Relevant bibliographies by topics / Accurate summation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Accurate summation'

Author: Grafiati
Published: 23 September 2022
Last updated: 28 September 2022

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Journal articles on the topic "Accurate summation"

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Rump, Siegfried M. "Ultimately Fast Accurate Summation." SIAM Journal on Scientific Computing 31, no. 5 (2009): 3466–502. http://dx.doi.org/10.1137/080738490.

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Demmel, James, and Yozo Hida. "Accurate and Efficient Floating Point Summation." SIAM Journal on Scientific Computing 25, no. 4 (2004): 1214–48. http://dx.doi.org/10.1137/s1064827502407627.

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Cooker, Mark J. "The Accurate Summation of Some Awkward Series." Mathematical Gazette 82, no. 493 (1998): 48. http://dx.doi.org/10.2307/3620150.

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McNamee, John Michael. "A comparison of methods for accurate summation." ACM SIGSAM Bulletin 38, no. 1 (2004): 1–7. http://dx.doi.org/10.1145/980175.980177.

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Eisinberg, A., and G. Fedele. "Accurate floating-point summation: a new approach." Applied Mathematics and Computation 189, no. 1 (2007): 410–24. http://dx.doi.org/10.1016/j.amc.2006.11.095.

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Song, Jiming, and Sidharath Jain. "Midpoint Summation: A Method for Accurate and Efficient Summation of Series Appearing in Electromagnetics." IEEE Antennas and Wireless Propagation Letters 9 (2010): 1084–87. http://dx.doi.org/10.1109/lawp.2010.2091488.

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Blanchard, Pierre, Nicholas J. Higham, and Theo Mary. "A Class of Fast and Accurate Summation Algorithms." SIAM Journal on Scientific Computing 42, no. 3 (2020): A1541—A1557. http://dx.doi.org/10.1137/19m1257780.

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Rump, Siegfried M., Takeshi Ogita, and Shin'ichi Oishi. "Accurate Floating-Point Summation Part I: Faithful Rounding." SIAM Journal on Scientific Computing 31, no. 1 (2008): 189–224. http://dx.doi.org/10.1137/050645671.

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Lindbo, Dag, and Anna-Karin Tornberg. "Spectrally accurate fast summation for periodic Stokes potentials." Journal of Computational Physics 229, no. 23 (2010): 8994–9010. http://dx.doi.org/10.1016/j.jcp.2010.08.026.

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Akbari, Hesam, Muhammad Tariq Sadiq, Malih Payan, Somayeh Saraf Esmaili, Hourieh Baghri, and Hamed Bagheri. "Depression Detection Based on Geometrical Features Extracted from SODP Shape of EEG Signals and Binary PSO." Traitement du Signal 38, no. 1 (2021): 13–26. http://dx.doi.org/10.18280/ts.380102.

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Late detection of depression is having detrimental consequences including suicide thus there is a serious need for an accurate computer-aided system for early diagnosis of depression. In this research, we suggested a novel strategy for the diagnosis of depression based on several geometric features derived from the Electroencephalography (EEG) signal shape of the second-order differential plot (SODP). First, various geometrical features of normal and depression EEG signals were derived from SODP including standard descriptors, a summation of the angles between consecutive vectors, a summation of distances to coordinate, a summation of the triangle area using three successive points, a summation of the shortest distance from each point relative to the 45-degree line, a summation of the centroids to centroid distance of successive triangles, central tendency measure and summation of successive vector lengths. Second, Binary Particle Swarm Optimization was utilized for the selection of suitable features. At last, the features were fed to support vector machine and k-nearest neighbor (KNN) classifiers for the identification of normal and depressed signals. The performance of the proposed framework was evaluated by the recorded bipolar EEG signals from 22 normal and 22 depressed subjects. The results provide an average classification accuracy of 98.79% with the KNN classifier using city-block distance in a ten-fold cross-validation strategy. The proposed system is accurate and can be used for the early diagnosis of depression. We showed that the proposed geometrical features are better than extracted features in the time, frequency, time-frequency domains as it helps in visual inspection and provide up to 17.56% improvement in classification accuracy in contrast to those features.
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Dissertations / Theses on the topic "Accurate summation"

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Zhang, Huaijian. "Boundary Integral Techniques in Three Dimensions for Deep Water Waves." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306712208.

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Benmouhoub, Farah. "Optimisation de la précision numérique des codes parallèles." Thesis, Perpignan, 2022. http://www.theses.fr/2022PERP0009.

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Les nombres flottants sont utilisés à la place des nombres réels pour les calculs sur ordinateurs. L'utilisation de ces nombres introduit des erreurs d'arrondi qui sont en général acceptables dans la mesure où le résultat produit par la machine est proche de celui que l'on aurait obtenu en utilisant des nombres réels. Cependant, elles peuvent aussi être amplifiées par propagation, dénuant de sens le résultat d'un calcul, ce qui peut avoir des conséquences catastrophiques dans de nombreux domaines d'application comme par exemple l'aéronautique ou la finance. La précision des calculs en nombres flottants dépend de nombreux facteurs: types d'opérations effectuées, valeurs et types de données employés, ordinateurs utilisés. En outre, la précision des calculs dépend fortement de l'ordre dans lequel sont effectuées les opérations et le parallélisme démultiplie les ordonnancements possibles. Le sujet de thèse proposé concerne ce dernier point : améliorer la précision de codes de calcul scientifique massivement parallèles tels que ce que l'on trouve dans le domaine du HPC (High Performance Computing) Ces dernières années, des techniques automatiques ont été mises au point afin de valider et réécrire les codes de calcul scientifique afin de les rendre plus précis. Ces techniques rencontrent un vif intérêt tant scientifique qu'industriel. Cependant les techniques existantes acceptent uniquement des programmes séquentiels ce qui exclut les nombreux codes de calcul intensif développés dans le domaine du HPC. Or ces codes parallèles, utilisés pour réaliser des simulations numériques complexes dans de nombreux domaines scientifiques et techniques, sont particulièrement sujets aux erreurs introduites par les nombres flottants car le parallélisme modifie l'ordre dans lequel sont effectués les calculs, voire rend cet ordre aléatoire. Les résultats obtenus peuvent alors être altérés ou non reproductibles (plusieurs si mulations identiques donnant des résultats différents)<br>In high performance computing, nearly all the implementations and published experiments use foating-point arithmetic. However, since foating-point numbers are finite approximations of real numbers, it may result in hazards because of the accumulated errors.These round-off errors may cause damages whose gravity varies depending on the critical level of the application. Parallelism introduces new numerical accuracy problems due to the order of operations in this kind of systems. The proposed thesis subject concerns this last point: improving the precision of massively parallel scientific computing codes such as those found in the field of HPC (High Performance Computing)
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Mattsson, Ken. "Summation-by-Parts Operators for High Order Finite Difference Methods." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3434.

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Linders, Viktor. "Error analysis of summation-by-parts formulations : Dispersion, transmission and accuracy." Doctoral thesis, Linköpings universitet, Beräkningsmatematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143059.

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In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to weakly impose boundary conditions. The SBP-SAT framework combines high order of accuracy with a systematic construction of provably stable boundary procedures, which renders it suitable for a wide range of problems. The first part of the thesis treats wave propagation problems discretised using SBP operators on coarse grids. Unless special care is taken, inaccurate approximations of the underlying dispersion relation materialises in the form of an incorrect propagation speed. We present a procedure for constructing SBP operators with minimal dispersion error. Experiments indicate that they outperform higher order non-optimal SBP operators for flow problems involving high frequencies and long simulation times. In the second part of the thesis, the formal order of accuracy of SBP operators near boundaries is analysed. We prove that the order in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. This generalises the classical theory posed on uniform and conforming grids. We further show that for a common class of SBP operators, the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid. In the final contribution if the thesis, we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability analyses are performed for continuous and discrete problems. A general condition is obtained that is necessary and sufficient for the transmission problem to satisfy an energy estimate. The theory provides insights into the coupling of fluid flow models, multi-block formulations, numerical filters, interpolation and multi-grid implementations.
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Eriksson, Sofia. "Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-182953.

