4,763 research outputs found
Decompactifications and Massless D-Branes in Hybrid Models
A method of determining the mass spectrum of BPS D-branes in any phase limit
of a gauged linear sigma model is introduced. A ring associated to monodromy is
defined and one considers K-theory to be a module over this ring. A simple but
interesting class of hybrid models with Landau-Ginzburg fibres over CPn are
analyzed using special Kaehler geometry and D-brane probes. In some cases the
hybrid limit is an infinite distance in moduli space and corresponds to a
decompactification. In other cases the hybrid limit is at a finite distance and
acquires massless D-branes. An example studied appears to correspond to a novel
theory of supergravity with an SU(2) gauge symmetry where the gauge and
gravitational couplings are necessarily tied to each other.Comment: PDF-LaTeX, 34 pages, 2 mps figure
A fast and well-conditioned spectral method for singular integral equations
We develop a spectral method for solving univariate singular integral
equations over unions of intervals by utilizing Chebyshev and ultraspherical
polynomials to reformulate the equations as almost-banded infinite-dimensional
systems. This is accomplished by utilizing low rank approximations for sparse
representations of the bivariate kernels. The resulting system can be solved in
operations using an adaptive QR factorization, where is
the bandwidth and is the optimal number of unknowns needed to resolve the
true solution. The complexity is reduced to operations by
pre-caching the QR factorization when the same operator is used for multiple
right-hand sides. Stability is proved by showing that the resulting linear
operator can be diagonally preconditioned to be a compact perturbation of the
identity. Applications considered include the Faraday cage, and acoustic
scattering for the Helmholtz and gravity Helmholtz equations, including
spectrally accurate numerical evaluation of the far- and near-field solution.
The Julia software package SingularIntegralEquations.jl implements our method
with a convenient, user-friendly interface
A lifting and recombination algorithm for rational factorization of sparse polynomials
We propose a new lifting and recombination scheme for rational bivariate
polynomial factorization that takes advantage of the Newton polytope geometry.
We obtain a deterministic algorithm that can be seen as a sparse version of an
algorithm of Lecerf, with now a polynomial complexity in the volume of the
Newton polytope. We adopt a geometrical point of view, the main tool being
derived from some algebraic osculation criterions in toric varieties.Comment: 22 page
GPU-accelerated discontinuous Galerkin methods on hybrid meshes
We present a time-explicit discontinuous Galerkin (DG) solver for the
time-domain acoustic wave equation on hybrid meshes containing vertex-mapped
hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable
formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto
(Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions
for hybrid meshes are derived by bounding the spectral radius of the DG
operator using order-dependent constants in trace and Markov inequalities.
Computational efficiency is achieved under a combination of element-specific
kernels (including new quadrature-free operators for the pyramid), multi-rate
timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM
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