Browsing by Subject "Computational geometry"

Now showing 1 - 17 of 17

Open Access
Analytical evaluation of the MoM matrix elements
(Institute of Electrical and Electronics Engineers, 1996-04) Alatan, L.; Aksun, M. I.; Mahadevan, K.; Birand, M. T.
Derivation of the closed-form Green's functions has eliminated the computationally expensive evaluation of the Sommerfeld integrals to obtain the Green's functions in the spatial domain. Therefore, using the closed-form Green's functions in conjunction with the method of moments (MoM) has unproved the computational efficiency of the technique significantly. Further improvement can be achieved on the calculation of the matrix elements involved in the MoM, usually double integrals for planar geometries, by eliminating the numerical integration. The contribution of this paper is to present the analytical evaluation of the matrix elements when the closed-form Green's functions are used, and to demonstrate the amount of improvement in computation time. © 1996 IEEE.
Open Access
Animation of boiling phenomena
(IEEE, 2008-05) Bülbül, Abdullah; Küçüktunç, Onur; Özgüç, Bülent
Phenomenon of boiling is a challenging topic for computer graphics due to its complex hydrodynamics and formulation. Realistic fluid animations require very heavy three-dimensional fluid flow calculations, and surface estimations as well. However, realism and performance are the two important objectives of the boiling animation for a real-time application. We present an efficient method for the simulation of boiling water in this paper. The method is based on modeling the bubbles and waves as particles. Grid-based approach is used both for the heating and the fluid surface. Our technique makes it possible to produce the animation of boiling phenomena nearly in real-time. ©2008 IEEE.
Open Access
An approximation algorithm for computing the visibility region of a point on a terrain and visibility testing
(IEEE, 2014-01) Alipour, S.; Ghodsi, M.; Güdükbay, Uğur; Golkari, M.
Given a terrain and a query point p on or above it, we want to count the number of triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and then we run it on the real data sets. The experimental results show that our approximation solution is very close to the real solution and compare to the other similar works, the running time of our algorithm is better than their algorithm. The analysis of time complexity of algorithm is also presented. Also, we consider visibility testing problem, where the goal is to test whether p and a given triangle of train are visible or not. We propose an algorithm for this problem and show that the average running time of this algorithm will be the same as running time of the case where we want to test the visibility between two query point p and q.
Open Access
Continuous knapsack sets with divisible capacities
(Springer, 2016) Wolsey, L. A.; Yaman, H.
We study two continuous knapsack sets (Formula presented.) and (Formula presented.) with (Formula presented.) integer, one unbounded continuous and (Formula presented.) bounded continuous variables in either (Formula presented.) or (Formula presented.) form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and (Formula presented.) polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable. The latter convex hulls are completely described by an exponential family of partition inequalities and a polynomial size extended formulation is known in the (Formula presented.) case. We also provide an extended formulation for the (Formula presented.) case. It follows that, given a specific objective function, optimization over both (Formula presented.) and (Formula presented.) can be carried out by solving (Formula presented.) polynomial size linear programs. A further consequence of these results is that the coefficients of the continuous variables all take the values 0 or 1 (after scaling) in any non-trivial facet-defining inequality of the convex hull of such sets.
Open Access
An efficient method for electromagnetic characterization of 2-D geometries in stratified media
(IEEE, 2002) Aksun, M. I.; Çalışkan, F.; Gürel, Levent
A numerically efficient technique, based on the spectral-domain method of moments (MoM) in conjunction with the generalized pencil-of-functions (GPOF) method, is developed for the characterization of two-dimensional geometries in multilayer planar media. This approach provides an analytic expression for all the entries of the MoM matrix, explicitly including the indexes of the basis and testing functions provided that the Galerkin's MoM is employed. This feature facilitates an efficient modification of the geometry without the necessity of recalculating the additional elements in the MoM matrix. To assess the efficiency of the approach, the results and the matrix fill times are compared to those obtained with two other efficient methods, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, and a fast Fourier transform algorithm to evaluate the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries.
Open Access
Finite element modeling of micro-particle separation using ultrasonic standing waves
(ASME, 2014) Büyükkoçak, S.; Çetin, Barbaros; Özer, M. B.
Acoustophoresis which means separation of particles and cells using acoustic waves is becoming an intensive research subject. The method is based on inducing an ultrasonic compression standing wave inside a microchannel. A finite element approach is used to model the acoustic and electro-mechanical behavior of the piezoelectric material, the micro-channel geometry as well as the fluid inside the channel. The choices of silicon and PDMS materials are investigated as the chip materials for the resonator. A separation channel geometry which is commonly used in the literature is implemented in this study and the fluid flow inside the microchannel geometry is simulated using computational fluid dynamics. The acoustic field inside the fluid channel is also be simulated using the finite element method. For the separation process to be successful micro-particles of different diameter groups should end up in different channels of the micro-separator. In order to simulate real life scenarios, each particle size group have a size distribution within themselves. For realistic simulation results the particles will be released into the micro separator from a different starting locations (starting location distribution). The results of this Monte-Carlo based finite element simulation approach will be compared with the reported experimental results.
Open Access
Iterative solution of the normal-equations form of the electric-field integral equation
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
In this paper, we show that transforming the original equations into normal equations improves the convergence of EFIE significantly. We present the solutions of EFIE by employing the least-squares QR (LSQR) algorithm, which corresponds to a stable application of the conjugate gradient (CG) algorithm on the normal equations. Despite the squaring of the condition number due to such a transformation into the normal equations, LSQR improves the convergence rate of the iterative solutions of EFIE and performs better than many other iterative algorithms that are commonly used in the literature. In addition to LSQR, we present the accelerated convergence of the normal equations in the context of the generalized minimal residual (GMRES) algorithm, where the memory requirement is reduced significantly due to the improved convergence characteristics.
Open Access
Lattice dynamics and elastic properties of lanthanum monopnictides
(2008) Gökoǧlu G.; Erkişi, A.
In this study, first principles calculation results of the second order elastic constants and lattice dynamics of two lanthanum monopnictides, LaN and LaBi, which crystallize in rock-salt structure (B1 phase), are presented. Calculations were based on plane wave basis sets and pseudopotential methods in the framework of Density Functional Theory (DFT) with generalized gradient approximation. Elastic constants are calculated by tetragonal and orthorhombic distortions on cubic structure. Phonon dispersion spectra was constructed in the linear response approach of the Density Functional Perturbation Theory (DFPT). The complete phonon softening with negative frequencies and large elastic anisotropy were observed for LaN single crystal as a sign of the structural instability. The phonon dispersion curve for LaBi is typical for lanthanum monopnictides and does not show any anomalous physical property. The calculated structural quantities for both LaN and LaBi systems agree well with the available experimental and theoretical data. © 2008 Elsevier Ltd. All rights reserved.
Open Access
Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices
(Academic Press, 2008-05) Aykanat, Cevdet; Cambazoglu, B. B.; Uçar, B.
K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms perform considerably worse when used in the multiple constraint and fixed vertex formulations. We discuss possible reasons for this performance degradation. We describe a careful implementation of a multi-level direct K-way hypergraph partitioning algorithm, which performs better than a well-known recursive-bisection-based partitioning algorithm in hypergraph partitioning with multiple constraints and fixed vertices. We also experimentally show that the proposed algorithm is effective in standard hypergraph partitioning. © 2007 Elsevier Inc. All rights reserved.
Open Access
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems
(ESA Publications, 2006) Ergül, Özgür; Gürel, Levent
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL functions, the accuracy of MFIE and CFIE can be improved to the levels of EFIE without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions.
Open Access
Radius of curvature estimation and localization of targets using multiple sonar sensors
(A I P Publishing LLC, 1999-04) Barshan, B.; Sekmen, A. S.
Acoustic sensors have been widely used in time-of-flight ranging systems since they are inexpensive and convenient to use. One of the most important limitations of these sensors is their low angular resolution. To improve the angular resolution and the accuracy, a novel, flexible, and adaptive three- dimensional (3-D) multi-sensor sonar system is described for estimating the radius of curvature and location of cylindrical and spherical targets. Point, line, and planar targets are included as limiting cases which are important for the characterization of typical environments. Sensitivity analysis of the curvature estimate with respect to measurement errors and certain system parameters is provided. The analysis and the simulations are verified by experiments in 2-D with specularly reflecting cylindrical and planar targets, using a real sonar system. Typical accuracies in range and azimuth are 0.18 mm and 0.1°, respectively. Accuracy of the curvature estimation depends on the target type and system parameters such as transducer separation and operating range. The adaptive configuration brings an improvement varying between 35% and 45% in the accuracy of the curvature estimate. The presented results are useful for target differentiation and tracking applications.A flexible and adaptive three-dimensional multisensor sonar system capable of estimating the location and radius of curvature of spherical and cylindrical targets is presented. The performance radius of curvature estimation is analyzed to provide information for differentiating reflectors with different radii. Results showed that the adaptive configuration improved the accuracy of the curvature estimate between 35% and 45%.