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In numerical simulations, problems stemming from aerodynamics pose many challenges for the method used. Some of these are addressed in this thesis, such as the fluid interacting with objects, the presence of shocks, and various types of boundary conditions. Scenarios of the kind mentioned above are described mathematically by initial boundary value problems (IBVPs). We discretize the IBVPs using high order accurate finite difference schemes on summation by parts form (SBP), combined with weakly imposed boundary conditions, a technique called simultaneous approximation term (SAT). By using the energy method, stability can be shown. The weak implementation is compared to the more commonly used strong implementation, and it is shown that the weak technique enhances the rate of convergence to steady state for problems with solid wall boundary conditions. The analysis is carried out for a linear problem and supported numerically by simulations of the fully non-linear Navier–Stokes equations. Another aspect of the boundary treatment is observed for fluid structure interaction problems. When exposed to eigenfrequencies, the coupled system starts oscillating, a phenomenon called flutter. We show that the strong implementation sometimes cause instabilities that can be mistaken for flutter. Most numerical schemes dealing with flows including shocks are first order accurate to avoid spurious oscillations in the solution. By modifying the SBP-SAT technique, a conservative and energy stable scheme is derived where the order of accuracy can be lowered locally. The new scheme is coupled to a shock-capturing scheme and it retains the high accuracy in smooth regions. For problems with complicated geometry, one strategy is to couple the finite difference method to the finite volume method. We analyze the accuracy of the latter on unstructured grids. For grids of bad quality the truncation error can be of zeroth order, indicating that the method is inconsistent, but we show that some of the accuracy is recovered. We also consider artificial boundary closures on unbounded domains. Non-reflecting boundary conditions for an incompletely parabolic problem are derived, and it is shown that they yield well-posedness. The SBP-SAT methodology is employed, and we prove that the discretized problem is stable.
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Simmerer, Julia L. "The Characteristics of Accurate Assessors on the Resident Educator Summative Assessment (RESA) Required for Advancing Licensure in Ohio." Ohio University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1617187913030287.

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Svärd, Magnus. "Stable High-Order Finite Difference Methods for Aerodynamics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4621.

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In this thesis, the numerical solution of time-dependent partial differential equations (PDE) is studied. In particular high-order finite difference methods on Summation-by-parts (SBP) form are analysed and applied to model problems as well as the PDEs governing aerodynamics. The SBP property together with an implementation of boundary conditions called SAT (Simultaneous Approximation Term), yields stability by energy estimates. The first derivative SBP operators were originally derived for Cartesian grids. Since aerodynamic computations are the ultimate goal, the scheme must also be stable on curvilinear grids. We prove that stability on curvilinear grids is only achieved for a subclass of the SBP operators. Furthermore, aerodynamics often requires addition of artificial dissipation and we derive an SBP version. With the SBP-SAT technique it is possible to split the computational domain into a multi-block structure which simplifies grid generation and more complex geometries can be resolved. To resolve extremely complex geometries an unstructured discretisation method must be used. Hence, we have studied a finite volume approximation of the Laplacian. It can be shown to be on SBP form and a new boundary treatment is derived. Based on the Laplacian scheme, we also derive an SBP artificial dissipation for finite volume schemes. We derive a new set of boundary conditions that leads to an energy estimate for the linearised three-dimensional Navier-Stokes equations. The new boundary conditions will be used to construct a stable SBP-SAT discretisation. To obtain an energy estimate for the discrete equation, it is necessary to discretise all the second derivatives by using the first derivative approximation twice. According to previous theory that would imply a degradation of formal accuracy but we present a proof that this is not the case.
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Berg, Jens. "Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-187204.

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Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software. We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models. The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.
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Wang, Siyang. "Finite Difference and Discontinuous Galerkin Methods for Wave Equations." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320614.

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Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.
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Almquist, Martin. "Efficient Simulation of Wave Phenomena." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-310124.

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Wave phenomena appear in many fields of science such as acoustics, geophysics, and quantum mechanics. They can often be described by partial differential equations (PDEs). As PDEs typically are too difficult to solve by hand, the only option is to compute approximate solutions by implementing numerical methods on computers. Ideally, the numerical methods should produce accurate solutions at low computational cost. For wave propagation problems, high-order finite difference methods are known to be computationally cheap, but historically it has been difficult to construct stable methods. Thus, they have not been guaranteed to produce reasonable results. In this thesis we consider finite difference methods on summation-by-parts (SBP) form. To impose boundary and interface conditions we use the simultaneous approximation term (SAT) method. The SBP-SAT technique is designed such that the numerical solution mimics the energy estimates satisfied by the true solution. Hence, SBP-SAT schemes are energy-stable by construction and guaranteed to converge to the true solution of well-posed linear PDE. The SBP-SAT framework provides a means to derive high-order methods without jeopardizing stability. Thus, they overcome most of the drawbacks historically associated with finite difference methods. This thesis consists of three parts. The first part is devoted to improving existing SBP-SAT methods. In Papers I and II, we derive schemes with improved accuracy compared to standard schemes. In Paper III, we present an embedded boundary method that makes it easier to cope with complex geometries. The second part of the thesis shows how to apply the SBP-SAT method to wave propagation problems in acoustics (Paper IV) and quantum mechanics (Papers V and VI). The third part of the thesis, consisting of Paper VII, presents an efficient, fully explicit time-integration scheme well suited for locally refined meshes.
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Books on the topic "Accurate summation"

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Shaw, Brian P. Music Assessment for Better Ensembles. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190603144.001.0001.

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Assessment is central to ensemble music. Yet, teachers do not always have the expertise to harness its potential to improve rehearsals and performances, and promote and document student learning. Written specifically for band, choir, and orchestra teachers at all levels, this book contains all of the information necessary to design and use assessment in a thriving music classroom. The first section addresses foundations such as learning targets, metacognition, and growth mindset. Assessment jargon such as formative assessment, summative assessment, Assessment for Learning, self and peer assessment, and authentic assessment is clarified and illustrated with music examples. Readers will learn practical strategies for choosing which concepts to assess, which methods to use, and how to use results to provide accurate and effective feedback to students. The second section brings assessment fundamentals into the music room. Filled with practical advice, each chapter examines a different facet of musicianship. Sample assessments in all performance areas are provided, including concert preparation, music literacy, fundamentals and technique, terminology, interpretation, evaluation and critique, composition and improvisation, beliefs and attitudes, and more. The final section is an examination of grading practices in music classes. Readers will gain information about ensemble grades that communicate what students know and are able to do. The book concludes with ways for music educators to take their first steps toward implementing these strategies in their own teaching, including the use of instructional technology. Assessing like an expert is possible, and this book is just what teachers need to get started.
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Book chapters on the topic "Accurate summation"

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Benmouhoub, Farah, Pierre-Loic Garoche, and Matthieu Martel. "Parallel Accurate and Reproducible Summation." In Lecture Notes in Networks and Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80119-9_21.

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He, Kang, Roberto Barrio, Lin Chen, et al. "A Class of Fast and Accurate Multi-layer Block Summation and Dot Product Algorithms." In Lecture Notes in Computer Science. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93571-9_6.

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Benmouhoub, Farah, Pierre-Loic Garoche, and Matthieu Martel. "An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods." In Lecture Notes in Computer Science. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95561-8_10.

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Goldsmith, Mike. "2. Water waves." In Waves: A Very Short Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/actrade/9780198803782.003.0002.

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Water waves may in fact be the most complex of all; out at sea, the water surface is a summation of an ever-changing mix of waves of many sizes, speeds, and directions, thanks largely to the fact that some waves can last for weeks, and in that time they can travel thousands of kilometres. Until recently, many wave parameters were hard to measure, but accurate measurements can now be made by a number of techniques including dual frequency radar altimetry. ‘Water waves’ describes many different waves and how they build, including capillary waves, breakers, edge waves, harbour resonance, seiches, tides, and tsunamis.
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"4. Summation." In Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, 2002. http://dx.doi.org/10.1137/1.9780898718027.ch4.

