Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A well-conditioned direct PinT algorithm for first-and second-order
  evolutionary equations   In this paper, we propose a direct parallel-in-time (PinT) algorithm for
time-dependent problems with first- or second-order derivative. We use a
second-order boundary value method as the time integrator that leads to a
tridiagonal time discretization matrix. Instead of solving the corresponding
all-at-once system iteratively, we diagonalize the time discretization matrix,
which yields a direct parallel implementation across all time levels. A crucial
issue on this methodology is how the condition number of the eigenvector matrix
$V$ grows as $n$ is increased, where $n$ is the number of time levels. A large
condition number leads to large roundoff error in the diagonalization
procedure, which could seriously pollute the numerical accuracy. Based on a
novel connection between the characteristic equation and the Chebyshev
polynomials, we present explicit formulas for computing $V$ and $V^{-1}$, by
which we prove that $\mathrm{Cond}_2(V)=\mathcal{O}(n^{2})$. This implies that
the diagonalization process is well-conditioned and the roundoff error only
increases moderately as $n$ grows and thus, compared to other direct PinT
algorithms, a much larger $n$ can be used to yield satisfactory parallelism.
Numerical results on parallel machine are given to support our findings, where
over 60 times speedup is achieved with 256 cores.

36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org