Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the algebraic construction of sparse multilevel approximations of
  elliptic tensor product problems   We consider the solution of elliptic problems on the tensor product of two
physical domains as e.g. present in the approximation of the solution
covariance of elliptic partial differential equations with random input.
Previous sparse approximation approaches used a geometrically constructed
multilevel hierarchy. Instead, we construct this hierarchy for a given
discretized problem by means of the algebraic multigrid method (AMG). Thereby,
we are able to apply the sparse grid combination technique to problems given on
complex geometries and for discretizations arising from unstructured grids,
which was not feasible before. Numerical results show that our algebraic
construction exhibits the same convergence behaviour as the geometric
construction, while being applicable even in black-box type PDE solvers.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol