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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.
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary eleme
This paper is concerned with the Tucker decomposition based low rank tensor completion problem, which is about reconstructing a tensor $mathcal{T}inmathbb{R}^{ntimes ntimes n}$ of a small multilinear rank from partially observed entries. We study the
Our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software p
Smoothed particle hydrodynamics (SPH) is positioned as having ideal conservation properties. When properly implemented, conservation of total mass, energy, and both linear and angular momentum is guaranteed exactly, up to machine precision. This is p
It is proposed a new method of compressing laser pulse by fast extending plasma gratings(FEPG), which is created by ionizing the hypersound wave generated by stimulated Brillouin scattering(SBS) in the background gas. Ionized by a short laser pulse,