374,057 research outputs found
Dual band fss with fractal elements
Experimental and computed results of a frequency selective surface (FSS) based on a certain type of fractal element are presented. The fractal element is a two iteration Sierpinski gasket dipole. Owing to the dual band behaviour of the two iteration Sierpinski gasket dipole, two stopbands are exhibited within the operating frequency band. This behaviour is obtained by arraying one simple element in a single layer frequency selective surface (FSS)Peer ReviewedPostprint (published version
Aggregation-based aggressive coarsening with polynomial smoothing
This paper develops an algebraic multigrid preconditioner for the graph
Laplacian. The proposed approach uses aggressive coarsening based on the
aggregation framework in the setup phase and a polynomial smoother with
sufficiently large degree within a (nonlinear) Algebraic Multilevel Iteration
as a preconditioner to the flexible Conjugate Gradient iteration in the solve
phase. We show that by combining these techniques it is possible to design a
simple and scalable algorithm. Results of the algorithm applied to graph
Laplacian systems arising from the standard linear finite element
discretization of the scalar Poisson problem are reported
Computational aspects of helicopter trim analysis and damping levels from Floquet theory
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated
On the Number of Places of Convergence for Newton's Method over Number Fields
Let f be a polynomial of degree at least 2 with coefficients in a number
field K, let x_0 be a sufficiently general element of K, and let alpha be a
root of f. We give precise conditions under which Newton iteration, started at
the point x_0, converges v-adically to the root alpha for infinitely many
places v of K. As a corollary we show that if f is irreducible over K of degree
at least 3, then Newton iteration converges v-adically to any given root of f
for infinitely many places v. We also conjecture that the set of places for
which Newton iteration diverges has full density and give some heuristic and
numerical evidence.Comment: 9 pages; minor changes from the previous version; to appear in
Journal de Th\'eorie des Nombres de Bordeau
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