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

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.

[1]  Jin-Fa Lee,et al.  High speed interconnects of multi-layer PCB analysis by using non-conformal domain decomposition method , 2010, 2010 IEEE International Symposium on Electromagnetic Compatibility.

[2]  L. Daniel,et al.  Magnetic resonance specific integral equation solver based on precomputed numerical Green functions , 2013, 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[3]  Duo Chen,et al.  A Direct Domain-Decomposition-Based Time- Domain Finite-Element Method of Linear Complexity for Simulating Multiscaled Structures in Integrated Circuit Systems , 2012, IEEE Transactions on Antennas and Propagation.

[4]  Jacob K. White,et al.  Fast Electromagnetic Analysis of MRI Transmit RF Coils Based on Accelerated Integral Equation Methods , 2016, IEEE Transactions on Biomedical Engineering.

[5]  Xiaochuan Wang,et al.  A domain decomposition method for analysis of three-dimensional large-scale electromagnetic compatibility problems , 2012 .

[6]  Nathan Halko,et al.  Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions , 2009, SIAM Rev..

[7]  Jacob K. White,et al.  A precorrected-FFT method for electrostatic analysis of complicated 3-D structures , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Jacob K. White,et al.  Reduced-Order Models for Electromagnetic Scattering Problems , 2014, IEEE Transactions on Antennas and Propagation.

[9]  Wei Hong,et al.  A Fast Domain Decomposition Method for Solving Three-Dimensional Large-Scale Electromagnetic Problems , 2008, IEEE Transactions on Antennas and Propagation.

[10]  A. Taflove,et al.  Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects , 1986 .

[11]  Özgür Salih Ergül Fast multipole method for the solution of electromagnetic scattering problems , 2003 .

[12]  Xin-Qing Sheng,et al.  DOMAIN DECOMPOSITION FE-BI-MLFMA METHOD FOR SCATTERING BY 3D INHOMOGENEOUS OBJECTS , 2013 .

[13]  M. Bleszynski,et al.  AIM: Adaptive integral method for solving large‐scale electromagnetic scattering and radiation problems , 1996 .

[14]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[15]  Jin-Fa Lee,et al.  Non-conformal domain decomposition methods for time-harmonic Maxwell equations , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  M. Vouvakis,et al.  The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems , 2005, IEEE Transactions on Electromagnetic Compatibility.

[17]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .