A one-equation turbulence model for aerodynamic flows

Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

This Key Note presents a summary of the development of the Finite Element Method in the field of Electromagnet ic Engineering, together with a description of several contributions of the authors to the Finite Element Method and its application to the solution of electromagnetic problems. First, a self-adaptive mesh scheme is presented in the context of the quasi-static and full-wave analysis of general anisotropic multiconductor arbitrary shaped waveguiding structures. A comparison between two a posteriori error estimates is done. The first one is based on the complete residual of the differential equations defining the problem. The second one is based on a recovery or smoothing technique of the electromagnetic field. Next, an implementation of the first family of Nedelec's curl-conforming elements done by the authors is outlined. Its features are highlighted and compared with other curl-conforming elements. A presentation of an iterative procedure using a numerically exact radiation condition for the analysis of open (scattering and radiation) problems follows. Other contributions of the authors, like the use of wavelet like basis functions and an implementation of a Time Domain Finite Element Method in the context of two-dimensional scattering problems are only mentioned due to the lack of space.

The finite element method in electromagnetics

A new set of benchmarks has been developed for the performance evaluation of highly parallel supercom puters. These consist of five "parallel kernel" bench marks and three "simulated application" benchmarks. Together they mimic the computation and data move ment characteristics of large-scale computational fluid dynamics applications. The principal distinguishing feature of these benchmarks is their "pencil and paper" specification-all details of these benchmarks are specified only algorithmically. In this way many of the difficulties associated with conventional bench- marking approaches on highly parallel systems are avoided.

