13,517 research outputs found
Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods
This paper is concerned with the reformulation of Neumann-Neumann Waveform
Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR)
methods, a family of parallel space-time approaches to solving time-dependent
PDEs. By changing the order of the operations, pipeline-parallel computation of
the waveform iterates are possible without changing the final solution. The
parallel efficiency and the increased communication cost of the pipeline
implementation is presented, along with weak scaling studies to show the
effectiveness of the pipeline NNWR and DNWR algorithms.Comment: 20 pages, 8 figure
Anti-chiral edge states in an exciton polariton strip
We present a scheme to obtain anti-chiral edge states in an exciton-polariton
honeycomb lattice with strip geometry, where the modes corresponding to both
edges propagate in the same direction. Under resonant pumping the effect of a
polariton condensate with nonzero velocity in one linear polarization is
predicted to tilt the dispersion of polaritons in the other, which results in
an energy shift between two Dirac cones and the otherwise flat edge states
become tilted. Our simulations show that due to the spatial separation from the
bulk modes the edge modes are robust against disorder.Comment: 6 pages, 5 figure
Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation for the Wave Equation
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and
Neumann-Neumann algorithms for the wave equation in space time. Each method is
based on a non-overlapping spatial domain decomposition, and the iteration
involves subdomain solves in space time with corresponding interface condition,
followed by a correction step. Using a Laplace transform argument, for a
particular relaxation parameter, we prove convergence of both algorithms in a
finite number of steps for finite time intervals. The number of steps depends
on the size of the subdomains and the time window length on which the
algorithms are employed. We illustrate the performance of the algorithms with
numerical results, and also show a comparison with classical and optimized
Schwarz WR methods.Comment: 8 pages, 6 figures, presented in 22nd International conference on
Domain Decomposition Methods, to appear in Domain Decomposition in Science
and Engineering XXII, LNCSE, Springer-Verlag 201
-SELC: Optimization by sequential elimination of level combinations using genetic algorithms and Gaussian processes
Identifying promising compounds from a vast collection of feasible compounds
is an important and yet challenging problem in the pharmaceutical industry. An
efficient solution to this problem will help reduce the expenditure at the
early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu
and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm.
Although powerful, it fails to extract substantial information from the data to
guide the search efficiently, as this methodology is not based on any
statistical modeling. The proposed approach uses Gaussian Process (GP) modeling
to improve upon SELC, and hence named -SELC. The performance of
the proposed methodology is illustrated using four and five dimensional test
functions. Finally, we implement the new algorithm on a real pharmaceutical
data set for finding a group of chemical compounds with optimal properties.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS199 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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