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Статті в журналах з теми "Numerical computation"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 16 вересня 2023

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1

Smolensky, Paul. "Symbolic functions from neural computation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1971 (July 28, 2012): 3543–69. http://dx.doi.org/10.1098/rsta.2011.0334.

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Is thought computation over ideas? Turing, and many cognitive scientists since, have assumed so, and formulated computational systems in which meaningful concepts are encoded by symbols which are the objects of computation. Cognition has been carved into parts, each a function defined over such symbols. This paper reports on a research program aimed at computing these symbolic functions without computing over the symbols. Symbols are encoded as patterns of numerical activation over multiple abstract neurons, each neuron simultaneously contributing to the encoding of multiple symbols. Computation is carried out over the numerical activation values of such neurons, which individually have no conceptual meaning. This is massively parallel numerical computation operating within a continuous computational medium. The paper presents an axiomatic framework for such a computational account of cognition, including a number of formal results. Within the framework, a class of recursive symbolic functions can be computed. Formal languages defined by symbolic rewrite rules can also be specified, the subsymbolic computations producing symbolic outputs that simultaneously display central properties of both facets of human language: universal symbolic grammatical competence and statistical, imperfect performance.

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2

Ruhe, Axel, M. G. Cox, and S. Hammarling. "Reliable Numerical Computation." Mathematics of Computation 59, no. 199 (July 1992): 298. http://dx.doi.org/10.2307/2152999.

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3

Sofroniou, Mark, and Giulia Spaletta. "Precise numerical computation." Journal of Logic and Algebraic Programming 64, no. 1 (July 2005): 113–34. http://dx.doi.org/10.1016/j.jlap.2004.07.007.

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4

Alaa Ismail, Abdalla Mostafa Elmarhomy, Abd El-Aziz Morgan, and Ashraf Mostafa Hamed. "Numerical Modeling and Geometry Enhancement of a Reactive Silencer." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 106, no. 1 (June 19, 2023): 147–57. http://dx.doi.org/10.37934/arfmts.106.1.147157.

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Internal combustion engines and blowers frequently utilize silencers to reduce exhaust noise. In the current paper, the transmission loss of reactive silencers is predicted using the plane wave decomposition method and a three-dimensional (3-D) time-domain computational fluid dynamics (CFD) approach. A mass-flow-inlet boundary condition is first used to perform a steady flow computation, which serves as an initial condition for the two subsequent unsteady flow computations. At the model's inlet, an impulse (acoustic excitation) is placed over the constant mass flow to perform the first unstable flow computation. Once the impulse has fully propagated into the silencer, the non-reflecting boundary condition (NRBC) is then added. For the scenario without acoustic excitation at the inlet, a second unsteady flow computation is performed. During the two transient computations, the time histories of the pressure and velocity at the upstream measuring points as well as the history of the pressures at the downstream measuring point are recorded. The related acoustic quantities show variations between the two unsteady flow computational findings. As a result, the transmitted sound pressure signal is just the sound pressure downstream, while the incident sound pressure signal is obtained by utilizing plane wave decomposition upstream. The transmission loss (TL) of the silencer is then calculated after the Fast Fourier Transform (FFT) converts the two sound pressure signals from the time domain to the frequency domain. The numerical calculations and the reported data are in good agreement for the published results, in addition to geometry enhancement by increasing number of holes in the cross section for muffler.

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5

Xiao, Shuangshuang, Kemin Li, Xiaohua Ding, and Tong Liu. "Numerical Computation of Homogeneous Slope Stability." Computational Intelligence and Neuroscience 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/802835.

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To simplify the computational process of homogeneous slope stability, improve computational accuracy, and find multiple potential slip surfaces of a complex geometric slope, this study utilized the limit equilibrium method to derive expression equations of overall and partial factors of safety. This study transformed the solution of the minimum factor of safety (FOS) to solving of a constrained nonlinear programming problem and applied an exhaustive method (EM) and particle swarm optimization algorithm (PSO) to this problem. In simple slope examples, the computational results using an EM and PSO were close to those obtained using other methods. Compared to the EM, the PSO had a small computation error and a significantly shorter computation time. As a result, the PSO could precisely calculate the slope FOS with high efficiency. The example of the multistage slope analysis indicated that this slope had two potential slip surfaces. The factors of safety were 1.1182 and 1.1560, respectively. The differences between these and the minimum FOS (1.0759) were small, but the positions of the slip surfaces were completely different than the critical slip surface (CSS).

