Memory Footprint Reduction for the FFT-Based Volume Integral Equation Method via Tensor Decompositions

We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations. The arising Green's function tensors have low multilinear rank, which allows Tucker decomposition to be employed for their compression, thereby greatly reducing the...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2019-12, Vol.67 (12), p.7476-7486
Main Authors: Giannakopoulos, Ilias I., Litsarev, Mikhail S., Polimeridis, Athanasios G.
Format: Article
Language:English
Subjects:
Acceleration
Canonical polyadic (CP) model
Computer simulation
Decomposition
Footprints
Graphics processing units
Green's function methods
higher order singular value decomposition (HOSVD)
Integral equations
Iterative methods
Iterative solution
Magnetic resonance imaging
Mathematical analysis
Memory management
Method of moments
NMR
Nuclear magnetic resonance
Parallel processing
Reduction
Simulation
Tensors
Tucker decomposition
Volume integral equations
volume integral equations (VIEs)
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Summary:We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations. The arising Green's function tensors have low multilinear rank, which allows Tucker decomposition to be employed for their compression, thereby greatly reducing the required memory storage for numerical simulations. Consequently, the compressed components are able to fit inside a graphical processing unit (GPU) on which highly parallelized computations can vastly accelerate the iterative solution of the arising linear system. In addition, the elementwise products throughout the iterative solver's process require additional flops, thus, we provide a variety of novel and efficient methods that maintain the linear complexity of the classic elementwise product with an additional multiplicative small constant. We demonstrate the utility of our approach via its application to VIE simulations for the magnetic resonance imaging (MRI) of a human head. For these simulations, we report an order of magnitude acceleration over standard techniques.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2019.2930126