/pdf/the-nas-parallel-benchmarks-1v48ldcocu.pdf

The Nas Parallel Benchmarks

Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities

The authors present a new method of writer identification, employing the full power of multiple experiments, which yields a statistically significant result. Each individual binarized and segmented character is represented as a histogram of 512 binary pixel patterns—3 × 3 black and white patches. In the process of comparing two given inscriptions under a “single author” assumption, the algorithm performs a Kolmogorov–Smirnov test for each letter and each patch. The resulting p-values are combined using Fisher’s method, producing a single p-value. Experiments on both Modern and Ancient Hebrew data sets demonstrate the excellent performance and robustness of this approach. c © 2017 Society for Imaging Science and Technology. [DOI: 10.2352/J.ImagingSci.Technol.2017.61.1.010404] INTRODUCTION The current article deals with the challenging task of writer identification in historical documents. In what follows, we provide a short overview of the existing approaches to this task, and present the main contribution of this article. Prior Work The problem of computerized writer identification within historical documents exists in the literature for several decades.1 Several features and their combination methods have been proposed for that purpose. The article Ref. 1 uses run-length histograms, combined via PCA (first two components). Article Ref. 2 continues the use of run-length distributions, supplementing them with allographic features (grapheme codebook generated using self-organizing map); the feature fusion is performed via simple or weighted averaging distances due to the individual features. Similar allographic features (‘‘fraglets’’), optionally supplemented with edge-directional feature (‘‘hinge’’) are present in Ref. 3, with Hamming distance measures between the normalized features. The article Ref. 4 presents another feature combination technique; extracting 8 types of features pertaining to various relations between foreground and background pixels of segmented characters, as well as their central moments. The features are selected via dimension reduction techniques Received July 18, 2016; accepted for publication Nov. 12, 2016; published online Dec. 8, 2016. Associate Editor: Zeev Zalevsky. 1062-3701/2017/61(1)/010404/9/$25.00 such as sequential forward floating selection and linear discriminant analysis, classifying the reduced feature vectors via a linear Bayes classifier or K-nearest neighbors. Yet another set of classifiers based on grid microstructure, allograph level and topological features, combined via weighting procedure, is presented in Ref. 5. Article Ref. 6 provides a wealth of contour-based, oriented basic image, as well as SIFT, features classified by a voting procedure and SVM; Ref. 7 uses a similar setup, adding HOG features. An adaptation of SIFT features is also used in Ref. 8, with dimensionality reduced via PCA, resulting in a visual vocabulary. The features are clustered using a Gaussian Mixture Model and employing the Fisher kernel. A recent use of KDA in a setting involving both chain-code and edge-based directional features can be found in Ref. 9. A thoroughly different approach is demonstrated in Ref. 10, operating on a segmented character level, and treating them as realizations of estimated ‘‘Ideal Prototypes.’’ The identity or distinction among writers is made via several techniques, employing comparisons of the contours of the realizations to various ideals, and using heuristics and maximum likelihood estimations procedure combining information from different letters in order to find similar writers. A similar method is described in Ref. 11, with comparisons between character or ideal contours solved analytically. A review of these articles, as well as surveys of the broader field of writer identification,12,13 demonstrate the common denominators of most of these algorithms: a series of features (e.g., based on edge, allograph or topological information, or using ‘‘classical’’ computer vision features such as SIFT,HOGandGabor filters) is extracted.Optionally, the dimensionality is reduced (e.g., via weighting, LDA, PCA or KDA methods), followed by writer classification of the resulting feature vectors (e.g., by employing KNN, SVM, MLE or the Fisher Kernel). Usually, the question is whether a given document, according to some metric, is written by the same author as the most closely matching document. Alternatively, several (e.g., 5 or 10) ‘‘closest’’ documents are fetched for the purpose of identifying at least one identical writer. The algorithm’s performance is checked based on an existing ground truth. Although some of these methods perform reasonably for their tasks and data sets, their typical output is an J. Imaging Sci. Technol. 010404-1 Jan.-Feb. 2017 Shaus and Turkel: Writer identification in modern and historical documents abstract distance between two given inscriptions, or else a table indicating the distances between several inscriptions. However, these distances do not yield any probabilistic information. Thus, it is difficult to interpret such an output outside a well ground-truthed framework. In particular the distances, by themselves, are insufficient for the different task of analyzing a corpus ofmany inscriptions, with an unknown number of authors. The existing approaches can be contrasted with the direct predecessor of this article,14 which proposes a statistical approach. The article used a sophisticated concatenation and subsequent combination of SIFT, Zernike, DCT, and Kd -tree, image projections, CMI15–17 and L1 features and distances. Subsequently, on an inscriptions’ pair-wise basis, the writer identification analysis was performed independently for each letter. This resulted in different statistical p-values, estimating the probability of a single author producing the different letter instances of the two inscriptions. These independent p-values were later combined into a ‘‘meta’’ p-value via Fisher’s Method (a brief explanation is provided below), typically resulting in more significant results. Contrary to the existing approaches, such an approach can be easily utilized in order to detect different authors within any given corpus, by detecting ‘‘meta’’ p-values below certain threshold. Finally, we rely on previously developed document preprocessing techniques. In particular, we assume the existence of a suitable binarization, segmentation and (if needed) restoration of characters, whose quality is suitable for our needs. The inputs for the described method are individual black and white images of single characters, reflecting the original writing as reliably as possible (e.g., not thinned, no slant correction, etc.). Such automatic or semimanual techniques are described, for our data sets, in Refs. 17–19 and especially in Refs. 14, 20; for other approaches, consult the references mentioned in Ref. 4, 10, 11. Formethods assessing the adherence of character’s reconstruction to its image, as well as the general quality of the resulting binarization, see Refs. 15, 16, 21, 22. Additional details regarding the preparation of the different data sets are provided below.distance between two given inscriptions, or else a table indicating the distances between several inscriptions. However, these distances do not yield any probabilistic information. Thus, it is difficult to interpret such an output outside a well ground-truthed framework. In particular the distances, by themselves, are insufficient for the different task of analyzing a corpus ofmany inscriptions, with an unknown number of authors. The existing approaches can be contrasted with the direct predecessor of this article,14 which proposes a statistical approach. The article used a sophisticated concatenation and subsequent combination of SIFT, Zernike, DCT, and Kd -tree, image projections, CMI15–17 and L1 features and distances. Subsequently, on an inscriptions’ pair-wise basis, the writer identification analysis was performed independently for each letter. This resulted in different statistical p-values, estimating the probability of a single author producing the different letter instances of the two inscriptions. These independent p-values were later combined into a ‘‘meta’’ p-value via Fisher’s Method (a brief explanation is provided below), typically resulting in more significant results. Contrary to the existing approaches, such an approach can be easily utilized in order to detect different authors within any given corpus, by detecting ‘‘meta’’ p-values below certain threshold. Finally, we rely on previously developed document preprocessing techniques. In particular, we assume the existence of a suitable binarization, segmentation and (if needed) restoration of characters, whose quality is suitable for our needs. The inputs for the described method are individual black and white images of single characters, reflecting the original writing as reliably as possible (e.g., not thinned, no slant correction, etc.). Such automatic or semimanual techniques are described, for our data sets, in Refs. 17–19 and especially in Refs. 14, 20; for other approaches, consult the references mentioned in Ref. 4, 10, 11. Formethods assessing the adherence of character’s reconstruction to its image, as well as the general quality of the resulting binarization, see Refs. 15, 16, 21, 22. Additional details regarding the preparation of the different data sets are provided below. The Main Contribution of this Article In this research, we advance the ideas of Ref. 14 to the next level. The analysis is performed independently, not only on a level of a single letter, but also on the level of a single feature, unleashing the full statistical power of multiple experiments. The main changes from Ref. 14 are: an entirely different, and much larger set of features (using 512 different binary pixel patterns instead of a combination of 7 features); a two-step experimental process, working on both individual feature (by compari

Writer Identification in Modern and Historical Documents via Binary Pixel Patterns, Kolmogorov-Smirnov Test and Fisher's Method.

A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values.

/pdf/asynchronous-and-corrected-asynchronous-numerical-solutions-x7qk4ds3u6.pdf

Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors

An explicit multistage Runge-Kutta type of time-stepping scheme is used for solving transonic flow past a transport type wing/fuselage configuration. Solutions for both Euler and Navier-Stokes equations are obtained for quantitative assessment of boundary layer interaction effects. The viscous solutions are obtained on both a medium resolution grid of approximately 270,000 points and a find grid of 460,000 points to assess the effects of grid density on the solution. Computed pressure distributions are compared with the experimental data.

/pdf/the-3-d-euler-and-navier-stokes-calculations-for-aircraft-2y0r2ybctf.pdf

The 3-D Euler and Navier-Stokes calculations for aircraft components

Varieties of meshless computational methods have been developed in recent years for the numerical solution of different problems of science and technology. In particular, these methods have found extensive application in fracture mechanics, where it is difficult to solve problems with standard finite elements.

Eli Turkel

Papers

Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities

Writer Identification in Modern and Historical Documents via Binary Pixel Patterns, Kolmogorov-Smirnov Test and Fisher's Method.

Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors

The 3-D Euler and Navier-Stokes calculations for aircraft components

Advance Diffraction Method as a Tool for Solution of Complex Non–Convex Boundary Problems—Implementation and Practical Application