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6

GUCKENHEIMER, JOHN, KATHLEEN HOFFMAN, and WARREN WECKESSER. "NUMERICAL COMPUTATION OF CANARDS." International Journal of Bifurcation and Chaos 10, no. 12 (December 2000): 2669–87. http://dx.doi.org/10.1142/s0218127400001742.

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Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuation of solutions of boundary value problems. One of these periodic orbits contains canards, trajectory segments that follow unstable portions of a slow manifold. We identify several mechanisms that lead to the formation of these and other canards in this example.

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7

Das, JN. "A Least Squares Computational Method for the Scattering Amplitude." Australian Journal of Physics 41, no. 1 (1988): 47. http://dx.doi.org/10.1071/ph880047.

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A new least squares computational method for the scattering amplitude is proposed. This may be applied without difficulty to atomic and other scattering computations. The approach is expected to give converged results of high accuracy and also to be free from major numerical instabilities. As an example a numerical computation is carried out following the method and some results are presented in partial support of the claim.

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8

Sathyan, Sabin, Ugur Aydin, and Anouar Belahcen. "Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method." Energies 13, no. 1 (January 3, 2020): 245. http://dx.doi.org/10.3390/en13010245.

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This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

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9

Kim, Boram, Kwang Seok Yoon, and Hyung-Jun Kim. "GPU-Accelerated Laplace Equation Model Development Based on CUDA Fortran." Water 13, no. 23 (December 4, 2021): 3435. http://dx.doi.org/10.3390/w13233435.

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In this study, a CUDA Fortran-based GPU-accelerated Laplace equation model was developed and applied to several cases. The Laplace equation is one of the equations that can physically analyze the groundwater flows, and is an equation that can provide analytical solutions. Such a numerical model requires a large amount of data to physically regenerate the flow with high accuracy, and requires computational time. These numerical models require a large amount of data to physically reproduce the flow with high accuracy and require computational time. As a way to shorten the computation time by applying CUDA technology, large-scale parallel computations were performed on the GPU, and a program was written to reduce the number of data transfers between the CPU and GPU. A GPU consists of many ALUs specialized in graphic processing, and can perform more concurrent computations than a CPU using multiple ALUs. The computation results of the GPU-accelerated model were compared with the analytical solution of the Laplace equation to verify the accuracy. The computation results of the GPU-accelerated Laplace equation model were in good agreement with the analytical solution. As the number of grids increased, the computational time of the GPU-accelerated model gradually reduced compared to the computational time of the CPU-based Laplace equation model. As a result, the computational time of the GPU-accelerated Laplace equation model was reduced by up to about 50 times.

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10

Yue, Chun Guo, Xin Long Chang, You Hong Zhang, and Shu Jun Yang. "Numerical Calculation of a Missile's Aerodynamic Characteristic." Advanced Materials Research 186 (January 2011): 220–24. http://dx.doi.org/10.4028/www.scientific.net/amr.186.220.

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In virtue of Fluent of CFD software, numerical computations of aerodynamics of an air-to-air missile in different mach numbers and different attack angles were carried though. The movement trends of lift coefficient, drag coefficient and pitching moment coefficient with variety of mach numbers and attack angles were gained, meanwhile, distributing trends of pressure, temperature and weather velocity were also obtained. The results indicated that the basis and references could be offered by numerical computation results for shape design of missile and definite preponderances were showed than traditionary numerical computation methods.

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11

Feichtinger, Anna, Aleksander Makaruk, Ewa Weinmüller, Anton Friedl, and Michael Harasek. "Collocation Method for the Modeling of Membrane Gas Permeation Systems." International Journal of Nonlinear Sciences and Numerical Simulation 16, no. 3-4 (June 1, 2015): 141–49. http://dx.doi.org/10.1515/ijnsns-2014-0001.

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AbstractIn this work, we describe a numerical method which enables an efficient computation of membrane gas permeation processes that involve multiple membrane stages and multiple gas components. The utilized numerical approach is a collocation method equipped with a grid adaptation strategy based on a dependable error estimate of the numerical approximation. The comparison of the results provided by the collocation method with those calculated from an experimentally validated finite difference method has demonstrated that the accuracy of both numerical approximations is practically the same. However, the current procedure is characterized by a much better computational efficiency that allows to considerably reduce the computational time. This is a crucial feature when combining computation of membrane permeation processes with optimization algorithms. In such a setting the computation of the permeation process is frequently repeated and naturally, results in long computational times when the efficiency is not adequately improved.

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12

Jankov, Dimitrije, Binhang Yuan, Shangyu Luo, and Chris Jermaine. "Distributed numerical and machine learning computations via two-phase execution of aggregated join trees." Proceedings of the VLDB Endowment 14, no. 7 (March 2021): 1228–40. http://dx.doi.org/10.14778/3450980.3450991.

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When numerical and machine learning (ML) computations are expressed relationally, classical query execution strategies (hash-based joins and aggregations) can do a poor job distributing the computation. In this paper, we propose a two-phase execution strategy for numerical computations that are expressed relationally, as aggregated join trees (that is, expressed as a series of relational joins followed by an aggregation). In a pilot run, lineage information is collected; this lineage is used to optimally plan the computation at the level of individual records. Then, the computation is actually executed. We show experimentally that a relational system making use of this two-phase strategy can be an excellent platform for distributed ML computations.

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13

Denis-Vidal, Lilianne, Ghislaine Joly-Blanchard, and Céline Noiret. "System Identifiability (Symbolic Computation) and Parameter Estimation (Numerical Computation)." Numerical Algorithms 34, no. 2-4 (December 2003): 283–92. http://dx.doi.org/10.1023/b:numa.0000005366.05704.88.

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14

Laguna, Javier Rodriguez Rodriguez, and Manuel Pancorbo Castro. "Online manual on numerical computation." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 5 (November 16, 2017): 17–22. http://dx.doi.org/10.18844/prosoc.v4i5.2668.

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We present a tutorial on numerical computation for undergrads in Sciences, Maths and Engineering, based on Octave, a popular framework for numerical analysis which, in addition, is FOSS (Free & Open Source Software). So it can be freely run on several operating systems: Windows, MacOS, any GNU-Linux flavour, FreeBSD and, even, on Android mobile platform. The tutorial is given as a static web page with almost no extra complexities, such as database engine, dynamic rendering via PHP or similar. All the workflow is arranged through FOSS with full respect to standards. Keywords: FOSS; octave; webpage; tutorial; markup language; markdown

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15

Williamson, Alan G., J. Murphy, D. Ridout, and Brigid McShane. "Numerical Analysis, Algorithms and Computation." Mathematical Gazette 73, no. 465 (October 1989): 250. http://dx.doi.org/10.2307/3618471.

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16

Jin Yunsheng, 金云声, 谭福利 Tan Fuli, 贺佳 He Jia, 李牧 Li Mu, 张永强 Zhang Yongqiang, 张红平 Zhang Hongping, and 赵剑衡 Zhao Jianheng. "Numerical inverse computation of reflectivity." High Power Laser and Particle Beams 25, no. 3 (2013): 549–52. http://dx.doi.org/10.3788/hplpb20132503.0549.

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17

Mehtre, Vishal V. "Interpolation Techniques in Numerical Computation." International Journal for Research in Applied Science and Engineering Technology 7, no. 11 (November 30, 2019): 672–74. http://dx.doi.org/10.22214/ijraset.2019.11108.

