Journal articles on the topic 'Finite differences Computer programs'
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1
Vafidis, A., F. Abramovici, and E. R. Kanasewich. "Elastic wave propagation using fully vectorized high order finite‐difference algorithms." GEOPHYSICS 57, no. 2 (February 1992): 218–32. http://dx.doi.org/10.1190/1.1443235.
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Two finite‐difference schemes for solving the elastic wave equation in heterogeneous two‐dimensional media are implemented on a vector computer. A modified Lax‐Wendroff scheme that is second‐order accurate both in time and space and is a version of the MacCormack scheme that is second‐order accurate in time and fourth‐order in space. The algorithms are based on the matrix times vector by diagonals technique that is fully vectorized and is described using a novel notation for vector supercomputer operations. The technique described can be implemented on a vector processor of modest dimensions and increase the applicability of finite differences. The two difference operators are compared and the programs are tested for a simple case of standing sinusoidal waves for which the exact solution is known and also for a two‐layer model with a line source. A comparison of the results for an actual well‐to‐well experiment verifies the usefulness of the two‐dimensional approach in modeling the results.
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Small, Gregory E., and Sidney H. Simmonds. "Spreadsheet solutions of elastic plate–beam problems." Canadian Journal of Civil Engineering 17, no. 6 (December 1, 1990): 931–39. http://dx.doi.org/10.1139/l90-105.
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Spreadsheets are among the most common microcomputer programs used by engineers because they provide an easy means of formulating equations in algebraic format. By introducing appropriate stiffness equations with numerical values representative of material properties, boundary conditions, and loading, spreadsheet templates can be developed to model specific structural systems. These equations are mutually dependent and may be solved using the iteration techniques that are part of the spreadsheet program. A common structural problem that is difficult to solve without a special computer program is the analysis of a slab arbitrarily supported on elastic beams and columns. The use of readily available spreadsheet programs to solve this problem is demonstrated. Equations for slab bending and for beams with finite flexural and torsional stiffnesses are derived using finite difference operators. These equations are then recast into a form more convenient for an iterative solution. The use of these equations is demonstrated with numerical examples. Key words: analysis, convergence criteria, deflections, finite difference, plates, spreadsheets.
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Thomas, B. G., and B. Ho. "Spread Sheet Model of Continuous Casting." Journal of Engineering for Industry 118, no. 1 (February 1, 1996): 37–44. http://dx.doi.org/10.1115/1.2803646.
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Spreadsheet programs, such as Microsoft Excel, Informix WINGZ, and Lotus 123, provide a framework for very fast and easy development of simple engineering models. The present paper describes a model of the continuous casting process that has been developed using a spreadsheet program, Microsoft Excel, running on a Macintosh II personal computer. The model consists of two-dimensional (2-D) steady-state finite-difference heat conduction calculations within a continuous casting mold coupled to a one-dimensional (1-D) transient solidification heat transfer model of the solidifying shell. The model structure and equations are described and the model predictions are compared with previous solutions. Practical examples using the model are discussed and sample results are provided. Spreadsheet programs running on personal computers are capable of relatively complex calculations that would require extensive effort using conventional programming languages.
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Horstmann, Martin, Alexander T. Topham, Petra Stamm, Sebastian Kruppert, John K. Colbourne, Ralph Tollrian, and Linda C. Weiss. "Scan, extract, wrap, compute—a 3D method to analyse morphological shape differences." PeerJ 6 (June 8, 2018): e4861. http://dx.doi.org/10.7717/peerj.4861.
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Quantitative analysis of shape and form is critical in many biological disciplines, as context-dependent morphotypes reflect changes in gene expression and physiology, e.g., in comparisons of environment-dependent phenotypes, forward/reverse genetic assays or shape development during ontogenesis. 3D-shape rendering methods produce models with arbitrarily numbered, and therefore non-comparable, mesh points. However, this prevents direct comparisons. We introduce a workflow that allows the generation of comparable 3D models based on several specimens. Translocations between points of modelled morphotypes are plotted as heat maps and statistically tested. With this workflow, we are able to detect, model and investigate the significance of shape and form alterations in all spatial dimensions, demonstrated with different morphotypes of the pond-dwelling microcrustacean Daphnia. Furthermore, it allows the detection even of inconspicuous morphological features that can be exported to programs for subsequent analysis, e.g., streamline- or finite-element analysis.
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Nazaruddin, N., and Richard Siallagan. "Software Engineering Development of Finite Element Method Programming Applications in 2D Frame Structures Using Python Programs." Journal of Physics: Conference Series 2049, no. 1 (October 1, 2021): 012031. http://dx.doi.org/10.1088/1742-6596/2049/1/012031.
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Abstract The application of the Finite Element Method as one of the numerical methods to solve various engineering problems is of course inseparable from the development of computers with various other related fields such as Computer Aided Design (CAD) and Computer Aided Engineering (CAE) which continuously becomes a concentration of interest in the engineering field. Element analysis has so far been in great demand by various industries due to its reliability and speed in terms of optimization in the world of design and analysis. There are many finite element software such as Abaqus, Nastran, Ansys, CosmosWork, LS-Dyna, Pro-Mecanica, SAP2000. However, the application is paid at a relatively high cost and has quite strict licensing rules, of course this is an obstacle for students at the University of Riau who want to use it. From these problems the author is interested in developing a programming application that can be an alternative to analyzing a structure. The solution that the author can propose is to develop an application using the python programming language to analyze a two-dimensional (2D) frame structure that is under load and is in an elastic condition. From the results of the research that has been carried out, the simulation results of the frame A model obtained data on the 2nd frame model of frame A, the horizontal displacement of -0.06098 m, the vertical displacement of -0.00002857 m, and the angular displacement of 0.00762 rad. These results are compared with manual solutions, analytical solutions, and previous research, it can be concluded that the results of calculations in the developed application show values that are close to that comparison, where the percentage error is not more than 3%, with the highest percentage difference of 2.5%.
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Luo, Zhizhong. "Computation of Two-Dimensional Poisson Equation Using the Third-Order Discrete Scheme of Finite Difference Method Based on Node Set Vector." Journal of Physics: Conference Series 2381, no. 1 (December 1, 2022): 012039. http://dx.doi.org/10.1088/1742-6596/2381/1/012039.
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Abstract A novel third-order discrete scheme of finite difference method based on node set vector for two dimensional Poisson equation is proposed in this paper. Studies on the basic discrete scheme of this method as well as the discrete scheme of the interior node and boundary node are carried out in detail. Computer programs are also developed to emulate a computation sample. The numerical computation results show that this discrete scheme is effective for the numerical computation of two dimensional Poisson equation.
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MISZCZAK, Andrzej, and Krzysztof WIERZCHOLSKI. "ANALYSIS OF THE VALUES OF HYDRODYNAMIC PRESSURE AND LOAD CARRYING CAPACITIES FOR VARIOUS METHODS OF SOLVING A REYNOLDS TYPE EQUATION." Tribologia 280, no. 4 (August 1, 2018): 55–62. http://dx.doi.org/10.5604/01.3001.0012.7532.
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Calculations of the hydrodynamic pressure distribution in the slide bearing gap occur most often on the basis of ready-made computer programs based on CFD methods or one’s own calculation procedures based on various numerical methods. The use of one’s own calculation procedures and, for example, the finite difference method, allows one to include in the calculations of various additional non-classical effects on the lubricant (e.g., the influence of the magnetic field on ferrofluid, the influence of pressure or temperature on viscosity changes, non-Newtonian properties of lubricant or various non-classical models of dynamic viscosity changes). The aim of the authors’ research is to check how large the differences in results may be obtained using the two most frequently used methods of solving a Reynolds type equation. In this work, the authors use the small parameter method and the method of subsequent approximations to determine the distribution of hydrodynamic pressure. For numerical calculations, the finite difference method and our own calculation procedures and Mathcad 15 software were used. With both methods, identical conditions and parameters were assumed and the influence of pressure and temperature on viscosity change was taken into account. In the hydrodynamic pressure calculations, a laminar flow of the lubricating liquid and a non-isothermal lubrication model of the slide bearing were adopted. The classic Newtonian model was used as a constitutive equation. A cylindrical-type slide bearing of finite length with a smooth pan with a full wrap angle was accepted for consideration. In the thin layer of the oil film, the density and thermal conduction coefficient of the oil were assumed to remain unchanged.