Open Access
Simultaneous extraction of geometry and surface properties of targets using infrared intensity signals
(IEEE, 2005) Aytaç, Tayfun; Barshan, Billur
We propose the use of angular intensity signals obtained with low-cost infrared sensors and present an algorithm to simultaneously extract the geometry and surface properties of commonly encountered targets in indoor environments. The method is verified experimentally with planes, 90° corners, and 90° edges covered with aluminum, white cloth, and Styrofoam packaging material. An average correct classification rate of 80% of both geometry and surface over all target types is achieved and targets are localized within absolute range and azimuth errors of 1.5 cm and 1.1°, respectively. Taken separately, the geometry and surface type of targets can be correctly classified with rates of 99% and 81%, respectively, indicating that the geometrical properties of the targets are more distinctive than their surface properties, and surface determination is the limiting factor. The method demonstrated shows that simple infrared sensors, when coupled with appropriate signal processing, can be used to extract substantially more information than such devices are commonly employed for.
Open Access
Solutions of large integral-equation problems with preconditioned MLFMA
(IEEE, 2007) Ergül, Özgür; Malas, Tahir; Ünal, Alper; Gürel, Levent
We report the solution of the largest integral-equation problems in computational electromagnetics. We consider matrix equations obtained from the discretization of the integral-equation formulations that are solved iteratively by employing parallel multilevel fast multipole algorithm (MLFMA). With the efficient parallelization of MLFMA, scattering and radiation problems with millions of unknowns are easily solved on relatively inexpensive computational platforms. For the iterative solutions of the matrix equations, we are able to obtain accelerated convergence even for ill-conditioned matrix equations using advanced preconditioning schemes, such as nested preconditioned based on an approximate MLFMA. By orchestrating these diverse activities, we have been able to solve a closed geometry formulated with the CFIE containing 33 millions of unknowns and an open geometry formulated with the EFIE containing 12 millions of unknowns, which are the largest problems of their classes, to the best of our knowledge.
Open Access
The splittable flow arc set with capacity and minimum load constraints
(Elsevier, 2013) Yaman, H.
We study the convex hull of the splittable flow arc set with capacity and minimum load constraints. This set arises as a relaxation of problems where clients have demand for a resource that can be installed in integer amounts and that has capacity limitations and lower bounds on utilization. We prove that the convex hull of this set is the intersection of the convex hull of the set with a capacity constraint and the convex hull of the set with a minimum load constraint.
Open Access
A synthetic aperture imaging system using surface wave modes
(IEEE, 1995) Bozkurt, Ayhan; Arıkan, Orhan; Atalar, Abdullah
A synthetic aperture acoustic imaging system with a novel inversion algorithm is described. Data is obtained by using a transducer insonifying the sample surface at a critical angle which is excited by a short electrical pulse. The critical angle is chosen for a suitable surface wave or Lamb wave mode that exists on the object. The transducer is mechanically scanned in only one direction during which many pulse excitations and subsequent recordings are realized. The received signal is sampled in time and digitized to be processed by using the new inversion approach providing an optimal 2-D image of the surface reflectivity.
Open Access
Target classification with simple infrared sensors using artificial neural networks
(IEEE, 2008-10) Aytaç, T.; Barshan, Billur
This study investigates the use of low-cost infrared (IR) sensors for the determination of geometry and surface properties of commonly encountered features or targets in indoor environments, such as planes, corners, edges, and cylinders using artificial neural networks (ANNs). The intensity measurements obtained from such sensors are highly dependent on the location, geometry, and surface properties of the reflecting target in a way which cannot be represented by a simple analytical relationship, therefore complicating the localization and classification process. We propose the use of angular intensity scans and feature vectors obtained by modeling of angular intensity scans and present two different neural network based approaches in order to classify the geometry and/or the surface type of the targets. In the first case, where planes, 90° corners, and 90° edges covered with aluminum, white cloth, and Styrofoam packaging material are differentiated, an average correct classification rate of 78% of both geometry and surface over all target types is achieved. In the second case, where planes, 90° edges, and cylinders covered with different surface materials are differentiated, an average correct classification rate of 99.5% is achieved. The method demonstrated shows that ANNs can be used to extract substantially more information than IR sensors are commonly employed for. © 2008 IEEE.
Open Access
Walkthrough in complex environments at interactive rates using level-of-detail
(TÜBİTAK, 2002) Selçuk, Alper; Güdükbay, Uğur; Özgüç, Bülent
One of the biggest problems in computer graphics is displaying huge geometric models at interactive rates. A lot of work has been done to achieve the required frame-rates in architecture, simulation, computer-aided design and entertainment applications. In this paper, a system that enables walkthrough in complex environments using level-of-detail approximations is explained. The system uses hierarchical triangulated models as input. In the preprocessing phase, multiresolution models of objects are created using polygonal simplification techniques. During walkthrough, fast frustum culling based on bounding boxes is performed to eliminate branches of hierarchy that are not visible. An appropriate level for detail of objects is selected and displayed depending on the distance of the objects to the camera. For far nodes in the hierarchy, geometric data in lower levels is ignored and textured bounding boxes are displayed. The system achieves interactive frame rates for moderately complex models containing up to a million polygons.