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.Index Terms-multi-solver domain decomposition method (MS-DDM); MRI scattering; discrete empirical interpolation method (DEIM); proper orthogonal decomposition (POD).

Maximum-Entropy Density Estimation for MRI Stochastic Surrogate Models

“…All parameters are assumed Gaussian with their standard deviations being 25% of the norminal values. In this example, the ANOVA-based stochastic testing solver [17] is combined with the deterministic MRI solver [15] to obtain a sparse generalized polynomial-chaos expansion for the loop antenna impedance, and the tensor-train-based three-term recurrence relation is employed to construct some orthonormal polynomials [21]. The numerical results are plotted in Fig.…”

“…A FEM-BEM domain decomposition field solver is implemented to simulate deterministic MRI scattering problems consisting of several loop antennas placed around a human body [15]. In this approach, the whole computational domain is divided into two sub-domains, which are the set of loop antennas and the human body.…”

“…Since the coupling computation is dominant in the whole solution of the system, a randomized SVD combined with discrete empirical interpolation [16] is employed to accelerate the computation [15]. In stochastic simulation, the developed MRI field solver is used as a black box.…”

“…These parameters are assumed Gaussian, with their standard deviations being 15% of their nominal values. We combine the black-box domaindecomposition MRI solver [15] with stochastic testing [7] to obtain a 3rd-order generalized polynomial-chaos expansion for the magnitude of impedance. Six orthonormal polynomials are used (with m = 5) to generate a closed-form probability density function of y.…”