Abstract-Stochastic spectral methods can generate accurate compact stochastic models for electromagnetic problems with material and geometric uncertainties. This letter presents an improved implementation of the maximum-entropy algorithm to compute the density function of an obtained generalized polynomial chaos expansion in Magnetic Resonance Imaging (MRI) applications. Instead of using statistical moments, we show that the expectations of some orthonormal polynomials can be better constraints for the optimization flow. The proposed algorithm is coupled with a finite element-boundary element method (FEM-BEM) domain decomposition field solver to obtain a robust computational prototyping for MRI problems with low and high dimensional uncertainties.
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).
Existing Full-wave Model Order Reduction (FMOR) approaches are based on Expanded Taylor Series Approximations (ETAS) of the oscillatory full-wave system matrix. The accuracy of such approaches hinges on the worst case interaction distances, producing accurate models over a very narrow band of frequencies. In this paper we present Segregation by Primary Phase Factors (SPPF), a novel algorithm for FMOR enabling wideband interconnect impedance analysis. SPPF extracts exponential terms (primary phase factors) and then approximates the smoother remainder with an ETAS, thus resulting in good accuracies over a very wide band of frequencies. We also present a technique to improve conditioning for the required computation. Example results are given for simple interconnect structures modeled using a discretized mixed potential integral equation formulation.
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