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arXiv · 2103.05822

Compression of Far-Fields in the Fast Multipole Method via Tucker Decomposition

Cheng Qian·Mingyu Wang·Abdulkadir C. Yucel
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Abstract

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which are stored in three-dimensional (3-D) arrays (or tensors). The compressed tensors are then used to perform fast tensor-vector multiplications during the aggregation and disaggregation stages of the FMM. For many practical scenarios, the proposed Tucker decomposition yields a significant reduction in the far-fields' memory requirement while dramatically accelerating the aggregation and disaggregation stages. For the electromagnetic scattering analysis of a 30{\lambda}-diameter sphere, it reduces the memory requirement of the far-fields more than 87% while it expedites the aggregation and disaggregation stages by a factor of 15.8 and 15.2, respectively, where {\lambda} is the wavelength in free space.

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Cheng Qian, Mingyu Wang, Abdulkadir C. Yucel. 2021-03-10. Compression of Far-Fields in the Fast Multipole Method via Tucker Decomposition. https://doi.org/10.1109/tap.2021.3070113

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