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Hadim, A., A. T. Chang, A. Chu, and A. Yskamp. "An Interfacing Software Package for Thermal Analysis: Application to Microelectronics." Journal of Electronic Packaging 111, no. 1 (March 1, 1989): 54–60. http://dx.doi.org/10.1115/1.3226509.
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A software package called: INterfacing Software for Thermal ANalysis (INSTAN) is developed to interface finite element general purpose programs with finite-difference thermal network analyzers for detailed analysis of complex thermal problems. The finite element mesh is used to generate the thermal network representation of the problem. INSTAN performs automatically the thermal network calculations and generates a complete input file for the thermal analysis program. The INSTAN software package is a powerful modeling tool which uses the preprocessing and postprocessing features available in a finite element program. It has also the flexibility and heat transfer calculation capabilities of a finite-difference program. It can handle problems with three-dimensional irregular geometries, time and temperature dependent properties, and anisotropic materials. The software possesses enhanced capabilities that make it suitable for thermal analysis of microelectronic equipment.
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Harutyunyan, Robert. "Computer Modeling and Optimization of Soil Thawing Using Microwave Energy." Известия высших учебных заведений. Электромеханика 63, no. 6 (2020): 37–43. http://dx.doi.org/10.17213/0136-3360-2020-6-37-43.
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A mathematical model is developed to calculate the electromagnetic field A mathematical model is formu-lated, and a finite-difference method and computer programs are developed that allow effective computer mod-eling and optimization of high-speed soil thawing processes in various ways, including using magnetrons. As the main modeling method, a variant of the end-to-end "enthalpy" method without smoothing the concentrated heat capacity is used. A series of calculations was performed for the informative case of Sandstone and sandy loam during thawing by magnetrons of standard structures. The significant influence of nonlinearities of ther-mal parameters, phase transitions of melting and evaporation, and the type of boundary conditions on the val-ues of temperature and electric fields is established. The effect of losses on convective cooling and evaporation is negligible. The results of the work can be applied in the practice of research and design of earthmoving op-erations in the cryolithozone.
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Wulandari, Tika Ermita. "Prediksi Penurunan Konsolidasi Menggunakan Preloading dan Prefabricated Vertical Drain dengan Software Metode Elemen Hingga." JOURNAL OF CIVIL ENGINEERING BUILDING AND TRANSPORTATION 5, no. 2 (September 24, 2021): 99–108. http://dx.doi.org/10.31289/jcebt.v5i2.5844.
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Consolidation is the process of removing water from the pores of the soil which causes changes in the volume of the soil which results in damage to the construction above it. This is more fatal if the decline that occurs is local. Nowadays the use of vertical drains is increasingly in demand, especially with the Prefabricated Vertical Drain (PVD) system which can reduce the time of the soil consolidation process significantly from several years to a matter of months and with technological advances, software is created that can make it easier to calculate construction work with computer programs, one of which is the only finite element method software (Plaxis) to calculate the consolidation settlement process. This study aims to analyze using Finite Element Method software with the help of 2D and 3D plaxis programs to get the consolidation settlement size. The results of 2D and 3D modeling will be compared so that the results that are closest to the field conditions are obtained. From the results of the analysis, it can be concluded that the magnitude of the decrease in Plaxis 3D is closer to the settlement plate data S29 with a decrease of 6.956m or a difference of -0.234m, while the magnitude of the decrease in Plaxis 2D is 7.491 with a difference of decrease of 0.301m.
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Naseem, Amir, M. A. Rehman, and Jihad Younis. "A New Root-Finding Algorithm for Solving Real-World Problems and Its Complex Dynamics via Computer Technology." Complexity 2021 (November 29, 2021): 1–10. http://dx.doi.org/10.1155/2021/6369466.
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Nowadays, the use of computers is becoming very important in various fields of mathematics and engineering sciences. Many complex statistics can be sorted out easily with the help of different computer programs in seconds, especially in computational and applied Mathematics. With the help of different computer tools and languages, a variety of iterative algorithms can be operated in computers for solving different nonlinear problems. The most important factor of an iterative algorithm is its efficiency that relies upon the convergence rate and computational cost per iteration. Taking these facts into account, this article aims to design a new iterative algorithm that is derivative-free and performs better. We construct this algorithm by applying the forward- and finite-difference schemes on Golbabai–Javidi’s method which yields us an efficient and derivative-free algorithm whose computational cost is low as per iteration. We also study the convergence criterion of the designed algorithm and prove its quartic-order convergence. To analyze it numerically, we consider nine different types of numerical test examples and solve them for demonstrating its accuracy, validity, and applicability. The considered problems also involve some real-life applications of civil and chemical engineering. The obtained numerical results of the test examples show that the newly designed algorithm is working better against the other similar algorithms in the literature. For the graphical analysis, we consider some different degrees’ complex polynomials and draw the polynomiographs of the designed quartic-order algorithm and compare it with the other similar existing methods with the help of a computer program. The graphical results reveal the better convergence speed and the other graphical characteristics of the designed algorithm over the other comparable ones.
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Padmaja, R., R. Ravinder Rao, B. Kotiveerachari, and P. B. Godbole. "Comparative Evaluation of Finite Element Models and Types of Analyses for a Bolted Joint." Journal of Mechanical Design 127, no. 6 (February 9, 2005): 1207–10. http://dx.doi.org/10.1115/1.2118647.
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The present work is aimed at evaluating different ways in which a given joint can be analyzed using the Finite Element Method. The bolt is modeled using line elements (link) or area elements (continuum) and a comparative evaluation is carried out. Each of these types is further subdivided into three categories viz., plane stress, axisymmetric, and three-dimensional models. Thus a total of six models are proposed to be analyzed and compared. As the bolt shares only a small fraction of external load in a well-tightened joint, the relative flexibility of a bracket is also studied as an example in the present work. Comparing the results of these analyses it was found that the type of model used for the bolt is more important than the type of analysis. This aspect is probed further to find the essential difference between bolt as link and bolt as continuum. The analysis is carried out using ANSYS, which enables writing many parametric programs.
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Durst, F., B. Schönung, K. Selanger, and M. Winter. "Bubble-driven liquid flows." Journal of Fluid Mechanics 170 (September 1986): 53–82. http://dx.doi.org/10.1017/s0022112086000800.
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Detailed information is provided in this paper on the physics of momentum transfer in bubble-driven liquid flows. Experimental information is obtained on the flow around bubbles and on the axisymmetric bubble-driven liquid flow inside liquid-filled cylinders located with their axes in the vertical direction. A laser-Doppler anemometer extended for particulate two-phase flows is employed for these measurements to yield local fluid velocity information as well as the rise velocity of bubbles. The bubble top radius and the bubble shape were also found from these measurements.Utilizing experimentally gained information and employing the basic equations for particulate two-phase flows, permits finite difference equations to be formulated that allow bubble-driven liquid flows to be computed. Results are presented for boundary conditions corresponding to those of the experimental studies. Comparisons of numerical and experimental results are shown to be in good agreement. This is taken as a justification to employ the developed computer programs to carry out parameter studies for bubble-driven liquid flow inside circular cylinders. Results of these studies are presented and discussed.
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Obrebski, J. B. "Application of the WDKM Program System to Analysis of Space Structures." International Journal of Space Structures 1, no. 2 (June 1985): 93–98. http://dx.doi.org/10.1177/026635118500100204.
