Abstract
In this article authors present a new method to construct low-rank approximations of dense huge-size matrices. The method develops mosaic-skeleton method and belongs to kernel-independent methods. In distinction from a mosaic-skeleton method, the new one utilizes the hierarchical structure of matrix not only to define matrix block structure but also to calculate factors of low-rank matrix representation. The new method was applied to numerical calculation of boundary integral equations that appear from 3D problem of scattering monochromatic electromagnetic wave by ideal-conducting bodies. The solution of model problem is presented as an example of method evaluation.
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Acknowledgments
The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.
Funding
This work was supported by the Russian Science Foundation, grant no. 19-11-00338.
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Submitted by E. E. Tyrtyshnikov
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Aparinov, A.A., Setukha, A.V. & Stavtsev, S.L. Low Rank Methods of Approximation in an Electromagnetic Problem. Lobachevskii J Math 40, 1771–1780 (2019). https://doi.org/10.1134/S1995080219110064
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DOI: https://doi.org/10.1134/S1995080219110064