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Nersessian, Anry. "A Fast Method for Numerical Realization of Fourier Tools." In Real Perspective of Fourier Transforms [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94186.

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This chapter presents new application of author’s recent algorithms for fast summations of truncated Fourier series. A complete description of this method is given, and an algorithm for numerical implementation with a given accuracy for the Fourier transform is proposed.
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Chandra, A., and C. Bose. "Error Probability for Coherent Modulations in Rician Fading Channel." In Networking and Telecommunications. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-60566-986-1.ch112.

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Simple closed-form solutions for the average error rate of several coherent modulation schemes including square M-QAM, DBPSK and QPSK operating over slow flat Rician fading channel are derived. Starting from a novel unified expression of conditional error probability the error rates are analysed using PDF based approach. The derived end expressions composed of infinite series summations of Gauss hypergeometric function are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity and Rayleigh fading. Error probabilities are graphically displayed for the modulation schemes for different values of the Rician parameter K. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size, numerical results are plotted for various values of M. The generality of the analytical results presented offers valuable insight into the performance evaluation over a fading channel in a unified manner.
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Huang, Stephen. "Cardiac output measurement." In Oxford Textbook of Advanced Critical Care Echocardiography, edited by Anthony McLean, Stephen Huang, and Andrew Hilton. Oxford University Press, 2020. http://dx.doi.org/10.1093/med/9780198749288.003.0011.

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Cardiac output (CO) is an important measurement in intensive care unit, especially in the management of patients with shock. The main utility of CO measurement is for the evaluation of the type of shock, and for evaluating the response of patients to fluid or inotropes. Traditionally, to measure CO, clinicians rely mostly on thermodilution method using pulmonary artery catheter. Apart from being invasive, the method only measures CO indirectly by temperature change and its accuracy is subjected to various factors (e.g. speed and during of injection of the cold saline, the presence of tricuspid regurgitation and intracardiac shunts, and output state of the patient). On the other hand, CO measurement by echocardiography, especially transthoracic echocardiography (TTE), provides a non-invasive alternative to thermodilution. There are two TTE methods: Simpson’s method of disc summation and Doppler echocardiography. To date, nearly all stroke volume (SV) and CO measurements are performed using Doppler TTE as the method is less reliant on image quality and various assumptions. Apart from assuming that the cross-section of the left ventricular outflow tract is circular in shape, Doppler TTE accuracy depends only on the skills and experience of echocardiographers. This chapter will cover the theories and pitfalls of both Simpson’s method and Doppler echocardiographic of SV and CO measurements.
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MacDougall, David. "Observation in the cinema." In The looking machine. Manchester University Press, 2019. http://dx.doi.org/10.7228/manchester/9781526134097.003.0010.

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In this chapter the author notes that for some people ‘observation’ connotes an attitude of surveillance towards the subject. Despite this, the term is a useful summation of the original documentary idea, which was to show viewers as accurately as possible what the filmmaker had seen. ‘Observational cinema’ emerged as one of several closely related documentary approaches of the 1960s, with close ties to anthropology. Unlike other forms, it placed the filmmaker at the centre of the film as an investigator of on-going events, a position shared with the viewer. This approach was encouraged by the introduction of new, light-weight cameras and sound recorders and was inspired partly by Italian Neorealism and partly by live television. While often perceived as aspiring to detachment and scientific objectivity, it was in fact a highly authored form involving a close relationship between filmmaker and subject and representing the limited point of view of the individual observer. The author argues that while the long camera take is often regarded as the primary characteristic of observational cinema, its true marker is a commitment to the sustained witnessing of specific events. A further consequence of observational filmmaking is that it has stimulated reflection on what it means to observe.
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Monahan, David. "Interpretation of Bathymetry." In Continental Shelf Limits. Oxford University Press, 2000. http://dx.doi.org/10.1093/oso/9780195117820.003.0016.

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The two previous chapters described how depth measurements are made and elaborated on the accuracy and strengths of each type of data. Clearly, it would be wonderful if the entire world ocean were covered with multibeam data, but at the present time, there is only limited coverage; only a few ships are equipped with multibeam, and their speed remains slow. Therefore, we must use the other, older types of data available to us. States wishing to prepare a claim under the Convention may be able to follow up interpretations of older data with multibeam surveys aimed at the most important targets identified from analyzing the earlier data. This chapter is aimed at those wishing to produce new bathymetric maps by converting various types of data into information about the shape of the seafloor. The chapter discusses maps, in particular the elements of maps and mapping that apply to bathymetry. It explains the differences between navigation charts and bathymetry maps and describes how to prepare a bathymetry map. A great deal of the evidence assembled for any claim under the Convention will be portrayed on maps. Although maps are part of most people's life experience and are included in the training of hydrographers and earth scientists, it is a good idea to review some of the fundamentals of maps and mapping to ensure that those viewing the maps are aware of the limitations and strengths of this particular medium. Bathymetric maps and navigation charts—indeed, all maps—are caricatures. A chart distorts reality, just as the cartoonist distorts the facial features of some well-known personality. Yet the intent is always clear: The viewer knows who or what is being portrayed despite or perhaps because of the distortion. But to do this well calls for a careful distortion of just the right features. A good caricature has an uncanny precision behind the distortion; so it is with a chart. Put more scientifically, a map or chart comprises a summation of a large number of measurements carefully filtered and designed to give its main user an unambiguous image of the situation it portrays. This section describes the design process and the filters applied.
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Conference papers on the topic "Accurate summation"

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Jankovic, Jelena, Milos Subotic, and Vladimir Marinkovic. "One solution of the accurate summation using fixed-point accumulator." In 2015 23rd Telecommunications Forum Telfor (TELFOR). IEEE, 2015. http://dx.doi.org/10.1109/telfor.2015.7377518.

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Abramov, S. A., and M. Petkovšsek. "Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula." In the 2005 international symposium. ACM Press, 2005. http://dx.doi.org/10.1145/1073884.1073888.

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Wu, Wen‐Jing. "A fast and accurate 3‐D prestack Kirchhoff summation time migration." In SEG Technical Program Expanded Abstracts 1999. Society of Exploration Geophysicists, 1999. http://dx.doi.org/10.1190/1.1820820.

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Hotta, Kazuhiro. "Fast, Accurate and Robust Recognition Based On Local Normalized Linear Summation Kernel." In 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications (DICTA 2007). IEEE, 2007. http://dx.doi.org/10.1109/dicta.2007.4426834.

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Pierson, Ronald, Gregory Harris, Hans J. Johnson, Steve Dunn, and Vincent A. Magnotta. "Maximize uniformity summation heuristic (MUSH): a highly accurate simple method for intracranial delineation." In SPIE Medical Imaging, edited by Josien P. W. Pluim and Benoit M. Dawant. SPIE, 2009. http://dx.doi.org/10.1117/12.812322.

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Linders, Viktor, Marco Kupiainen, Steven H. Frankel, Yann Delorme, and Jan Nordstrom. "Summation-by-Parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations." In 54th AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-1329.

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Lee, Chan Hui, Keun Bok Song, and Heui Won Kim. "Vibration Analysis and Evaluation for the Offshore Structure Using Simplified Model and RSS Method." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-84053.

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The evaluation of the vibration characteristics of offshore structure in the design stage is important to ensure the safety of structure, equipment and worker. Conventionally, the vibration analysis of the offshore structure is carried out according to its own analysis procedure including the selection of vibrating equipment, FE modeling, evaluation of excitation forces and criteria. The efficient modeling of the vibration equipment and the consideration of the phase of excitation forces are necessary to reduce the calculation time and to increase the accuracy of analysis. In this paper, the efficient and accurate vibration analysis method is introduced including the simplified model of equipment and the RSS (root squared summation) method. The vibration equipment was modeled as the simplified model of which mesh size is reduced by 90%, however, its vibration characteristics such as natural frequency and vibration modes are not changed. In addition, the RSS method was applied in the forced vibration analysis to consider appropriate phase of excitation forces. As the RSS method is the summation of all the vibration response with respect to each excitation forces, it presents more reasonable and conservative vibration evaluation. The proposed vibration analysis method has been confirmed by conducting various offshore projects and is expected to be more efficient for the design of offshore structure.
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Omori, Toshiaki, Shunichi Yamaguchi, and Toru Fusegi. "Computational Heat Transfer Analysis of a Furnace Using the WSGG Model." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1372.

