Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using hierarchical matrices in the solution of the time-fractional heat
  equation by multigrid waveform relaxation   This work deals with the efficient numerical solution of the time-fractional
heat equation discretized on non-uniform temporal meshes. Non-uniform grids are
essential to capture the singularities of "typical" solutions of
time-fractional problems. We propose an efficient space-time multigrid method
based on the waveform relaxation technique, which accounts for the nonlocal
character of the fractional differential operator. To maintain an optimal
complexity, which can be obtained for the case of uniform grids, we approximate
the coefficient matrix corresponding to the temporal discretization by its
hierarchical matrix (${\cal H}$-matrix) representation. In particular, the
proposed method has a computational cost of ${\cal O}(k N M \log(M))$, where
$M$ is the number of time steps, $N$ is the number of spatial grid points, and
$k$ is a parameter which controls the accuracy of the ${\cal H}$-matrix
approximation. The efficiency and the good convergence of the algorithm, which
can be theoretically justified by a semi-algebraic mode analysis, are
demonstrated through numerical experiments in both one- and two-dimensional
spaces.

19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph