Browsing by Subject "Discretizations"

Now showing 1 - 8 of 8

Open Access
Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations
(IEEE, 2016) Ergül, Ö.; Karaosmanoğlu, B.; Takrimi, Manouchehr; Ertürk, Vakur B.
We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA solvers employing conventional tree structures, are demonstrated on practical problems.
Open Access
Improving iterative solutions of the electric-field integral equation via transformations into normal equations
(Taylor and Francis, 2012-04-03) Ergül, Özgür; Gürel, Levent
We consider the solution of electromagnetics problems involving perfectly conducting objects formulated with the electric-field integral equation (EFIE). Dense matrix equations obtained from the discretization of EFIE are solved iteratively by the generalized minimal residual (GMRES) algorithm accelerated with a parallel multilevel fast multipole algorithm. We show that the number of iterations is halved by transforming the original matrix equations into normal equations. This way, memory required for the GMRES algorithm is reduced by more than 50%, which is significant when the problem size is large.
Open Access
Integral-equation study of ray effects and natural-mode resonances in a 2-D dielectric prism
(IEEE, 2015) Sukharevsky, İlya O.; Altıntaş, Ayhan
We analyze the interplay of two different types of electromagnetic behavior demonstrated by a 2-D dielectric prism: Geometrical Optics and resonance. As it is shown, the first is responsible, for instance, for enhanced reflection from an isosceles 90-degree prism of arbitrary epsilon and size, if illuminated from the base. The second is responsible for the peaks in the total scattering and absorption cross-sections (RCS) at the natural-mode frequencies. The numerical model is based on Nystrom discretization of Muller-type integral equations that provides guarantied convergence.
Open Access
Landau levels in lattices with long - range hopping
(American Physical Society, 2013) Atakişi, Hakan; Oktel, M. Özgür
Landau levels (LLs) are broadened in the presence of a periodic potential, forming a barrier for accurate simulation of the fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight-binding lattice if a particular form of long-range hopping is introduced. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long-range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wave functions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restores the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wave functions is as large as the space spanned by continuum wave functions, and we find the constraints on the magnetic field for this condition to be satisfied. Finally, using these constraints and the first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.
Open Access
Signal processing issues in diffraction and holographic 3DTV
(IEEE, 2005) Onural, Levent; Özaktaş, Haldun M.
Image capture and image display will most likely be decoupled in future 3DTV systems. For this reason, as well as the need to convert abstract representations to display driver signals, and the need to explicitly consider diffraction and propagation effects, it is expected that signal processing issues will play a fundamental role in achieving 3DTV operation. Since diffraction between two parallel planes is equivalent to a 2D linear shift-invariant system, various signal processing techniques play an important role. Diffraction between tilted planes can also be modeled as a relatively simple system, leading to efficient discrete computations. Two fundamental problems are digital computation of the optical field due to a 3D object, and finding the driver signals for a given optical device so as to generate the desired optical field in space. The discretization of optical signals leads to several interesting issues; for example, it is possible to violate the Nyquist rate while sampling, but still maintain full reconstruction. The fractional Fourier transform is another signal processing tool which finds application in optical wave propagation.
Open Access
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS
(2012) Temizer, I.; Wriggers, P.; Hughes, T. J. R.
A three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume. © 2011 Elsevier B.V.
Open Access
Wave scattering by one and many thin material strips: singular integral equations, Meshless Nystrom discretization, and periodicity caused resonances
(IEEE, 2014) Shapoval, O. V.; Sukharevsky, Ilya. O.; Altıntaş, Ayhan; Sauleau, R.; Nosich, A. I.
We consider the medial-line singular-integral equation technique for the analysis of the scattering by multiple thin material strips. Their discretization is performed using the Nystrom-type scheme that guarantees convergence. Numerical study of the scattering by periodic arrays of a few hundred or more strips reveals specific high-Q resonances caused by the periodicity.
Open Access
The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity
(Elsevier, 2013) Yazici, M. A.; Akar, N.
We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.