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Abstract Accurate radiative heat transfer analysis is challenging due to the strongly spectral-dependent absorption coefficient and the requirement for satisfying both the summation and reciprocity laws in thermodynamics. In the paper, nongray radiation is treated by way of a computationally efficient Weighted Sum of Gray Gases (WSGG) model without much sacrificing prediction accuracy. In the present model, three gray gas components are used, one of which simulates the radiative window. The thermodynamic laws are simultaneously treated using a Monte Carlo method subject to a symmetrization procedure. As a test problem, radiative heat transfer in an industrial model furnace is solved to demonstrate effects of gray/nongray radiation and the grid size for CFD and radiation calculations.
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Li, Like, Renwei Mei, and James F. Klausner. "Heat Transfer in Thermal Lattice Boltzmann Equation Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87990.

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The evaluation of the boundary heat flux and total heat transfer in the lattice Boltzmann equation (LBE) simulations is investigated. The boundary heat fluxes in the discrete velocity directions of the thermal LBE (TLBE) model are obtained directly from the temperature distribution functions at the lattice nodes. With the rectangular lattice uniformly spaced the effective surface area for the discrete heat flux is the unit spacing distance, thus the heat flux integration becomes simply a summation of all the discrete heat fluxes with constant surface areas. The present method for the evaluation of total heat transfer is very efficient and robust for curved boundaries because it does not require the determination of the normal heat flux on the boundary and the surface area. To validate its applicability and accuracy, several numerical tests with analytical solutions are conducted, including 2-dimensional (2D) steady thermal flow in a channel, 1-D transient heat conduction in an inclined semi-infinite solid, 2-D transient conduction inside a circle, and 3-D steady thermal flow in a circular pipe. For straight boundaries perpendicular to one of the discrete velocity vectors, the total heat transfer is second-order accurate. For curved boundaries only first-order accuracy is obtained for the total heat transfer due to the irregularly distributed lattice fractions cut by the curved boundary.
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Phan, Hien M., and Li He. "Efficient Steady and Unsteady Flow Modeling for Arbitrarily Mis-Staggered Bladerow Under Influence of Inlet Distortion." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-16204.

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Abstract Accurate and efficient predictions of the steady and unsteady flow responses due to the blade-to-blade variation as well as due to the non-axisymmetric inlet distortion have been continually pursued. Computation of two problems concurrently has been rarely done in the past partly because of the need to perform whole annulus bladerow simulations, despite the advances in the current state-of-the-art methods with the phaseshift single passage simulations. The current work attempts to deal with this challenge by developing a new computational approach based on the principle of the multiscale method in the framework of a commercial solver (CFX). The methodology formulation relies on summation of the constituent source terms, each of which corresponds to a particular flow perturbation. The source term element corresponding to the blade-to-blade variation effect is linearly superimposed as in the classical Influence Coefficient Method. Only the relative positions between the reference blade and its neighbor matter in this method, thus enables an arbitrarily mis-staggered bladerow to be computed efficiently. In addition, the source term arisen due to the inlet distortion is calculated based on spatial Fourier transform. A key enabler is that the source term can be pre-computed using a small set of identical blade passages. The source term is then propagated to different spatial and temporal locations depending on the combination of the mis-staggering pattern and the inlet distortion. The multiscale treatment makes it possible to predict a high-resolution flow field effects on the base coarse mesh as if the fine mesh is solved, while achieving a computational gain. The source term summation method proposed in the current work has been validated using a uniformly staggered bladerow, and an arbitrarily mis-staggered bladerow in a clean inflow condition as well as that subject to an inlet distortion.
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