904 research outputs found
An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis
This paper outlines an energy-minimization finite-element approach to the
computational modeling of equilibrium configurations for nematic liquid
crystals under free elastic effects. The method targets minimization of the
system free energy based on the Frank-Oseen free-energy model. Solutions to the
intermediate discretized free elastic linearizations are shown to exist
generally and are unique under certain assumptions. This requires proving
continuity, coercivity, and weak coercivity for the accompanying appropriate
bilinear forms within a mixed finite-element framework. Error analysis
demonstrates that the method constitutes a convergent scheme. Numerical
experiments are performed for problems with a range of physical parameters as
well as simple and patterned boundary conditions. The resulting algorithm
accurately handles heterogeneous constant coefficients and effectively resolves
configurations resulting from complicated boundary conditions relevant in
ongoing research.Comment: 31 pages, 3 figures, 3 table
Gamma-Ray Bursts: Temporal Scales and the Bulk Lorentz Factor
For a sample of Swift and Fermi GRBs, we show that the minimum variability
timescale and the spectral lag of the prompt emission is related to the bulk
Lorentz factor in a complex manner: For small 's, the variability
timescale exhibits a shallow (plateau) region. For large 's, the
variability timescale declines steeply as a function of (). Evidence is also presented for an intriguing
correlation between the peak times, t, of the afterglow emission and the
prompt emission variability timescale.Comment: Accepted for publication in Ap
Multigrid reduction-in-time convergence for advection problems: A Fourier analysis perspective
A long-standing issue in the parallel-in-time community is the poor
convergence of standard iterative parallel-in-time methods for hyperbolic
partial differential equations (PDEs), and for advection-dominated PDEs more
broadly. Here, a local Fourier analysis (LFA) convergence theory is derived for
the two-level variant of the iterative parallel-in-time method of multigrid
reduction-in-time (MGRIT). This closed-form theory allows for new insights into
the poor convergence of MGRIT for advection-dominated PDEs when using the
standard approach of rediscretizing the fine-grid problem on the coarse grid.
Specifically, we show that this poor convergence arises, at least in part, from
inadequate coarse-grid correction of certain smooth Fourier modes known as
characteristic components, which was previously identified as causing poor
convergence of classical spatial multigrid on steady-state advection-dominated
PDEs. We apply this convergence theory to show that, for certain
semi-Lagrangian discretizations of advection problems, MGRIT convergence using
rediscretized coarse-grid operators cannot be robust with respect to CFL number
or coarsening factor. A consequence of this analysis is that techniques
developed for improving convergence in the spatial multigrid context can be
re-purposed in the MGRIT context to develop more robust parallel-in-time
solvers. This strategy has been used in recent work to great effect; here, we
provide further theoretical evidence supporting the effectiveness of this
approach
Strange form factors of the nucleon in a two-component model
The strange form factors of the nucleon are studied in a two-component model
consisting of a three-quark intrinsic structure surrounded by a meson cloud. A
comparison with the available experimental world data from the SAMPLE, PVA4,
HAPPEX and G0 collaborations shows a good overall agreement. The strange
magnetic moment is found to be positive, 0.315 nm.Comment: 11 pages, 2 tables, 5 figures, accepted for publication in J. Phys.
G. Revised version, new figures, extra table, new results, updated reference
Monolithic Multigrid for Magnetohydrodynamics
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics
applications and are characterized by a nonlinear system of partial
differential equations that strongly couples a charged fluid with the evolution
of electromagnetic fields. After discretization and linearization, the
resulting system of equations is generally difficult to solve due to the
coupling between variables, and the heterogeneous coefficients induced by the
linearization process. In this paper, we investigate multigrid preconditioners
for this system based on specialized relaxation schemes that properly address
the system structure and coupling. Three extensions of Vanka relaxation are
proposed and applied to problems with up to 170 million degrees of freedom and
fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to
20,000 for time-dependent problems
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