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18

Driscoll, Tobin, Alex Townsend, Jean-Paul Berrut, Bengt Fornberg, Anne Greenbaum, Nicholas J. Higham, Randy LeVeque, and Ian H. Sloan. "New Directions in Numerical Computation." Notices of the American Mathematical Society 63, no. 04 (April 1, 2016): 398–400. http://dx.doi.org/10.1090/noti1363.

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19

Herrmann, G. "Numerical computation of diffraction coefficients." IEEE Transactions on Antennas and Propagation 35, no. 1 (January 1987): 53–61. http://dx.doi.org/10.1109/tap.1987.1143971.

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20

Zhao, Daqing, and Richard N. Zare. "Numerical computation of 9-jsymbols." Molecular Physics 65, no. 5 (December 10, 1988): 1263–68. http://dx.doi.org/10.1080/00268978800101761.

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21

van Veldhuizen, M., J. A. Hendriks, and C. A. J. Appelo. "Numerical computation in heterovalent chromatography." Applied Numerical Mathematics 28, no. 1 (September 1998): 69–89. http://dx.doi.org/10.1016/s0168-9274(98)00016-6.

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22

Javanbakht, Masoumeh, and Tomas Sauer. "Numerical computation of H-bases." BIT Numerical Mathematics 59, no. 2 (October 6, 2018): 417–42. http://dx.doi.org/10.1007/s10543-018-0733-x.

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23

Hauenstein, Jonathan D., Jose Israel Rodriguez, and Frank Sottile. "Numerical Computation of Galois Groups." Foundations of Computational Mathematics 18, no. 4 (June 14, 2017): 867–90. http://dx.doi.org/10.1007/s10208-017-9356-x.

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24

López-Gómez, Julián, Marcela Molina-Meyer, and Mónica Villarreal. "Numerical Computation of Coexistence States." SIAM Journal on Numerical Analysis 29, no. 4 (August 1992): 1074–92. http://dx.doi.org/10.1137/0729065.

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25

Darulova, Eva, and Viktor Kuncak. "Trustworthy numerical computation in Scala." ACM SIGPLAN Notices 46, no. 10 (October 18, 2011): 325–44. http://dx.doi.org/10.1145/2076021.2048094.

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26

Galperin, Michael, Sivan Toledo, and Abraham Nitzan. "Numerical computation of tunneling fluxes." Journal of Chemical Physics 117, no. 23 (December 15, 2002): 10817–26. http://dx.doi.org/10.1063/1.1522404.

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27

Doedel, Eusebius J., and Mark J. Friedman. "Numerical computation of heteroclinic orbits." Journal of Computational and Applied Mathematics 26, no. 1-2 (June 1989): 155–70. http://dx.doi.org/10.1016/0377-0427(89)90153-2.

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28

Tam, Christopher K. W. "Advances in Numerical Boundary Conditions for Computational Aeroacoustics." Journal of Computational Acoustics 06, no. 04 (December 1998): 377–402. http://dx.doi.org/10.1142/s0218396x98000259.

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Advances in computational aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high-quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some of the much-needed research in numerical boundary conditions for CAA.

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29

Ohnaka, Susumu, Akira Watanabe, and Mashiko Isobe. "NUMERICAL MODELING OF WAVE DEFORMATION WITH A CURRENT." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 27. http://dx.doi.org/10.9753/icce.v21.27.

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A numerical computation method for a wave field coexisting with a current is presented to study wave-current interaction on a slowly varying bottom topography. Derivation is given for a new set of time-dependent mildslope equations extended to a wave and current coexisting field, which can deal with wave deformation due to combined refraction, diffraction, reflection and breaking as well as to wave-current interaction. Discussion is made on the numerical computation schemes, boundary conditions and breaking conditions. Some examples of the numerical computations are shown for wave and current coexisting fields.

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30

ILIE, Marcel, Augustin Semenescu, Gabriela Liliana STROE, and Sorin BERBENTE. "NUMERICAL COMPUTATIONS OF THE CAVITY FLOWS USING THE POTENTIAL FLOW THEORY." ANNALS OF THE ACADEMY OF ROMANIAN SCIENTISTS Series on ENGINEERING SCIENCES 13, no. 2 (2021): 78–86. http://dx.doi.org/10.56082/annalsarscieng.2021.2.78.

