Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Range-separated tensor representation of the discretized
  multidimensional Dirac delta and elliptic operator inverse   In this paper, we introduce the operator dependent range-separated tensor
approximation of the discretized Dirac delta in $\mathbb{R}^d$. It is
constructed by application of the discrete elliptic operator to the
range-separated decomposition of the associated Green kernel discretized on the
Cartesian grid in $\mathbb{R}^d$. The presented operator dependent local-global
splitting of the Dirac delta can be applied for solving the potential equations
in non-homogeneous media when the density in the right-hand side is given by
the large sum of pointwise singular charges. We show how the idea of the
operator dependent RS splitting of the Dirac delta can be extended to the
closely related problem on the range separated tensor representation of the
elliptic resolvent. The numerical tests confirm the expected localization
properties of the obtained operator dependent approximation of the Dirac delta
represented on a tensor grid. As an example of application, we consider the
regularization scheme for solving the Poisson-Boltzmann equation for modeling
the electrostatics in bio-molecules.

24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th