Relevant bibliographies by topics / The symplectic Euler method

Contents

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

Academic literature on the topic 'The symplectic Euler method'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "The symplectic Euler method"

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Fu, Fangfang. "Symplectic Euler Method for Nonlinear High Order Schrödinger Equation with a Trapped Term." Advances in Applied Mathematics and Mechanics 1, no. 5 (2009): 699–710. http://dx.doi.org/10.4208/aamm.09-m0929.

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Yang, Man, Hongyuan Fang, Fuming Wang, Yuke Wang, Xueming Du, and Jianwei Lei. "First-order symplectic Euler method for ground penetrating radar forward simulations in dispersive medium." Construction and Building Materials 299 (September 2021): 123904. http://dx.doi.org/10.1016/j.conbuildmat.2021.123904.

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Rivera, Jorge, Florentino Chavira, and Alexander Loukianov. "On the Discrete-Time Modeling of a DC-to-DC Power Converter and Control Design with Discrete-Time Sliding Modes." Mathematical Problems in Engineering 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/460281.

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This work presents a novel discrete-time modeling of a boost dc-to-dc power converter by means of the symplectic Euler method. Then, on the basis of this model, a discrete-time sliding mode regulator is designed in order to force the power converter to behave as a dc-to-ac power converter. Simulation and experimental results are carried on, where the great performance of the proposed methodology is verified.
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Fang, Hongyuan, Gao Lin, and Ruili Zhang. "The First-Order Symplectic Euler Method for Simulation of GPR Wave Propagation in Pavement Structure." IEEE Transactions on Geoscience and Remote Sensing 51, no. 1 (2013): 93–98. http://dx.doi.org/10.1109/tgrs.2012.2202121.

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Zhong Shuang-Ying and Wu Xin. "Comparison of second-order mixed symplectic integrator between semi-implicit Euler method and implicit midpoint rule." Acta Physica Sinica 60, no. 9 (2011): 090402. http://dx.doi.org/10.7498/aps.60.090402.

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Liu, Xuemei, and Zichen Deng. "Generalized Multi-Symplectic Numerical Implementation of Dynamic Responses for Saturated Poroelastic Timoshenko Beam." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 4 (2020): 774–83. http://dx.doi.org/10.1051/jnwpu/20203840774.

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Based on the porous media theory and Timoshenko beam theory, properties of dynamic responses in fluid-solid coupled incompressible saturated poroelastic Timoshenko beam are investigated by generalized multi-symplectic method. Dynamic response equation set of incompressible saturated poroelastic Timoshenko beam is presented at first. Then a first order generalized multi-symplectic form of this dynamic response equation set is constructed, and errors of generalized multi-symplectic conservation law, generalized multi-symplectic local momentum and generalized multi-symplectic local energy are also derived. A Preissmann Box generalized multi-symplectic scheme of the dynamic response equation set is presented, the discrete errors of generalized multi-symplectic conservation law, generalized multi-symplectic local momentum conservation law and generalized multi-symplectic local energy conservation law are also obtained. In view of the dynamic responses of incompressible saturated poroelastic Timoshenko cantilever beam with two ends permeable and free end subjected to the step load, the transverse dynamic response process of the solid skeleton is simulated numerically, the evolution processes of solid effective stress and the equivalent moment of the pore fluid pressure over time are also presented numerically. The effects of fluid-solid coupled interaction parameter and slenderness ratio of the beam on the solid dynamic response process are revealed, as well as the effects on all generalized multi-symplectic numerical errors are checked simultaneously. From results obtained, the processes for solid deflection, solid effective stress and the equivalent moment of the pore fluid pressure approaching to their steady response values are all shortened with increasing of fluid-solid coupled interaction parameter, while the response process of solid deflection and the pore fluid equivalent moment are lengthened with increasing of slenderness ratio of the beam. Moreover, the steady value of solid deflection is much closer to the static deflection value of classic single phase elastic Euler-Bernoulli beam with increasing of the slenderness ratio. As time goes on, the solid skeleton of the beam will support all outside load, so equivalent moment of the pore fluid pressure becomes zero at last. In addition, it is presented all generalized multi-symplectic numerical errors decrease with the decreasing of parameters representing the dissipation effect for the dynamic system.
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Yang, Dandan, Jianfei Huang, and Weijia Zhao. "A quasi-dynamic model and a symplectic algorithm of super slender Kirchhoff rod." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 03 (2017): 1750037. http://dx.doi.org/10.1142/s1793962317500374.