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Computational fluid dynamics of turbulent flows requires large computational resources or are not suitable for the computations of transient flows. Therefore methods such as Reynolds-averaged Navier-Stokes equations are not suitable for the computation of transient flows. The direct numerical simulation provides the most accurate solution, but it is not suitable for high-Reynolds number flows. Large-eddy simulation (LES) approach is computationally less demanding than the DNS but still computationally expensive. Therefore, alternative computational methods must be sought. This research concerns the modelling of inviscid incompressible cavity flow using the potential flow. The numerical methods employed the finite differences approach. The time and space discretization is achieved using second-order schemes. The studies reveal that the finite differences approach is a computationally efficient approach and large computations can be performed on a single computer. The analysis of the flow physics reveals the presence of the recirculation region inside the cavity as well at the corners of the cavity

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31

Piqueras, M. A., R. Company, and L. Jódar. "Stable Numerical Solutions Preserving Qualitative Properties of Nonlocal Biological Dynamic Problems." Abstract and Applied Analysis 2019 (July 1, 2019): 1–7. http://dx.doi.org/10.1155/2019/5787329.

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This paper deals with solving numerically partial integrodifferential equations appearing in biological dynamics models when nonlocal interaction phenomenon is considered. An explicit finite difference scheme is proposed to get a numerical solution preserving qualitative properties of the solution. Gauss quadrature rules are used for the computation of the integral part of the equation taking advantage of its accuracy and low computational cost. Numerical analysis including consistency, stability, and positivity is included as well as numerical examples illustrating the efficiency of the proposed method.

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32

Guo, Yuling, and Jianguo Huang. "A Domain Decomposition Based Spectral Collocation Method for Lane-Emden Equations." Communications in Computational Physics 22, no. 2 (June 21, 2017): 542–71. http://dx.doi.org/10.4208/cicp.oa-2016-0181.

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AbstractA domain decomposition based spectral collocation method is proposed for numerically solving Lane-Emden equations, which are frequently encountered in mathematical physics and astrophysics. Compared with the existing methods, this method requires less computational cost and is particularly suitable for long-term computation. The related error estimates are also established, indicating the spectral accuracy of the method. The numerical performance and efficiency of the method are illustrated by several numerical experiments.

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33

BECCARIA, MATTEO, and GUIDO MACORINI. "A NUMERICAL TEST OF THE Y-SYSTEM IN THE SMALL SIZE LIMIT OF THE SU(2) × SU(2) PRINCIPAL CHIRAL MODEL." International Journal of Modern Physics A 26, no. 07n08 (March 30, 2011): 1229–52. http://dx.doi.org/10.1142/s0217751x11052864.

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Анотація:

Recently, Kazakov, Gromov and Vieira applied the discrete Hirota dynamics to study the finite size spectra of integrable two dimensional quantum field theories. The method has been tested from large values of the size L down to moderate values using the SU (2) × SU (2) principal chiral model as a theoretical laboratory. We continue the numerical analysis of the proposed nonlinear integral equations showing that the deep ultraviolet region L → 0 is numerically accessible. To this aim, we introduce a relaxed iterative algorithm for the numerical computation of the low-lying part of the spectrum in the U (1) sector. We discuss in detail the systematic errors involved in the computation. When a comparison is possible, full agreement is found with previous thermodynamical Bethe ansatz computations.

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34

Loja, Maria Amélia R., and Joaquim I. Barbosa. "Preface to Numerical and Symbolic Computation: Developments and Applications—2019." Mathematical and Computational Applications 25, no. 2 (May 11, 2020): 28. http://dx.doi.org/10.3390/mca25020028.

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Анотація:

This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications—2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and Symbolic Computation—SYMCOMP 2019—that took place in Porto, Portugal, from April 11th to April 12th 2019 [...]