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WDKM is designed for use in relation to the analysis of large regular structures. The programs of WDKM are capable of calculating any space bar structure of practically arbitrary global geometry and any type of loading. The system requires less data to be fed in than similar ones based on the finite element method. WDKM is based on the theory of difference-matrix description and the numerical algorithm is suitably prepared. Both static and dynamic analyses are possible. In addition, stability problems and frequency of natural vibrations can be analysed. Large displacements of nodes can be taken into consideration. Moreover, large longitudinal and shear forces in bars are taken into account. Effective computer-aided dimensioning of regular structures is also incorporated in the system.
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Brown, Samuel J. "Energy Release Protection for Pressurized Systems. Part II: Review of Studies Into Impact/Terminal Ballistics." Applied Mechanics Reviews 39, no. 2 (February 1, 1986): 177–201. http://dx.doi.org/10.1115/1.3143704.
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In order to assess whether or not there is a need for protection against the failure of a pressure system, the engineer must evaluate the hazards associated with rupture. The hazards are divided into two categories: (a) force/displacement and (b) degenerative. Force/displacement is classified into (1) kinetic energy associated with the atmosphere: blast, (2) kinetic energy of objects (fragmentation and impact of missiles), and (3) kinetic energy associated with foundations: soil foundation motion. The first article of this series [Energy release protection from pressurized systems: Part I Review of studies into blast and fragmentation, Appl Mech Rev38 (Dec), 1625–1651 (1985)] has set the stage for this paper, which reviews the studies into predicting the performance (mechanics) of a receptor (target, containment, barricade, shelter) that is impacted by a missile. The study into the prediction of target missile performance or terminal ballistics has occupied interests of man since the development of a projectile as a weapon. One of the earliest publications of terminal ballistics is reported by Robins (1742). A number of experimental studies during the 1800s are reported by Holie (1950). These early experiments set the pattern for the reliance on experimental programs to define semiempirical formula to predict missile–target responses (such as penetration, perforation, spalling, and scabbing) into the 20th century. This is due to the fact that theoretically derived equations to predict missile target performance have enjoyed only limited success because of the complexity of the problems to be solved. Numerical methods essentially had to wait for the development of the high speed digital computers in the early 1960s. Historically the finite difference methods have received the earliest use in simulating impact. They tend to be more computationally cost effective than finite element programs. However, because of the generality of the finite element method to idealize structures geometrically for a considerable range of mechanics problems, it has received the greater attention of research and development over the last two decades and is capable of solving wave propagation, nonlinear material, and nonlinear large deformation problems. The computer codes developed to solve impact problems are generally characterized as either Lagrangian or Eulerian. In this paper, a brief discussion will be provided covering the development of target/missile formulas, associated experimental programs and numerical methods.
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Azarnejad, A., and T. M. Hrudey. "A numerical study of thermal ice loads on structures." Canadian Journal of Civil Engineering 25, no. 3 (June 1, 1998): 557–68. http://dx.doi.org/10.1139/l97-119.
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A numerical model is presented for the prediction of the three-dimensional stress field in an ice sheet due to temperature changes, as a function of time, under a variety of conditions. The model relies on two separate computer programs for the thermal and mechanical aspects of the problem. The thermal program uses the finite difference method to calculate the temperature distribution through the thickness of the ice cover under a variety of meteorological input conditions. The mechanical part of the analysis is conducted using the finite element method. A degenerate shell element is used, which is capable of modeling both bending and membrane behaviors of the ice cover. Relevant features of the finite element model include variable temperature and properties through the thickness, an elastic foundation representation of the underlying water, nonlinear constitutive behavior of the ice, temperature-dependent mechanical properties, flexibility of resisting structures, and boundary conditions representing a variety of shoreline types. Results are presented from simulations conducted during verification of the model. Included are simulations of uniaxial and biaxial laboratory tests on the thermal expansion of ice as well as three thermal events for which field data were available. Conclusions are presented concerning the analytical prediction of thermal ice forces.Key words: ice loads, thermal loads, ice mechanics, hydraulic structures, dams.
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Rahman, Habib. "Pedagogical Approach to Teaching a First Course in Engineering Electromagnetics." International Journal for Innovation Education and Research 2, no. 3 (March 31, 2014): 25–29. http://dx.doi.org/10.31686/ijier.vol2.iss3.153.
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This paper presents a pedagogical approach to the development and teaching of a course in engineering electromagnetics to undergraduate students in electrical and computer engineering at Saint Louis University. It also discusses myriad problems and challenges in offering this course to accommodate the changing discipline boundaries. Engineering electromagnetics, by nature, is not a very popular course to many students because they incorrectly think it is full of complicated mathematics with little or no applications in the real world posing an intellectual and educational challenge to them. It makes this course appear insurmountable, abstract and abstruse. With the evolution of state-of-the-art technologies in electrical and computer engineering, the understanding the fundamental concepts in electromagnetics has become increasingly important. This approach provides tools of accurate analysis through computer methods, in addition to closed-form methods used for design analysis and synthesis. Difficult three-dimensional vector differential and integral concepts are discussed when they are encountered with emphasis being on physical insight. The course is modernized by briefly introducing the finite-difference method, and thereafter, integrating some prewritten computer programs to demonstrate graphical representation of some problems of practical interests. As a result, the students really begin to find a measure of joy in this course and emerge as engineers equipped with the best of the closed-form and computer worlds.
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Kulterbaev, H. P., I. M. Abdul-Salam, and M. M. Payzulaev. "FREE LONGITUDINAL VIBRATIONS OF A VERTICAL ROD WITH DISCRETE MASSES WITH DAMPING FORCES." Herald of Dagestan State Technical University. Technical Sciences 45, no. 3 (May 12, 2019): 8–17. http://dx.doi.org/10.21822/2073-6185-2018-45-3-8-17.
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Objectives. The longitudinal oscillations of a vertical rod of a continually discrete system with kinematic seismic disturbances in the form of a stationary random process are considered.Method. A method for determining the variance of the output process of displacements, using the representation of the input random process as a sum of harmonic deterministic perturbations, is proposed and implemented.Result. The dependence function of the dispersion of displacements on the longitudinal coordinate is determined. Longitudinal vibrations of vertical rods near the epicenter of earthquakes are dangerous for their strength and stability. The methods of finite differences and coordinate descent allow you to create universal algorithms and computer programs that easily solve complex spectral problems.Conclusion. To date, research on random vibrations of buildings and structures, as well as regulatory documents, has been devoted to horizontal seismic effects and transverse bending vibrations caused by them. Examples indicate the need to expand the scope of research with the inclusion of other types of vibrations: combinations of longitudinal with transverse, angular, torsional, parametric, etc. This design can be easily adapted to vibrations of rods of variable cross section, to vibrations of continually discrete rods.
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Kiciński, Radosław, and Bogdan Szturomski. "Pressure Wave Caused by Trinitrotoluene (TNT) Underwater Explosion—Short Review." Applied Sciences 10, no. 10 (May 15, 2020): 3433. http://dx.doi.org/10.3390/app10103433.
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The development of computational techniques and computer hardware has an impact the analysis of short-term (fast-changing) processes, such as the impact of a non-contact underwater explosion pressure waves. A theory of underwater explosions, gas bubble formation and pressure waves are presented. The course of the pressure wave in time, and its propagation in the acoustic medium are presented. The study presents empirical descriptions of non-contact pressure explosion waves. We propose to use them in simulations of ship hull strength and other objects immersed in liquids that are exposed to the effects of non-contact trinitrotoluene (TNT)-charge explosions. Pressure distributions and their time courses given by authors such as R.H. Cole, J.S. Nawagin, W. Stiepanow, T.E. Farley and H.G. Snay, T.L. Geers and K.S. Hunter are compared. A method of pressure wave modeling using acoustic media implemented in Computer Aided Engineering (CAE) programs is presented. The results of the values and the time course of the pressure acting on the underwater object are given. The influence of FEM (Finite Element Method) mesh density on the obtained results is examined and presented. The aim of the article is to expand our knowledge of underwater explosions, compare mathematical descriptions of the pressure waves developed by different authors and show the differences between them. In addition, we present the distinction between contact and non-contact explosions and analyze how changes in the mesh density of acoustic elements affects the reflection of the incident wave caused by an underwater explosion.
