11,800 research outputs found
Zero modes in magnetic systems: general theory and an efficient computational scheme
The presence of topological defects in magnetic media often leads to normal
modes with zero frequency (zero modes). Such modes are crucial for long-time
behavior, describing, for example, the motion of a domain wall as a whole.
Conventional numerical methods to calculate the spin-wave spectrum in magnetic
media are either inefficient or they fail for systems with zero modes. We
present a new efficient computational scheme that reduces the magnetic
normal-mode problem to a generalized Hermitian eigenvalue problem also in the
presence of zero modes. We apply our scheme to several examples, including
two-dimensional domain walls and Skyrmions, and show how the effective masses
that determine the dynamics can be calculated directly. These systems highlight
the fundamental distinction between the two types of zero modes that can occur
in spin systems, which we call special and inertial zero modes. Our method is
suitable for both conservative and dissipative systems. For the latter case, we
present a perturbative scheme to take into account damping, which can also be
used to calculate dynamical susceptibilities.Comment: 64 pages, 15 figure
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
GMRES-Accelerated ADMM for Quadratic Objectives
We consider the sequence acceleration problem for the alternating direction
method-of-multipliers (ADMM) applied to a class of equality-constrained
problems with strongly convex quadratic objectives, which frequently arise as
the Newton subproblem of interior-point methods. Within this context, the ADMM
update equations are linear, the iterates are confined within a Krylov
subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its
ability to accelerate convergence. The basic ADMM method solves a
-conditioned problem in iterations. We give
theoretical justification and numerical evidence that the GMRES-accelerated
variant consistently solves the same problem in iterations
for an order-of-magnitude reduction in iterations, despite a worst-case bound
of iterations. The method is shown to be competitive against
standard preconditioned Krylov subspace methods for saddle-point problems. The
method is embedded within SeDuMi, a popular open-source solver for conic
optimization written in MATLAB, and used to solve many large-scale semidefinite
programs with error that decreases like , instead of ,
where is the iteration index.Comment: 31 pages, 7 figures. Accepted for publication in SIAM Journal on
Optimization (SIOPT
Computational methods and software systems for dynamics and control of large space structures
Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers
Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations
A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization
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