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35

FERLIN, EDSON PEDRO, HEITOR SILVÉRIO LOPES, CARLOS R. ERIG LIMA, and MAURÍCIO PERRETTO. "A FPGA-BASED RECONFIGURABLE PARALLEL ARCHITECTURE FOR HIGH-PERFORMANCE NUMERICAL COMPUTATION." Journal of Circuits, Systems and Computers 20, no. 05 (August 2011): 849–65. http://dx.doi.org/10.1142/s0218126611007645.

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Many real-world engineering problems require high computational power, especially regarding the processing time. Current parallel processing techniques play an important role in reducing the processing time. Recently, reconfigurable computation has gained large attention thanks to its ability to combine hardware performance and software flexibility. Also, the availability of high-density Field Programmable Gate Array devices and corresponding development systems allowed the popularization of reconfigurable computation, encouraging the development of very complex, compact, and powerful systems for custom applications. This work presents an architecture for parallel reconfigurable computation based on the dataflow concept. This architecture allows reconfigurability of the system for many problems and, particularly, for numerical computation. Several experiments were done analyzing the scalability of the architecture, as well as comparing its performance with other approaches. Overall results are relevant and promising. The developed architecture has performance and scalability suited for engineering problems that demand intensive numerical computation.

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36

Ishak, Fuziyah, and Najihah Chaini. "Numerical computation for solving fuzzy differential equations." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 2 (November 1, 2019): 1026. http://dx.doi.org/10.11591/ijeecs.v16.i2.pp1026-1033.

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Fuzzy differential equations (FDEs) play important roles in modeling dynamic systems in science, economics and engineering. The modeling roles are important because most problems in nature are indistinct and uncertain. Numerical methods are needed to solve FDEs since it is difficult to obtain exact solutions. Many approaches have been studied and explored by previous researchers to solve FDEs numerically. Most FDEs are solved by adapting numerical solutions of ordinary differential equations. In this study, we propose the extended Trapezoidal method to solve first order initial value problems of FDEs. The computed results are compared to that of Euler and Trapezoidal methods in terms of errors in order to test the accuracy and validity of the proposed method. The results shown that the extended Trapezoidal method is more accurate in terms of absolute error. Since the extended Trapezoidal method has shown to be an efficient method to solve FDEs, this brings an idea for future researchers to explore and improve the existing numerical methods for solving more general FDEs.

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37

Arai, Yoshihide, Takashi Sago, Yuki Ueyama, and Masanori Harada. "MGV Obstacle Avoidance Trajectory Generation Considering Vehicle Shape." Journal of Robotics and Mechatronics 35, no. 2 (April 20, 2023): 262–70. http://dx.doi.org/10.20965/jrm.2023.p0262.

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This study investigates the application of obstacle avoidance trajectory generation considering the vehicle shape of a micro ground vehicle by successive convexification and state-triggered constraints. The avoidance trajectory is generated by numerical computation and path-following experiments are conducted to assess the generated trajectory. The numerical computation results indicate that the trajectory obtained by the algorithm successfully avoids obstacles considering the vehicle shape and satisfies the constraints. The experiment includes the model predictive control to follow the generated trajectory. Numerical computations and experiments confirm the usefulness of the trajectory generation algorithm.

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38

Domscheit, A., H. Rothert, and T. Winkelmann. "Refined Methods for Tire Computation." Tire Science and Technology 17, no. 4 (October 1, 1989): 291–304. http://dx.doi.org/10.2346/1.2141689.

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Abstract Realistic computation of automobile tires is best achieved by modeling the whole tire with finite element methods. A numerical solution of the quasi-static contact problem for the whole tire requires a refined mesh of elements with redundant degrees of freedom when nonlinear material assumptions are considered. Both laminated shell elements and incompressible continuum elements are used here. The stiffness matrix of a shell element is determined by numerically integrating all layers within the thickness of each element. Numerical studies have been made by a finite element technique that includes shell elements and Swanson's material model, which covers large deformations. The major contribution of this paper is implementation of a composite theory that includes effects of large displacements on the stiffness into an existing element. Swanson's material law was also simplified and implemented.