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BILIAIEVA, V. "MATHEMATICAL MODELS APPLICATION TO PREDICT HEAT AND CHEMICAL AIR POLLUTION IN WORKING AREARS." Ukrainian Journal of Civil Engineering and Architecture, no. 3 (June 1, 2021): 39–45. http://dx.doi.org/10.30838/j.bpsacea.2312.010721.39.765.
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Problem statement. The problem of prediction the level of air pollution in working areas is considered on the basis of mathematical models of aerodynamics and heat and mass transfer. The task is to calculate the concentration field of chemically hazardous substances and the temperature field in the working zones. The purpose of the article. Construction of numerical models that allow determine the distribution of temperature and concentration of chemically hazardous substances in work areas with a complex geometric shape. Methodology. For numerical modeling of the process of air pollution in working areas during the spread of chemically hazardous substances, G. Marchuk's equation is used, which takes into account the transfer of a chemically hazardous substance due to convection, as well as due to turbulent diffusion. The energy equation is used to model the thermal contamination of work areas. To simulate the wind speed field in the presence of various kinds of obstacles, the Laplace equation for the speed potential is used. The integration of the modeling equations is carried out on a rectangular grid. For the numerical integration of the equation describing the propagation of a chemically hazardous substance in the air of working areas, a finite-difference splitting scheme is used. For the numerical integration of the Laplace equation for the velocity potential, two splitting schemes are used. The unknown value of the velocity potential at each splitting step is calculated using an explicit formula. Numerical integration of the energy equation is carried out using an explicit difference scheme. Scientific novelty. The constructed numerical models that allow to calculate the zones of chemical and thermal pollution, taking into account a set of important physical factors. A feature of numerical models is the speed of calculation, which is important when serial calculations are carrying out in practice. Practical significance. A complex of applied programs was created on the basis of the developed numerical models. This complex of programs allows to analyze and predict the intensity and size of zones of thermal or chemical pollution. This set of programs can be useful in determining the affected areas in case of extreme situations at chemically hazardous facilities. Conclusions. Numerical models have been developed. On the basis of these models a complex of applied programs has been created that allow to study multiparameter processes of chemical and thermal air pollution of working areas using the method of computer modeling. The complex of programs can be implemented on computers of low and medium power. The results of a computational experiment are presented.
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Nasibullayev, I. Sh. "Application of free software to visualize the results of simulation of dynamic processes." Multiphase Systems 16, no. 3-4 (2021): 121–43. http://dx.doi.org/10.21662/mfs2021.3.016.
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The paper presents an overview of modern free tools for dynamic visualization and gives recommendations for choosing tools depending on the research method, the form of presentation of the initial data, and the specifics of the phenomenon under study. For the convenience of using the materials of the work, the source codes are given both for the programs of computational experiments of classical problems, and for creating a graphical visualization of the simulation results. To animate the process described by analytical formulas, it is proposed to use the gif terminal of the gnuplot program or the Python visualization library. An example of applying this approach to solving the modified Verhulst-Pearl equation, which describes the change in the population under periodic external influence, is given. When studying non-stationary phenomena distributed in space, the results can be presented in video format. The problem of natural convection in a horizontal layer of fluid or gas was simulated in the program FreeFem++ for solving differential equations by the finite element method with the conversion of the results using the GhostScript and MEncoder programs into a video format. An example of using the finite difference method in modeling self-oscillating chemical reactions in the Qt environment with saving animation frames as graphic files is given. To display the results of modeling three-dimensional dynamic processes, it is proposed to use the Blender computer graphics program. Modeling and visualization of oscillations of an elastic pendulum using the built-in Blender Python API interpreter are presented. An approach is shown for dividing a computational experiment and visualizing its results, which makes it possible to increase the efficiency of the use of computational resources. A universal Python-script is proposed for constructing three-dimensional object motion trajectories based on external source data.
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Ahmed, Shazad Shawki, and Hiwa Abdullah Rasol. "Numerical Computation of Mixed Volterra–Fredholm Integro-Fractional Differential Equations by Using Newton-Cotes Methods." Symmetry 14, no. 8 (August 15, 2022): 1693. http://dx.doi.org/10.3390/sym14081693.
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In this article, the numerical solution of the mixed Volterra–Fredholm integro-differential equations of multi-fractional order less than or equal to one in the Caputo sense (V-FIFDEs) under the initial conditions is presented with powerful algorithms. The method is based upon the quadrature rule with the aid of finite difference approximation to Caputo derivative usage collocation points. For treatments, our technique converts the V-FIFDEs into algebraic equations with operational matrices, some of which have the symmetry property, which is simple for evaluating. Furthermore, numerical examples are presented to show the technique’s validity and usefulness as well comparisons with previous results. The majority of programs are performed using MATLAB v. 9.7.
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Janda, Tomás, Renato P. Cunha, Pavel Kuklík, and Gérson M. Anjos. "Three Dimensional Finite Element Analysis and Back-analysis of CFA Standard Pile Groups and Piled Rafts Founded on Tropical Soil." Soils and Rocks 32, no. 1 (January 1, 2009): 3–18. http://dx.doi.org/10.28927/sr.321003.
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This paper deals with Plaxis 3D finite element simulations of the mechanical response of deep foundations founded in a collapsible tropical soil. Main attention is initially paid to differences between single continuous flight auger (CFA) pile behavior and the behavior of CFA piles in standard groups. The numerically computed load-settlement curves are compared to field load test data obtained at the experimental research site of the University of Brasília (UnB), leading to conclusions about the appropriateness of adopting laboratory, in situ or back calculated parameters as input of numerical programs that simulate 3D foundation systems. Further, the contribution of the contact surficial soil/top raft is numerically examined by simulating the behavior of identical “piled raft” systems founded in the same site. The numerical simulated results of “piled raft” and standard pile group systems are then compared in terms of load capacity, system stiffness, load share between pile tip, shaft and raft, and mean developed lateral pile shaft friction. Having the results at distinct loading stages, as at working and failure levels, the analyses show the differential behavior, and design obtained responses, one may expect from conventional pile groups and “piled rafts” of CFA floating piles when founded in tropical soils. It is a mixed theoretical/experimental paper with practical interest for foundation designers and constructors.
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Allart, Emilie, Joachim Niehren, and Cristian Versari. "Exact Boolean Abstraction of Linear Equation Systems." Computation 9, no. 11 (October 21, 2021): 113. http://dx.doi.org/10.3390/computation9110113.
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We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over the structure of booleans is equal to the boolean abstraction of the solution set of ϕ over the positive reals. Abstract interpretation over the booleans is thus complete for the boolean abstraction when restricted to exact linear equation systems, while it is not complete more generally. We present a new rewriting algorithm that makes linear equation systems exact for the boolean abstraction while preserving the solutions over the positive reals. The rewriting algorithm is based on the elementary modes of the linear equation system. The computation of the elementary modes may require exponential time in the worst case, but is often feasible in practice with freely available tools. For exact linear equation systems, we can compute the boolean abstraction by finite domain constraint programming. This yields a solution of the initial problem that is often feasible in practice. Our exact rewriting algorithm has two further applications. Firstly, it can be used to compute the sign abstraction of linear equation systems over the reals, as needed for analyzing function programs with linear arithmetics. Secondly, it can be applied to compute the difference abstraction of a linear equation system as used in change prediction algorithms for flux networks in systems biology.
