126,406 research outputs found
N–Dimensional Orthogonal Tile Sizing Problem
AMS subject classification: 68Q22, 90C90We discuss in this paper the problem of generating highly efficient code when a
n + 1-dimensional nested loop program is executed on a n-dimensional torus/grid
of distributed-memory general-purpose machines. We focus on a class of uniform
recurrences with non-negative components of the dependency matrix. Using tiling
the iteration space strategy we show that minimizing the total running time reduces
to solving a non-trivial non-linear integer optimization problem. For the later we
present a mathematical framework that enables us to derive an O(n log n) algorithm
for finding a good approximate solution. The theoretical evaluations and the experimental results show that the obtained solution approximates the original minimum
sufficiently well in the context of the considered problem. Such algorithm is realtime usable for very large values of n and can be used as optimization techniques in
parallelizing compilers as well as in performance tuning of parallel codes by hand
Approximated Computation of Belief Functions for Robust Design Optimization
This paper presents some ideas to reduce the computational cost of
evidence-based robust design optimization. Evidence Theory crystallizes both
the aleatory and epistemic uncertainties in the design parameters, providing
two quantitative measures, Belief and Plausibility, of the credibility of the
computed value of the design budgets. The paper proposes some techniques to
compute an approximation of Belief and Plausibility at a cost that is a
fraction of the one required for an accurate calculation of the two values.
Some simple test cases will show how the proposed techniques scale with the
dimension of the problem. Finally a simple example of spacecraft system design
is presented.Comment: AIAA-2012-1932 14th AIAA Non-Deterministic Approaches Conference.
23-26 April 2012 Sheraton Waikiki, Honolulu, Hawai
Voltage Stabilization in Microgrids via Quadratic Droop Control
We consider the problem of voltage stability and reactive power balancing in
islanded small-scale electrical networks outfitted with DC/AC inverters
("microgrids"). A droop-like voltage feedback controller is proposed which is
quadratic in the local voltage magnitude, allowing for the application of
circuit-theoretic analysis techniques to the closed-loop system. The operating
points of the closed-loop microgrid are in exact correspondence with the
solutions of a reduced power flow equation, and we provide explicit solutions
and small-signal stability analyses under several static and dynamic load
models. Controller optimality is characterized as follows: we show a one-to-one
correspondence between the high-voltage equilibrium of the microgrid under
quadratic droop control, and the solution of an optimization problem which
minimizes a trade-off between reactive power dissipation and voltage
deviations. Power sharing performance of the controller is characterized as a
function of the controller gains, network topology, and parameters. Perhaps
surprisingly, proportional sharing of the total load between inverters is
achieved in the low-gain limit, independent of the circuit topology or
reactances. All results hold for arbitrary grid topologies, with arbitrary
numbers of inverters and loads. Numerical results confirm the robustness of the
controller to unmodeled dynamics.Comment: 14 pages, 8 figure
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