Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On dual Schur domain decomposition method for linear first-order
  transient problems   This paper addresses some numerical and theoretical aspects of dual Schur
domain decomposition methods for linear first-order transient partial
differential equations. In this work, we consider the trapezoidal family of
schemes for integrating the ordinary differential equations (ODEs) for each
subdomain and present four different coupling methods, corresponding to
different algebraic constraints, for enforcing kinematic continuity on the
interface between the subdomains.
  Method 1 (d-continuity) is based on the conventional approach using
continuity of the primary variable and we show that this method is unstable for
a lot of commonly used time integrators including the mid-point rule. To
alleviate this difficulty, we propose a new Method 2 (Modified d-continuity)
and prove its stability for coupling all time integrators in the trapezoidal
family (except the forward Euler). Method 3 (v-continuity) is based on
enforcing the continuity of the time derivative of the primary variable.
However, this constraint introduces a drift in the primary variable on the
interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte
stabilization to limit this drift and we derive bounds for the stabilization
parameter to ensure stability.
  Our stability analysis is based on the ``energy'' method, and one of the main
contributions of this paper is the extension of the energy method (which was
previously introduced in the context of numerical methods for ODEs) to assess
the stability of numerical formulations for index-2 differential-algebraic
equations (DAEs).

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
3
The categories of this paper are: physics
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th