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Faflei, О. Ya, V. V. Mykhailiuk, R. V. Rachkevych, R. О. Deynega, А. І. Riznychuk, and R. S. Kravchuk. "Features of the study of threaded joints using the finite element method." Scientific Bulletin of Ivano-Frankivsk National Technical University of Oil and Gas, no. 1(50) (September 7, 2021): 62–69. http://dx.doi.org/10.31471/1993-9965-2021-1(50)-62-69.
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A significant number of computer programs exist today for various engineering calculations, research and development of equipment elements. The SolidWorks software has become widespread for such work, which allows you to minimize time, facilitate the performance of the necessary work, as well as analyze the strength, stiffness, stability and endurance of products of a wide range of complexity and purpose. The program uses the finite element method, which has both a number of advantages and certain disadvantages.
To investigate the possibilities of such a program, a model of a threaded connection of sucker rods has been built. Simulation of make-up torque for threaded connections remains problematic when modeling in SolidWorks Simulation. There are several ways to simulate the make-up moment during the study of the stress-strain state of threaded connections. To solve problems in an axisymmetric setting, the optimal method is to overlap the ends of the nipple and coupling by the required amount. The use of an axisymmetric model in the process of simulation does not impair the results obtained in comparison with 3D models. But it speeds up the calculation process, allows you to build a fine mesh of finite elements and get more accurate results.
The paper presents an algorithm for calculating the tension of the threaded connections of sucker rods, which can be applied to threaded connections of drill string elements with some adjustments. The only difference will be in the formula for determining the make-up moment, from which the value of the pre-tightening force and the areas of dangerous sections are derived. Also, in the work, a simulation study was carried out using the selected method using the example of a threaded connection of sucker rods with a diameter of 19 mm. A diagram of displacements and distribution of equivalent stresses in a threaded connection was obtained and the possibility of determining specific parameters at certain points of the model under study was shown with subsequent automated construction of their graphical dependencies.
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BILIAIEV, M. M., O. V. BERLOV, V. V. BILIAIEVA, V. A. KOZACHYNA, and T. I. RUSAKOVA. "NUMERICAL MODELING OF AIR POLLUTION NEAR THE HIGHWAY WITH PROTECTIVE BARRIERS." Ukrainian Journal of Civil Engineering and Architecture, no. 2 (July 9, 2022): 7–14. http://dx.doi.org/10.30838/j.bpsacea.2312.260422.7.846.
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Problem statement. The problem of predicting chemical pollution zones near the highway, where protective barriers are located, is considered. The protective barriers influence the aerodynamics of air flow and reduce the level of working areas chemical pollution near the highway. It is necessary to have mathematical models that allow such evaluation at the design stage in order to evaluate the effectiveness of protective barriers promptly. The purpose of the article. Development of a numerical multi-parameter model and computer program for evaluating the effectiveness of the protective barriers using near the highway to reduce the chemical contamination level of work areas. Methodology. A two-dimensional mass transfer equation is used for mathematical modeling of chemical hazardous substances spreading that are emitted from a car and spread near the highway. This simulation equation takes into account the wind direction, atmospheric diffusion, the intensity of chemically hazardous substance emission from the car, the emission source location, the car body and the location of protective barriers near the highway. The Navier − Stokes equation and the potential motion model both are used to solve the aerodynamics problem of determining the uneven air velocity field near the highway. An implicit splitting difference scheme is used to numerically integrate the vortex transfer equation. Two numerical schemes are used to numerically integrate the equation for the current function. An explicit difference scheme is used to numerically integrate the Laplace equation for the velocity potential. Based on the constructed numerical model the package of programs is developed. To solve numerically equation of pollutant transfer the finite difference schemes of splitting are used. Scientific novelty. To calculate the formation of chemical pollution areas for atmospheric air near the highway during emissions from vehicles numerical model is proposed. This model allow to estimate the protective barriers effectiveness for reducing air pollution in the working areas. Practical significance. Based on the developed model the code for quickly calculation of air pollution process both near the highway and in work areas protecting with barriers is created. Conclusions. The developed numerical model and the computer code implementing it allow to investigate the process of chemical hazardous substance spreading in the atmospheric air near the highway. The model allows to quickly determine the effectiveness of protective barriers using near the highway. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.
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BILIAIEV, M. M., V. A. KOZACHYNA, P. B. MASHYKHINA, and V. V. TSURKAN. "MATHEMATICAL MODELING IN WATER TREATMENT PROBLEMS." Ukrainian Journal of Civil Engineering and Architecture, no. 4 (October 22, 2022): 13–19. http://dx.doi.org/10.30838/j.bpsacea.2312.250822.13.872.
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Problem statement. Analysis of the treatment facilities efficiency in sewerage at the stage of their design is great importance. Also, at the stage of structures’ reconstruction or their operation adjustment under different load conditions, it is necessary to know the efficiency of water treatment in different areas of treatment facilities. Such information makes it possible to rationally operate facilities. For solving problems of this class, the most effective tool is the use of the numerical modeling method. The work considers development of numerical models set for solving problems of this class. Methodology. Two fundamental models are used to solve the velocity field determination of the wastewater flow in the sewage treatment plant. The first is a model of the vortex-free motion for an incompressible fluid. The second model is the Navier-Stokes equations written in Helmholtz variables. The mass transfer equation is used to determine impurity concentration fields in sewage treatment plants, which takes into account flow velocity, diffusion and the presence of impurity emission sources. Material balance equations for the substrate and activated sludge are used to calculate the process of biological wastewater treatment. Finite-difference schemes are used to build numerical models that allow calculating the hydrodynamics of the flow and the distribution of the impurity concentration in the facility. The Euler method is used for the numerical solution of the material balance equations. Results. Numerical models were built, which were used to develop a complex of computer programs. These computer programs allow real-time analysis of the water treatment efficiency in the facility. Scientific novelty. Numerical models have been developed that allow investigating the process of water treatment in facilities of the «settler» type and in aeration tanks, that is, for a significant class of treatment facilities used in practice. Practical value. The calculation time of the velocity field and the impurity concentration field in a water treatment plant with a complex geometric shape is few seconds. This allows usinge the developed numerical models for serial calculations in project organizations in daily work.
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V.S., Aswin, and Ashish Awasthi. "Iterative differential quadrature algorithms for modified Burgers equation." Engineering Computations 35, no. 1 (March 5, 2018): 235–50. http://dx.doi.org/10.1108/ec-04-2017-0140.
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Purpose This paper aims to investigate the features of three vectorized iterative numerical schemes used to simulate the behavior of modified Burgers equation (MBE). Design/methodology/approach Two of the schemes comprise differential quadrature and finite difference methods, while the third scheme consists of only differential quadrature for the derivative approximations. Proposed schemes are simulated for well-posed problems of MBE having known the analytic solution. The computational complexity of the schemes is examined through monitoring the time taken to complete the simulation. The results are compared with the analytic solution with the help of discrete error norms. Also, the accuracy of the proposed schemes is compared with that of the existing schemes in the literature. Vectorized MATLAB programs of the schemes are used for all investigations. Findings It is observed that all the three schemes succeeded in producing a good replication of the exact solution. The results are closer to the analytical solution than the results in the literature. Among the three schemes, the scheme labeled as FDTDQS is found highly accurate and computationally cheaper using fewer grid points. From the vectorized MATLAB programs provided, it is evident that the implementation of the schemes is simple. Originality/value This study gives an idea about three numerical schemes for a highly nonlinear problem. This mathematical framework can be adopted to any one-dimensional partial differential equation as well, and the provided program will be helpful to generate more fast and accurate vectorized code in MATLAB.
