77,386 research outputs found
An optimal way of moving a sequence of points onto a curve in two dimensions
Let s̲(t), 0 ≤ t ≤ T, be a smooth curve and let x̲i, i = 1, 2, ... , n, be a sequence of points in two dimensions. An algorithm is given that calculates
the parameters ti, i = 1,2, ... ,n, that minimize the function max{llx̲i-s̲(ti)ll₂:
i = 1, 2, ... , n} subject to the constraints 0 ≤ t₁≤ t₂≤ · · · ≤ tn ≤ T. Further, the
final value of the objective function is best lexicographically, when the distances
llx̲i-s̲(ti)ll₂, i= 1, 2, ... , n, are sorted into decreasing order. The algorithm finds
the global solution to this calculation. Usually the magnitude of the total work
is only about n when the number of data points is large. The efficiency comes
from techniques that use bounds on the final values of the parameters to split
the original problem into calculations that have fewer variables. The splitting
techniques are analysed, the algorithm is described, and some numerical results
are presented and discussed
Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
Given a tetrahedral mesh and objective functionals measuring the mesh quality
which take into account the shape, size, and orientation of the mesh elements,
our aim is to improve the mesh quality as much as possible. In this paper, we
combine the moving mesh smoothing, based on the integration of an ordinary
differential equation coming from a given functional, with the lazy flip
technique, a reversible edge removal algorithm to modify the mesh connectivity.
Moreover, we utilize radial basis function (RBF) surface reconstruction to
improve tetrahedral meshes with curved boundary surfaces. Numerical tests show
that the combination of these techniques into a mesh improvement framework
achieves results which are comparable and even better than the previously
reported ones.Comment: Revised and improved versio
On Minimal Trajectories for Mobile Sampling of Bandlimited Fields
We study the design of sampling trajectories for stable sampling and the
reconstruction of bandlimited spatial fields using mobile sensors. The spectrum
is assumed to be a symmetric convex set. As a performance metric we use the
path density of the set of sampling trajectories that is defined as the total
distance traveled by the moving sensors per unit spatial volume of the spatial
region being monitored. Focussing first on parallel lines, we identify the set
of parallel lines with minimal path density that contains a set of stable
sampling for fields bandlimited to a known set. We then show that the problem
becomes ill-posed when the optimization is performed over all trajectories by
demonstrating a feasible trajectory set with arbitrarily low path density.
However, the problem becomes well-posed if we explicitly specify the stability
margins. We demonstrate this by obtaining a non-trivial lower bound on the path
density of an arbitrary set of trajectories that contain a sampling set with
explicitly specified stability bounds.Comment: 28 pages, 8 figure
Optimised dragline planning model
The presenting company provided data for typical operating parameters used in dragline operation. The problem for the Study Group was to investigate whether an optimal model of dragline operation could be developed. The Study Group modelled the sequence of operations for a typical surface mining strip. Overall, a simulation approach seems necessary to fully represent the dragline operation. Some aspects of the operations that are amenable to optimisation are described in this report
Rectilinear partitioning of irregular data parallel computations
New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed
Green's functions for multiply connected domains via conformal mapping
A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations
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