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39

Chung, Hyuck, and Colin Fox. "Calculation of wave propagation into land-fast ice." Annals of Glaciology 33 (2001): 322–26. http://dx.doi.org/10.3189/172756401781818581.

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AbstractWe review the various numerical methods that have been developed for calculating the reflection and transmission of ocean waves at a land-fast ice boundary, including recent developments. While an integral form of the solution, found by the Wiener-Hopf technique, has been known for many years, direct numerical computation of this exact solution has been thought to be prohibitively difficult. Instead, several numerical "matching" procedures have been developed, including some that are only approximate, along with asymptotic solutions based on the integral form. Recently it has been discovered that direct calculation of the integral form is feasible, actually requiring less computation than the matching methods. We outline the actual computations required and contrast each method, and provide examples of computation from the integral form.

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40

Ito, Shin-ichi, Takeru Matsuda, and Yuto Miyatake. "Adjoint-based exact Hessian computation." BIT Numerical Mathematics 61, no. 2 (February 17, 2021): 503–22. http://dx.doi.org/10.1007/s10543-020-00833-0.

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AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the Hessian and a given vector. One of the ways to obtain an approximation of such Hessian-vector multiplication is to integrate the so-called second-order adjoint system numerically. However, the error in the approximation could be significant even if the numerical integration to the second-order adjoint system is sufficiently accurate. This paper presents a novel algorithm that computes the intended Hessian-vector multiplication exactly and efficiently. For this aim, we give a new concise derivation of the second-order adjoint system and show that the intended multiplication can be computed exactly by applying a particular numerical method to the second-order adjoint system. In the discussion, symplectic partitioned Runge–Kutta methods play an essential role.

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41

McCartin, Brian J. "Seven Deadly Sins of Numerical Computation." American Mathematical Monthly 105, no. 10 (December 1998): 929. http://dx.doi.org/10.2307/2589285.

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42

Genz, Alan. "Numerical Computation of Multivariate Normal Probabilities." Journal of Computational and Graphical Statistics 1, no. 2 (June 1992): 141. http://dx.doi.org/10.2307/1390838.

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43

Lohr, Sharon, and Ronald A. Thisted. "Elements of Statistical Computing: Numerical Computation." Journal of the American Statistical Association 84, no. 406 (June 1989): 613. http://dx.doi.org/10.2307/2289953.

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44

Kemp, C. D., and R. A. Thisted. "Elements of Statistical Computing: Numerical Computation." Biometrics 47, no. 1 (March 1991): 352. http://dx.doi.org/10.2307/2532534.

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45

UPPAL, Faisel, Suzanne LESECQ, Ron PATTON, and Alain BARRAUD. "DISTURBANCE DISTRIBUTION MATRIX COMPUTATION: NUMERICAL IMPROVEMENT." IFAC Proceedings Volumes 38, no. 1 (2005): 43–48. http://dx.doi.org/10.3182/20050703-6-cz-1902.01809.

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46

Csallner, András Erik, Tibor Csendes, and András Balázs Kocsis. "Reliable Numerical Computation in Civil Engineering." Numerical Algorithms 37, no. 1-4 (December 2004): 85–91. http://dx.doi.org/10.1023/b:numa.0000049488.06517.bb.

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47

LI, Zhiping. "Numerical computation of stress induced microstructure." Science in China Series A 47, no. 7 (2004): 165. http://dx.doi.org/10.1360/04za0015.

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48

Higham, N. J. "Numerical Computation: Methods, Software, And Analysis." IEEE Computational Science and Engineering 5, no. 1 (January 1998): 79. http://dx.doi.org/10.1109/mcse.1998.660318.

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49

Genz, Alan. "Numerical Computation of Multivariate Normal Probabilities." Journal of Computational and Graphical Statistics 1, no. 2 (June 1992): 141–49. http://dx.doi.org/10.1080/10618600.1992.10477010.

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50

Steele, Michael. "Elements of Statistical Computing: Numerical Computation." Technometrics 31, no. 4 (November 1989): 482–83. http://dx.doi.org/10.1080/00401706.1989.10488600.

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