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Majchrzak, Ewa, and Bohdan Mochnacki. "Numerical solutions of the second-order dual-phase-lag equation using the explicit and implicit schemes of the finite difference method." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (May 20, 2019): 2099–120. http://dx.doi.org/10.1108/hff-11-2018-0640.
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Purpose The purpose of this paper is the application of the finite difference method (FDM) for numerical modeling of the microscale heat transfer processes occurring in the domain of thin metal film subjected to a laser pulse. The problem discussed is described by the different variants of the second-order dual-phase-lag equation (DPLE). The laser action is taken into account by the introduction of internal volumetric heat source to the governing equation. The capacity of the source is dependent on the geometrical co-ordinates and duration of the laser beam. The modified forms of DPLE presented in the paper, resulting from the certain substitutions introduced to the basic equation. Design/methodology/approach At the stage of numerical computations, the different variants of the FDM are applied. Both the explicit and implicit FDM schemes are used. The formula determining the capacity of the internal heat source suggests the formulation of the task discussed using the cylindrical co-ordinate system. The in-house programs realizing the numerical computations concern the axially-symmetrical tasks. In this paper, the metal films made of the nickel and gold are considered. Findings The algorithms presented make possible to analyze the heating/cooling processes occurring in the domain of metal film having a thickness Z for the different laser parameters (laser intensity, characteristic time of laser pulse and laser beam radius) and the different materials (optical penetration depth, reflectivity of irradiated surface, lag times, thermal conductivity and volumetric specific heat). Research limitations/implications Not for all metals, one can find information on lag times. In the literature, analytical formulas can be found to calculate these values, but they are strongly approximated. It should be pointed out that there are some limitations concerning the delay times of material considered, which assure the physical correctness of the second-order DPLE. Originality/value The FDM algorithm concerns the three-dimensional cylindrical domain while a large majority of the second-order DPLE numerical solutions have been obtained for the one-dimensional tasks. Both the implicit and explicit numerical schemes are proposed and the testing computations confirm the correctness and effectiveness of the algorithms presented.
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Stout, K. J. "The Effect of Manufacturing Variations on the Performance of Externally Pressurized Gas-Lubricated Journal Bearings." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 4 (October 1985): 299–309. http://dx.doi.org/10.1243/pime_proc_1985_199_127_02.
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This paper extends the previous work on the hybrid operation of externally pressurized gas bearings to include the effects of manufacturing variations on design performance of the slot entry configuration. Six aspects of manufacture are considered, and include the departure from the design conditions of (a) bearing clearance, (b) feed slot thickness, (c) bearing form, (d) bearing roundness, (e) bearing member alignment, (f) feed slot geometry. Computer predictions of the above effects have been made by introducing modifications to the programs developed to model gas bearing performance developed for solution using a finite difference technique. The results show how the load capacity of the bearings is affected by the departure of dimensions from their design conditions. The magnitude of the departure from the design performance is demonstrated in the figures presented. The performance predictions for the slot entry bearing are compared with results obtained from the orifice compensated journal bearing previously reported. Guidance is given on the limits of departure from initial design conditions which should be allowed for both types of bearing. Confirmation of the accuracy of design predictions has been achieved in this investigation by conducting experiments using test bearings which were very carefully measured to establish the real tolerance on manufacture. These bearings were tested on a specially designed experimental rig.
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Shabana, Ahmed A., and Gengxiang Wang. "Durability analysis and implementation of the floating frame of reference formulation." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 232, no. 3 (September 26, 2017): 295–313. http://dx.doi.org/10.1177/1464419317731707.
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The finite element floating frame of reference (FFR) formulation, implemented in most commercial multibody system (MBS) computer programs, is widely used in the durability analysis by a large number of industry sectors. In this paper, a single-degree of freedom system is used to derive a new analytical model from the general nonlinear FFR equations. The obtained new analytical model, which can serve as a benchmark example, is used to address fundamental issues related to the accurate, efficient, and general implementation of the FFR formulation, including the treatment of the algebraic joint constraint equations, fundamental difference between the FFR reference conditions and the structural mechanics boundary conditions, the choice of the deformation modes, handling redundant MBS constraints, effect of the MBS joints on the oscillation frequencies, and difference between fixed and moving boundary conditions. Structural mechanics boundary conditions eliminate degrees of freedom and define the system topology, while the FFR reference conditions eliminate coordinate redundancy and do not introduce any motion constraints. The paper shows analytically how the MBS joint constraint equations change the system oscillation frequencies, demonstrates the effect of using inappropriate set of reference conditions, proves there is no single set of reference conditions suited for all applications, and uses other FE methods to verify the results and support the conclusions drawn. The results obtained in this investigation show that improper selection of the reference conditions can lead to solution errors that exceed 100%, making such a solution completely unreliable in any durability investigation. General implementation of the FFR formulation will significantly contribute to increasing reliance on virtual testing, less reliance on building actual prototypes, better understanding of flexible body dynamics, and better communication between various computer-aided engineering groups.
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Ng, S. F., and N. Bencharif. "A finite difference computer program for the modelling of thick rectangular plates." Computers & Structures 33, no. 4 (January 1989): 1011–16. http://dx.doi.org/10.1016/0045-7949(89)90436-7.
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Zhao, Ping. "An efficient computer program for wavefront calculation by the finite-difference method." Computers & Geosciences 22, no. 3 (April 1996): 239–51. http://dx.doi.org/10.1016/0098-3004(95)00076-3.
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Loginovskiy, O. V., L. Yu Kostyleva, A. A. Maksimov, and I. M. Yachikov. "Determination of the Parameters of the La¬mination of a Bimetallic Plate by Means of Active Thermal Non-Destructive Control." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 21, no. 4 (November 2021): 37–51. http://dx.doi.org/10.14529/ctcr210404.
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Bimetals are in many ways substitutes for scarce metals, while they represent an independent group of materials necessary for the creation of new machines, devices and other various products. The increasing volume of production of bimetals and products made from them requires an increase in their operational characteristics and, accordingly, an increase in the quality of finished products. One of the difficult technological tasks is the connection of aluminum and its alloys with steels of various classes, since there are many problems associated with the quality of the connection of me¬tals with different properties. To improve the reliability and durability of machines and other pro¬ducts made of bimetals, it is necessary to carry out continuous quality control, and the most effective methods are non-destructive testing. Quite promising in terms of simplicity and accessibility is the method of active thermal control, in which the investigated product is subjected to pulsed thermal action by means of a source of thermal loading. The amplitude, shape and time variation of temperature signals serve as informative parameters that allow an operator or an automated system to detect certain defects and evaluate their parameters. With all the availability of pulsed thermal control, the most difficult component is associated with specialized computer programs for processing experimental data and determining the parameters of a delamination defect. The aim of the study is to create a computer model of the thermal state of a bimetallic plate in the presence of an air bubble between the layers and, through computer simulation, to determine the size of defects during active pulse thermal non-destructive testing of steel-aluminum plates. Materials and methods. When performing the work, the methods of mathematical and computer modeling were used. The created software using the development tools of the MATLAB package was based on known methods for obtaining an approximate solution to a boundary value problem on a computer using the finite difference method. Results. A mathematical model has been developed, an algorithm for solving a boundary value problem, and a computer program has been created that allows simulating a pulse thermal control to determine the parameters of a delamination defect in a bimetallic plate. Conclusion. It was found that it is more efficient to measure the temperature difference from the side where the defect is located and the multilayer plate is heated. Heating the plates from the side opposite to the defect and their further cooling showed significantly lower efficiency in terms of obtaining a useful temperature signal. It is shown that in the presence of a defect, the greater the loading heat flux and the defect size, the greater the value of the useful signal determined by the temperature difference on the measured surface.
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Vollebregt, Edwin. "Abstract Level Parallelization of Finite Difference Methods." Scientific Programming 6, no. 4 (1997): 331–44. http://dx.doi.org/10.1155/1997/321965.