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Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA. The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff rod. In this paper, Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod, then a symplectic algorithm is applied in its numerical simulations. Finally, a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.
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Xu, Fangnuan, Zichen Deng, Bo Wang, Yi Wei, and Qingjun Li. "Dynamic Response of Solar Power Satellite Considering Solar Radiation Pressure." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 3 (2018): 590–96. http://dx.doi.org/10.1051/jnwpu/20183620590.

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The attitude and structural vibration of tethered solar power satellite were studied considering solar radiation pressure. Firstly, the simplified model of tethered solar power satellite was established. The solar panel was modeled as an Euler-Bernoulli Beam, the bus was modeled as a particle, and the tethers were modeled as massless springs. The equations of motion were derived based on absolute nodal coordinate formulation and Hamilton’s principle. Then, Symplectic Runge-Kutta method was adopted to solve the differential equations. The proposed model and numerical algorithm were validated through a numerical example. Finally, numerical simulations were carried out. Simulation results showed that solar radiation pressure as well as structural vibration cause small fluctuation of the attitude angle. Moreover, the effect of solar radiation pressure on structural vibration can be neglected.
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Mazzia, Francesca, and Alessandra Sestini. "On a Class of Conjugate Symplectic Hermite-Obreshkov One-Step Methods with Continuous Spline Extension." Axioms 7, no. 3 (2018): 58. http://dx.doi.org/10.3390/axioms7030058.

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The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by F. Loscalzo in 1968 for dealing with initial value problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic, which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore, a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss–Runge–Kutta schemes and Euler–Maclaurin formulas of the same order.
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Abarbanel, Henry D. I., Paul J. Rozdeba, and Sasha Shirman. "Machine Learning: Deepest Learning as Statistical Data Assimilation Problems." Neural Computation 30, no. 8 (2018): 2025–55. http://dx.doi.org/10.1162/neco_a_01094.

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We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in a feedforward artificial network setting is the analog of time in the data assimilation setting. This connection has been noted in the machine learning literature. We add a perspective that expands on how methods from statistical physics and aspects of Lagrangian and Hamiltonian dynamics play a role in how networks can be trained and designed. Within the discussion of this equivalence, we show that adding more layers (making the network deeper) is analogous to adding temporal resolution in a data assimilation framework. Extending this equivalence to recurrent networks is also discussed. We explore how one can find a candidate for the global minimum of the cost functions in the machine learning context using a method from data assimilation. Calculations on simple models from both sides of the equivalence are reported. Also discussed is a framework in which the time or layer label is taken to be continuous, providing a differential equation, the Euler-Lagrange equation and its boundary conditions, as a necessary condition for a minimum of the cost function. This shows that the problem being solved is a two-point boundary value problem familiar in the discussion of variational methods. The use of continuous layers is denoted “deepest learning.” These problems respect a symplectic symmetry in continuous layer phase space. Both Lagrangian versions and Hamiltonian versions of these problems are presented. Their well-studied implementation in a discrete time/layer, while respecting the symplectic structure, is addressed. The Hamiltonian version provides a direct rationale for backpropagation as a solution method for a certain two-point boundary value problem.
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Dissertations / Theses on the topic "The symplectic Euler method"

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Böjeryd, Jesper. "Long Time Integration of Molecular Dynamics at Constant Temperature with the Symplectic Euler Method." Thesis, KTH, Numerisk analys, NA, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-165324.

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Simulations of particle systems at constant temperature may be used to estimate several of the system’s physical properties, and some require integration over very long time to be accurate. To achieve sufficient accuracy in finite time the choice of numerical scheme is important and we suggest to use the symplectic Euler method combined with a step in an Ornstein-Uhlenbeck process. This scheme is computationally very cheap and is often used in applications of molecular dynamics. This thesis strives to motivate the usage of the scheme due to the lack of theoretical results and comparisons to alternative methods. We conduct three numerical experiments to evaluate the scheme. The design of each experiment aims to expose weaknesses or strengths of the method. For both model problems and more realistic experiments are the results positive in favor of the method; the symplectic Euler method combined with an Ornstein- Uhlenbeck step does perform well over long times.<br>Simuleringar av partikelsystem vid konstant temperatur kan användas för att uppskatta flera av systemets fysiska egenskaper. Vissa klasser av egenskaper kräver integration över väldigt lång tid för att uppnå hög noggrannhet och för att uppnå detta i ändlig tid är valet av numerisk metod viktigt. Vi föreslår att använda den symplektiska Euler-metoden i kombination med ett implicit steg i en Ornstein-Uhlenbeck-process. Detta stegschema kräver låg beräkning jämfört med andra scheman och används redan i olika applikationer av molekyldynamik. Detta examensarbete eftersträvar att än mer motivera användandet av schemat, eftersom teoretiska resultat som stödjer metoder är få, och avsaknaden av tidigare liknande studier är betydlig. Vi genomför tre numeriska experiment för att pröva schemat. Under utformningen av experimenten har vi försökt att inkorporera olika fenomen som kan orsaka svårigheter för metoden för att exponera svagheter eller styrkor hos den. För båda modellproblem och för ett mer realistiskt experiment är resultaten positiva till schemats fördel; metoden att kombinera ett symplektisk Euler-steg med ett steg i Ornstein-Uhlenbeck-processen presterar bra över lång tid.
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Tam, Laying. "The general Euler-Borel summability method /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683756124139.

