162,370 research outputs found
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).Comment: 22 Figures, 49 pages (double spacing using amsart
Simulation of stellar instabilities with vastly different timescales using domain decomposition
Strange mode instabilities in the envelopes of massive stars lead to shock
waves, which can oscillate on a much shorter timescale than that associated
with the primary instability. The phenomenon is studied by direct numerical
simulation using a, with respect to time, implicit Lagrangian scheme, which
allows for the variation by several orders of magnitude of the dependent
variables. The timestep for the simulation of the system is reduced appreciably
by the shock oscillations and prevents its long term study. A procedure based
on domain decomposition is proposed to surmount the difficulty of vastly
different timescales in various regions of the stellar envelope and thus to
enable the desired long term simulations. Criteria for domain decomposition are
derived and the proper treatment of the resulting inner boundaries is
discussed. Tests of the approach are presented and its viability is
demonstrated by application to a model for the star P Cygni. In this
investigation primarily the feasibility of domain decomposition for the problem
considered is studied. We intend to use the results as the basis of an
extension to two dimensional simulations.Comment: 15 pages, 10 figures, published in MNRA
Determination of the characteristic directions of lossless linear optical elements
We show that the problem of finding the primary and secondary characteristic
directions of a linear lossless optical element can be reformulated in terms of
an eigenvalue problem related to the unimodular factor of the transfer matrix
of the optical device. This formulation makes any actual computation of the
characteristic directions amenable to pre-implemented numerical routines,
thereby facilitating the decomposition of the transfer matrix into equivalent
linear retarders and rotators according to the related Poincare equivalence
theorem. The method is expected to be useful whenever the inverse problem of
reconstruction of the internal state of a transparent medium from optical data
obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM
Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen
Nuclear-polarizability corrections that go beyond unretarded-dipole
approximation are calculated analytically for hydrogenic (atomic) S-states.
These retardation corrections are evaluated numerically for deuterium and
contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our
results are in agreement with one previous numerical calculation, and the
retardation corrections completely account for the difference between two
previous calculations. The uncertainty in the deuterium polarizability
correction is substantially reduced. At the level of 0.01 kHz for deuterium,
only three primary nuclear observables contribute: the electric polarizability,
, the paramagnetic susceptibility, , and the third Zemach
moment, . Cartesian multipole decomposition of the virtual
Compton amplitude and its concomitant gauge sum rules are used in the analysis.Comment: 26 pages, latex, 1 figure -- Submitted to Phys. Rev. C -- epsfig.sty
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An asynchronous three-field domain decomposition method for first-order evolution problems
summary:We present an asynchronous multi-domain time integration algorithm with a dual domain decomposition method for the initial boundary-value problems for a parabolic equation. For efficient parallel computing, we apply the three-field domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. The implicit method for time discretization and the multi-domain spatial decomposition enable us to use different time steps (subcycling) on different parts of a computational domain, and thus efficiently capture the underlying physics with less computational effort. We illustrate the performance of the proposed multi-domain time integrator by means of a simple numerical example
SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
SecDec is a program which can be used for the factorization of dimensionally
regulated poles from parametric integrals, in particular multi-loop integrals,
and the subsequent numerical evaluation of the finite coefficients. Here we
present version 3.0 of the program, which has major improvements compared to
version 2: it is faster, contains new decomposition strategies, an improved
user interface and various other new features which extend the range of
applicability.Comment: 46 pages, version to appear in Comput.Phys.Com
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