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A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”). The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing). This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.
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DUBEIBE, F. L. "SOLVING THE TIME-DEPENDENT SCHRÖDINGER EQUATION WITH ABSORBING BOUNDARY CONDITIONS AND SOURCE TERMS IN MATHEMATICA 6.0." International Journal of Modern Physics C 21, no. 11 (November 2010): 1391–406. http://dx.doi.org/10.1142/s0129183110015919.
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In recent decades a lot of research has been done on the numerical solution of the time-dependent Schrödinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into these schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schrödinger equation by using a standard Crank–Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N × N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.
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Milić, I., and M. van Noort. "Spectropolarimetric NLTE inversion code SNAPI." Astronomy & Astrophysics 617 (September 2018): A24. http://dx.doi.org/10.1051/0004-6361/201833382.
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Context. Inversion codes are computer programs that fit a model atmosphere to the observed Stokes spectra, thus retrieving the relevant atmospheric parameters. The rising interest in the solar chromosphere, where spectral lines are formed by scattering, requires developing, testing, and comparing new non-local thermal equilibrium (NLTE) inversion codes. Aims. We present a new NLTE inversion code that is based on the analytical computation of the response functions. We named the code SNAPI, which is short for spectropolarimetic NLTE analytically powered inversion. Methods. SNAPI inverts full Stokes spectrum in order to obtain a depth-dependent stratification of the temperature, velocity, and the magnetic field vector. It is based on the so-called node approach, where atmospheric parameters are free to vary in several fixed points in the atmosphere, and are assumed to behave as splines in between. We describe the inversion approach in general and the specific choices we have made in the implementation. Results. We test the performance on one academic problem and on two interesting NLTE examples, the Ca II 8542 and Na I D spectral lines. The code is found to have excellent convergence properties and outperforms a finite-difference based code in this specific implementation by at least a factor of three. We invert synthetic observations of Na lines from a small part of a simulated solar atmosphere and conclude that the Na lines reliably retrieve the magnetic field and velocity in the range −3 < logτ < −0.5.
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Культербаев, Х. П., Л. А. Барагунова, and М. М. Лафишева. "CALCULATION OF A BEAM ON ELASTIC BASE ANALYTICAL AND NUMERICAL METHODS." Stroitelʹnaâ mehanika i konstrukcii, no. 4(35) (December 19, 2022): 16–23. http://dx.doi.org/10.36622/vstu.2022.35.4.002.
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Постановка задачи. Аналитическим и [2]численным методами решить задачу о балке на упругом основании. С этой целью построить эпюры: изгибающих моментов M, поперечных сил Q, прогибов v, углов поворота поперечных сечений φ, реактивного отпора основания q . Результаты. Цель данной статьи состоит в том, чтобы рассмотреть двутавровую балку, лежащую на упругом грунтовом основании и несущую силовые нагрузки в виде сосредоточенной силы, момента и распределённой нагрузки. Для таких балок практический интерес будет представлять множество выходных результатов нагружения: функция прогибов и углов поворота поперечных сечений, изгибающие моменты и поперечные силы в сечениях, реакции опор, реактивный отпор основания. Конкретный пример рассмотрен двумя методами: аналитическим и численным, получены результаты в виде эпюр. В обоих случаях использованы компьютерные технологии счёта и алгоритмический язык Matlab. В аналитическом решении применены функции А.Н. Крылова, в численном - метод конечных разностей. Проверена прочность балки при изгибе. Релевантность статьи состоит в том, чтобы получить ответы на запросы современной строительной практики при решении задач, усложнившихся в настоящее время при расчётах и конструировании фундаментов. Выводы. Два решения задачи, полученные аналитическим и численным методами, почти совпадают. Из этого следует, что оба решения верные. Аналитическое решение выполнено с привлечением функций А.Н. Крылова, тригонометрических и трансцендентных функций, операции над которыми требуют значительного времени. Решение задачи численным методом конечных разностей оказывается более коротким и связано с решением обыкновенного дифференциального уравнения с правой частью и системы алгебраических уравнений. Вычислительный комплекс Matlab c помощью несложных программ за весьма короткое время решает данные задачи. Problem statement. Solve the problem of a beam on an elastic foundation using analytical and numerical methods. For this purpose, plot diagrams: bending moments M , shear forces Q , deflections v , angles of rotation of cross sections φ , base rebound q . Results. The purpose of this article is to consider an I-beam lying on an elastic soil foundation and carrying power loads in the form of a concentrated force, a moment and a distributed load. For such beams, a variety of output loading results will be of practical interest: the function of deflections and angles of rotation of cross sections, bending moments and transverse forces in sections, support reactions, reactive rebound of the base. A specific example is considered by two methods: analytical and numerical, the results are obtained in the form of diagrams. In both cases, computer computing technologies and the Matlab programming platform were used. The functions of A.N. Krylov are used in the analytical solution, in the numerical solution - the method of finite differences. The bending strength of the beam has been tested. The relevance of the article is to get answers to the demands of modern construction practice in solving problems that have become more complicated at present calculations and design of foundations. Conclusions. Two solutions of the problem obtained by analytical and numerical methods almost coincide. It follows that both solutions are correct. It should be noted that the analytical solution was made using the functions of A.N. Krylov, trigonometric and transcendental functions, operations on which require considerable time.The solution of the problem by the numerical finite difference method turns out to be shorter and is associated with the solution of an ordinary differential equation with the right side and a system of algebraic equations. The Matlab computer complex solves these problems in a very short time with the help of simple programs.
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Keiswetter, Dean, Ross Black, and Chris Schmeissner. "A program for seismic wavefield modeling using finite-difference techniques." Computers & Geosciences 22, no. 3 (April 1996): 267–86. http://dx.doi.org/10.1016/0098-3004(95)00078-x.
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Solar-Lezama, Armando, Liviu Tancau, Rastislav Bodik, Sanjit Seshia, and Vijay Saraswat. "Combinatorial sketching for finite programs." ACM SIGPLAN Notices 41, no. 11 (November 2006): 404–15. http://dx.doi.org/10.1145/1168918.1168907.
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Nelson, Glenn D., and John E. Vidale. "Earthquake locations by 3-D finite-difference travel times." Bulletin of the Seismological Society of America 80, no. 2 (April 1, 1990): 395–410. http://dx.doi.org/10.1785/bssa0800020395.
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Abstract We present a new method for locating earthquakes in a region with arbitrarily complex three-dimensional velocity structure, called QUAKE3D. Our method searches a gridded volume and finds the global minimum travel-time residual location within the volume. Any minimization criterion may be employed. The L1 criterion, which minimizes the sum of the absolute values of travel-time residuals, is especially useful when the station coverage is sparse and is more robust than the L2 criterion (which minimizes the RMS sum) employed by most earthquake location programs. On a UNIX workstation with 8 Mbytes memory, travel-time grids of size 150 by 150 by 50 are reasonably employed, with the actual geographic coverage dependent on the grid spacing. Location precision is finer than the grid spacing. Earthquake recordings at six stations in Bear Valley are located as an example, using various layered and laterally varying velocity models. Locations with QUAKE3D are nearly identical to HYPOINVERSE locations when the same flat-layered velocity model is used. For the examples presented, the computation time per event is approximately 4 times slower than HYPOINVERSE, but the computation time for QUAKE3D is dependent only on the grid size and number of stations, and independent of the velocity model complexity. Using QUAKE3D with a laterally varying velocity model results in locations that are physically more plausible and statistically more precise. Compared to flat-layered solutions, the earthquakes are more closely aligned with the surface fault trace, are more uniform in depth distribution, and the event and station travel-time residuals are much smaller. Hypocentral error bars computed by QUAKE3D are more realistic in that the trade-off of depth versus origin time is implicit in our error estimation, but ignored by HYPOINVERSE.
