents on each domain is reduced to just a few observation points that can be located optimally and automatically by the DEIM algorithm. Furthermore, the compressed form of the coupling blocks generated by that approach significantly reduces the memory requirement and computational cost associated with the iterative solution of the global system matrix. In this paper, we focus on developing an implementation of such approach for a domain decomposition solver that combines finite element method (FEM) with boundary element method (BEM). Results on a simplified magnetic resonance imaging (MRI) scattering on human body are finally presented to validate our code implementation.