eli turkel - Profile on Academia.edu (original) (raw)

Papers by eli turkel

A multistage time-stepping scheme for the Navier-Stokes equations

23rd Aerospace Sciences Meeting

... Affiliation: AA(National Aeronautics and Space Administration. Langley Research Center, Hampt... more ... Affiliation: AA(National Aeronautics and Space Administration. Langley Research Center, Hampton,VA.), AB(National Aeronautics and Space Administration. Langley Research Center, Hampton, VA.). ... Langley Research Center, Hampton, VA. Publication Date: 02/1985. ...

Arti cial dissipation and central di erence schemes for the Euler and Navier-Stokes equations

Arti cial dissipation and central difference schemes for the Euler and Navier-Stokes equations

2012 10th IAPR International Workshop on Document Analysis Systems, 2012

The discipline of First Temple Period epigraphy (the study of writing) relies heavily on manually... more The discipline of First Temple Period epigraphy (the study of writing) relies heavily on manually-drawn facsimiles (black and white images) of ancient inscriptions. This practice may unintentionally mix up documentation and interpretation. The article proposes a new method for evaluating the quality of the facsimile. It is based on a measure, comparing the image of the inscription to the registered facsimile. Some empirical results, supporting the methodology, are presented. The technique is also relevant to quality evaluation of other types of facsimiles and binarization in general.

We deal with the general issue of handling statistical data in archaeology for the purpose of ded... more We deal with the general issue of handling statistical data in archaeology for the purpose of deducing sound, justified conclusions. The employment of various quantitative and statistical methods in archaeological practice has existed from its beginning as a systematic discipline in the 19th century (Drower 1995). Since this early period, the focus of archaeological research has developed and shifted several times. The last phase in this process, especially common in recent decades, is the proliferation of collaboration with various branches of the exact and natural sciences. Many new avenues of inquiry have been inaugurated, and a wealth of information has become available to archaeologists. In our view, the plethora of newly obtained data requires a careful reexamination of existing statistical approaches and a restatement of the desired focus of some archaeological investigations. We are delighted to dedicate this article to Israel Finkelstein, our teacher, adviser, colleague, an...

Proceedings of the 4th International Workshop on Historical Document Imaging and Processing, 2017

The problem of finding a prototype for typewritten or handwritten characters belongs to a family ... more The problem of finding a prototype for typewritten or handwritten characters belongs to a family of "shape prior" estimation problems. In epigraphic research, such priors are derived manually, and constitute the building blocks of "paleographic tables". Suggestions for automatic solutions to the estimation problem are rare in both the Computer Vision and the OCR/Handwriting Text Recognition communities. We review some of the existing approaches, and propose a new robust scheme, suitable for the challenges of degraded historical documents. This fast and easy to implement method is employed for ancient Hebrew inscriptions dated to the First Temple period.

Journal of Computational Physics, 2019

2016 15th International Conference on Frontiers in Handwriting Recognition (ICFHR), 2016

This article discusses the quality assessment of binary images. The customary, ground truth based... more This article discusses the quality assessment of binary images. The customary, ground truth based methodology, used in the literature is shown to be problematic due to its subjective nature. Several previously suggested alternatives are surveyed and are also found to be inadequate in certain scenarios. A new approach, quantifying the adherence of a binarization to its document image is proposed and tested using six different measures of accuracy. The measures are evaluated experimentally based on datasets from DIBCO and H-DIBCO competitions, with respect to different kinds of binarization degradations.

Our research team enjoyed the privilege of collaborating with Benjamin Sass over a period of seve... more Our research team enjoyed the privilege of collaborating with Benjamin Sass over a period of several years. We are happy to dedicate this article to him and wish to express our gratitude for what has been both a prodigious and enjoyable experience. The purpose of our joint endeavor has been the introduction of modern techniques from computer science and physics to the realm of Iron Age epigraphy. One of the most important issues addressed during our cooperation was the topic of facsimile creation. Facsimile creation is a necessary preliminary step in the process of deciphering and analyzing ancient inscriptions. Several manual facsimile construction techniques are currently in use: drawing upon collation of the artifact; outlining on transparent paper overlaid on a photograph of the inscription; and computer-aided depiction via software such as Adobe Photoshop, Adobe Illustrator, Gimp or Inkscape (see Summary section below for software web links). Despite their importance for the field of epigraphy, little attention has thus far been devoted to the methodology of facsimile creation (though the recent comprehensive treatment by Parker and Rollston 2016). Recent decades have seen rapid development and consolidation of various computerized image processing algorithms. Among the most basic and popular tasks in this field is the creation of a blackand-white version of a given image, denoted as image binarization (see Fig.1a-b). Often, such a binarized image is used as a first step for further image processing missions, such as Optical Character Recognition (OCR), texts digitization and text analysis tasks. An algorithmic creation of binarizations can therefore be seen as another method of facsimile creation. Furthermore, a relatively new sub-domain of image processing, Historical Imaging and Processing (HIP), specializes in handling antique documents of different types, periods and origins. Accordingly, binarization algorithms stemming from HIP are even more suitable for archaeological purposes.

Journal of Scientific Computing, 2012

The method of difference potentials was originally proposed by Ryaben'kii and can be interpreted ... more The method of difference potentials was originally proposed by Ryaben'kii and can be interpreted as a generalized discrete version of the method of Calderon's operators in the theory of partial differential equations. It has a number of important advantages; it easily handles curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity at the level of a finite-difference scheme on a regular structured grid. The method of difference potentials assembles the overall solution of the original boundary value problem by repeatedly solving an auxiliary problem. This auxiliary problem allows a considerable degree of flexibility in its formulation and can be chosen so that it is very efficient to solve. Compact finite difference schemes enable high order accuracy on small stencils at virtually no extra cost. The scheme attains consistency only on the solutions of the differential equation rather than on a wider class of sufficiently smooth functions. Unlike standard high order schemes, compact approximations require no additional boundary conditions beyond those needed for the differential equation itself. However, they exploit two stencils-one applies to the left-hand side of the equation and the other applies to the right-hand side of the equation. Dedicated to our friend Saul Abarbanel on the occasion of his 80th birthday.

We consider the use of a multigrid method with central differencing to solve the Navier-Stokes eq... more We consider the use of a multigrid method with central differencing to solve the Navier-Stokes equations for high-speed flows. The time-dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two-dimensional laminar flow over a circular cylinder and a 15 degree compression ramp.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ArXiv, 2021

We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition ... more We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon’s boundary equation with projection on its boundary. The unknowns for the Calderon’s equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon’s equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a straightforward direct solver. We provide numerical examples demonstrating that our method is insensitive to interior cross-points and mixed boundary conditions, as well as large jumps in the wavenumber for transmission problems, which are known to be problematic for many other Domain Decomposition Methods.

We consider problems that involve the propagation of waves over large regions of space with smoot... more We consider problems that involve the propagation of waves over large regions of space with smooth, but not necessarily constant, material characteristics, separated by interfaces of arbitrary shape. The external boundaries can also be arbitrarily shaped. We present a numerical methodology for solving such problems that provides high order accuracy. It is based on Calderon’s operators and the method of difference potentials and overcomes the difficulties inherent in more traditional approaches.

We develop a compact fourth order scheme for the three-dimensional elastic wave equation in frequ... more We develop a compact fourth order scheme for the three-dimensional elastic wave equation in frequency space, using the first order velocity-stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one-directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second order scheme.

We consider acoustic scattering about a general body. This is described by the Helmholtz equation... more We consider acoustic scattering about a general body. This is described by the Helmholtz equation exterior to the body. In order to truncate the infinite domain we use the BGT absorbing boundary condition. The resultant problem in a finite domain is solved by a finite element procedure. This yields a large sparse system of linear equations which is neither symmetric nor positive definite. We solve the system by an iterative Krylov space type method. To increase the rate of convergence a preconditioner is introduced. This preconditioner is based on a different Helmholtz equation with complex coefficients. This preconditioned system is again solved by a Krylov space method with an ILU preconditioner. Computations are presented to show the efficiency of this technique.

The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized d... more The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite difference schemes enable high order accuracy on small stencils and so require no additional boundary conditions beyond those needed for the differential equation itself. Previously, we have used difference potentials combined with compact schemes for solving transmission/scattering problems in regions of a simple shape. In this paper, we generalize our previous work to incorporate general shaped boundaries and interfaces.

Journal of Scientific Computing

We construct a family of compact fourth order accurate finite difference schemes for the three di... more We construct a family of compact fourth order accurate finite difference schemes for the three dimensional scalar wave (d'Alembert) equation with constant or variable propagation speed. High order accuracy is of key importance for the numerical simulation of waves as it reduces the dispersion error (i.e., the pollution effect). The schemes that we propose are built on a stencil that has only three nodes in any coordinate direction or in time, which eliminates the need for auxiliary initial or boundary conditions. These schemes are implicit in time and conditionally stable. A particular scheme with the maximum Courant number can be chosen within the proposed class. The inversion at the upper time level is done by FFT for constant coefficients and multigrid for variable coefficients, which keeps the overall complexity of time marching comparable to that of a typical explicit scheme. Keywords Unsteady wave propagation • Fourth order accurate approximation • Small stencil • Cartesian grid • Implicit scheme • Multigrid methods Mathematics Subject Classification 65M06 • 65M12 • 65M22 We dedicate this paper to the memory of Professor Saul (Shalom) Abarbanel who provided mentorship and inspiration to a whole generation of students and colleagues.

Journal of Computational Physics

We consider interior and exterior initial boundary value problems for the three-dimensional wave ... more We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing prehistory of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multiprocessor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.