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Cheremisinov, D. I. "Synthesis of computer programs that implement finite automata." Automatic Control and Computer Sciences 41, no. 4 (August 2007): 215–23. http://dx.doi.org/10.3103/s0146411607040050.
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Марченко, М. А., and Т. А. Сушкевич. "Parallel simulation of kinetic processes by Monte Carlo method (dedicated to the memory of the Chief Theoretiсian of Cosmonautics academician M.V. Keldysh in the 60th anniversary of the launch of the first artificial sputnik)." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (December 19, 2017): 434–46. http://dx.doi.org/10.26089/nummet.v18r436.
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В 2017 году мировая общественность отмечает 60-летний юбилей запуска 4 октября 1957 года в СССР первого искусственного спутника Земли, положившего начало космической эры. Баллистические расчеты проводились на первой серийной ЭВМ Стрела в Институте Келдыша. При решении сложнейших задач создания ракетно-ядерного щита были заложены основы новых направлений в математике - вычислительной математики и математического моделирования. И в СССР, и в США параллельно разрабатывались детерминированные и статистические численные методы. Методы Монте-Карло (ММК) как инструмент для прямого статистического моделирования были разработаны в США в рамках Манхэттонского проекта создания ядерного оружия. Джон фон Нейман первым предложил использовать саму ЭВМ для генерации случайных чисел. В 1949 году Джон фон Нейман и Станислав Улам предложили первый алгоритм получения псевдослучайных величин, который впоследствии был назван ММК и послужил основой для развития методики генерации псевдослучайных чисел с использованием ЭВМ. Разработка ММК и эффективность его применения всегда начинается с разработки генератора случайных или псевдослучайных чисел, который зависит от класса решаемых задач и конкретной структуры и архитектуры ЭВМ. Методы Монте-Карло стали массово применять на всех архитектурах вычислительных систем с параллельными и распределенными вычислениями. Сейчас в эпоху супервычислений преобладают ММК как следствие простоты их реализации. Но эта простота обманчива. В статье представлен разработанный отечественный комплексный методический подход, в котором на примере трех сложных больших задач, описывающих пространственно-неоднородные кинетические процессы диффузии, коагуляции и переноса заряженных частиц, системно рассматриваются теория методов и алгоритмов ММК и практика их реализации в формате не просто программ, а также параллельных генераторов псевдослучайных чисел, библиотек программ, средств обработки данных, управляющих программ и т.д., т.е. все этапы создания цифрового продукта. На примере вероятностных моделей для численного моделирования кинетических процессов диффузии, коагуляции и переноса заряженных частиц, когда ансамбли траекторий или частиц содержат по 10 в 7-13 степени элементов, продемонстрированы возможности и эффективность новых параллельных алгоритмов и распределенных вычислений ММК для решения больших и сложных задач не только для расчета отдельных функционалов или оценок, но и для всего фазового объема задачи. Это важнейшее достижение, которое повышает конкурентность ММК с детерминированными конечно-разностными и сеточными методами при параллельном моделировании. In 2017, the global community celebrates the 60th anniversary of the launch on 4 October 1957 in USSR of the first Earth sputnik, which ushered the space age. The ballistic calculations were conducted on the first production computer Strela in the Keldysh Institute. When solving the most complicated problems of creating a nuclear missile shield were laid the foundations for new directions in mathematics - computational mathematics and mathematical modeling. The USSR and the USA simultaneously developed the deterministic and statistical numerical methods. Methods Monte Carlo (MMC) as a tool for direct statistical simulation has been developed in the United States under the Manhattan project to create nuclear weapons. John von Neumann first proposed to use the computers to generate random numbers. In 1949, John von Neumann and Stanislaw Ulam proposed the first algorithm generating pseudo-random values, which was subsequently named MMC and was the basis for the development of the technique of generating pseudo-random numbers using a computer. The development of MMC and the effectiveness of its application always begins with the development of random or pseudo-random numbers, which depends on the class of tasks and the specific structure and architecture of computers. Methods Monte Carlo began to apply on all architectures of computing systems with parallel and distributed computing. Now in the era of superficially dominated by MMC as a result of the simplicity of their implementation. But this simplicity is deceptive. Developed a complex methodological approach on the example of three complicated big problems describing spatially inhomogeneous kinetic processes of diffusion, coagulation, and migration of charged particles, systematically discusses the theory of methods and algorithms for MMC and practice implementing them in the format of not just programs, as well as the parallel random number generators, libraries, data processing, control programs, etc., i.e., all the stages of creating a "digital product". For example, probabilistic models for numerical simulation of the kinetic processes of diffusion, coagulation, and migration of charged particles when the ensembles of trajectories or particles contain 10 in 7-13 degrees of elements, and demonstrated the potential and effectiveness of the MMC to resolve big and complex tasks not only for the calculation of particular functionals or estimates, but for the whole phase volume of the task. This is the most important achievement that increases MMC's competitiveness with the deterministic finite-difference and grid methods for parallel simulation.
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Kumar, Anand. "Isotropic finite-differences." Journal of Computational Physics 201, no. 1 (November 2004): 109–18. http://dx.doi.org/10.1016/j.jcp.2004.05.005.
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White, Chelsea C., and Hany K. El-Deib. "Parameter Imprecision in Finite State, Finite Action Dynamic Programs." Operations Research 34, no. 1 (February 1986): 120–29. http://dx.doi.org/10.1287/opre.34.1.120.
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Zhang, Wenqiang, Zhenguo Zhang, Mengyang Li, and Xiaofei Chen. "GPU implementation of curved-grid finite-difference modelling for non-planar rupture dynamics." Geophysical Journal International 222, no. 3 (June 13, 2020): 2121–35. http://dx.doi.org/10.1093/gji/ggaa290.
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SUMMARY A deep understanding of earthquake physics requires a large amount of numerical simulations on seismic wave propagation and dynamic rupture. However, the corresponding intensive computational expense of simulations at traditional CPU (central processing unit) platforms make related researches time-consuming. There are many mature graphics processing unit (GPU) programs that can dramatically accelerate the calculation of seismic wave propagation. Unfortunately, there are few discussions about GPU implementations for rupture dynamics. In this work, we extend our 3-D curved-grid finite-difference method (CG-FDM) for rupture dynamics to the GPU platform using the CUDA (compute unified device architecture) programming language. By taking advantage of the new features of the NVIDIA Volta architecture, we implement the GPU-based program for rupture dynamics that is not only efficient but also easy to maintain. The GPU-based CG-FDM program is two orders of magnitude faster than our previous serial CPU-based program and still has a considerable advantage compared with the parallel one. The reliability and correctness of the program are carefully examined by the comparisons of the benchmarks from the ‘Southern California Earthquake Center/U.S. Geological Survey (SCEC/USGS) Dynamic Earthquake Rupture Code Verification Exercise’. The performance improvements of the GPU-based CG-FDM can save a lot of computing time, allowing researchers to perform much more numerical simulations of rupture dynamics to reveal more details of earthquake physics.
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Chen, E. Jack. "Derivative Estimation with Finite Differences." SIMULATION 79, no. 10 (October 2003): 598–609. http://dx.doi.org/10.1177/0037549703039951.
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O'Leary, D. P. "Finite Differences and Finite Elements: Getting to Know You." Computing in Science and Engineering 7, no. 3 (May 2005): 72–79. http://dx.doi.org/10.1109/mcse.2005.49.
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Fleck, M. M. "Multiple widths yield reliable finite differences (computer vision)." IEEE Transactions on Pattern Analysis and Machine Intelligence 14, no. 4 (April 1992): 412–29. http://dx.doi.org/10.1109/34.126804.
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Kikuchi, Noboru. "Finite element programs for axisymmetric problems in engineering." Finite Elements in Analysis and Design 2, no. 3 (October 1986): 327. http://dx.doi.org/10.1016/0168-874x(86)90032-6.
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