2018/12/06 by Boris N. Khoromskij, Khoromskij, Boris N.
Chemistry · Engineering · Mathematics · Physics and Astronomy · #65F10 #65F30 #65F50 #65N35 #Advanced NMR Techniques and Applications #Elasticity and Material Modeling #Electromagnetic Scattering and Analysis #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1812.02684
openalex publication_date 2018/12/06 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
In this paper, we introduce the operator dependent range-separated tensor\napproximation of the discretized Dirac delta in \ℝd. It is\nconstructed by application of the discrete elliptic operator to the\nrange-separated decomposition of the associated Green kernel discretized on the\nCartesian grid in \ℝd. The presented operator dependent local-global\nsplitting of the Dirac delta can be applied for solving the potential equations\nin non-homogeneous media when the density in the right-hand side is given by\nthe large sum of pointwise singular charges. We show how the idea of the\noperator dependent RS splitting of the Dirac delta can be extended to the\nclosely related problem on the range separated tensor representation of the\nelliptic resolvent. The numerical tests confirm the expected localization\nproperties of the obtained operator dependent approximation of the Dirac delta\nrepresented on a tensor grid. As an example of application, we consider the\nregularization scheme for solving the Poisson-Boltzmann equation for modeling\nthe electrostatics in bio-molecules.\n