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Benner, P., and H. Faßbender. "A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800797.

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A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem is presented. The Lanczos vectors are constructed to form a symplectic basis. Breakdowns and near-breakdowns are overcome by inexpensive implicit restarts. The method is used to compute eigenvalues, eigenvectors and invariant subspaces of large and sparse Hamiltonian matrices and low rank approximations to the solution of continuous-time algebraic Riccati equations with large and sparse coefficient matrices.
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Yildirim, B. Gazi. "A global preconditioning method for the Euler equations." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-07152003-164237.

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毛生根 and Shenggen Mao. "Symplectic analysis of flexible structures by finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B3123754X.

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Mao, Shenggen. "Symplectic analysis of flexible structures by finite elements /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19471154.

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Choi, Sang Keun. "A Cartesian finite-volume method for the Euler equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/76511.

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A numerical procedure has been developed for the computation of inviscid flows over arbitrary, complex two-dimensional geometries. The Euler equations are solved using a finite-volume method with a non-body-fitted Cartesian grid. A new numerical formulation for complicated body geometries is developed in conjunction with implicit flux-splitting schemes. A variety of numerical computations have been performed to validate the numerical methodologies developed. Computations for supersonic flow over a flat plate with an impinging shock wave are used to verify the numerical algorithm, without geometric considerations. The supersonic flow over a blunt body is utilized to show the accuracy of the non-body-fitted Cartesian grid, along with the shock resolution of flux-vector splitting scheme. Geometric complexities are illustrated with the flow through a two-dimensional supersonic inlet with and without an open bleed door. The ability of the method to deal with subsonic and transonic flows is illustrated by computations over a non-lifting NACA 0012 airfoil. The method is shown to be accurate, efficient and robust and should prove to be particularly useful in a preliminary design mode, where flows past a wide variety of complex geometries can be computed without complicated grid generation procedures.<br>Ph. D.
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Zimmermann, Susanne A. "Properties of the method of transport for the Euler equations /." [S.l.] : [s.n.], 2001. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13957.

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Nazarov, Murtazo. "An adaptive finite element method for the compressible Euler Equations /." Licentiate thesis, Stockholm : Skolan för datavetenskap och kommunikation, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10582.

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Brock, Jerry S. "A consistent direct-iterative inverse design method for the Euler equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40033.

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A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods.<br>Ph. D.
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Books on the topic "The symplectic Euler method"

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Ta'asan, Shlomo. Canonical-variables multigrid method for steady-state Euler equations. Langley Research Center, 1994.

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Smith, Ralph C. Numerical recovery of material parameters in Euler-Bernoulli beam models. Institute for Computer Applications in Science and Engineering, 1991.

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Smith, Ralph C. A fully Sinc-Galerkin method for Euler-Bernoulli beam models. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1990.

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Smith, Ralph C. A fully Sinc-Galerkin method for Euler-Bernoulli beam models. Institute for Computer Applications in Science and Engineering, 1990.

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Cockburn, Bernardo. The Pl-RKDG method for two-dimensional Euler equations of gas dynamics. Institute for Computer Applications in Science and Engineering, 1991.

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Roberts, Thomas W. Solution method for a hovering helicopter rotor using the Euler equations. American Institute of Aeronautics and Astronautics, 1985.

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Iollo, Angelo. Pseudo-time method for optimal shape design using the Euler equations. Institute for Computer Applications in Science and Engineering, 1995.

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Dang, T. Q. An Euler correction method for two and three-dimensional transonic flows. AIAA, 1987.

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Iollo, Angelo. Shape optimization governed by the Euler equations using an adjoint method. Institute for Computer Applications in Science and Engineering, 1993.

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Manna, M. A three dimensional high resolution upwind finite volume Euler solver. Von Karman Institute for Fluid Dynamics, 1992.

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Book chapters on the topic "The symplectic Euler method"

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Hairer, Ernst, and Gerhard Wanner. "Euler Methods, Explicit, Implicit, Symplectic." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_111.

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Feng, Kang, and Mengzhao Qin. "The Generating Function Method." In Symplectic Geometric Algorithms for Hamiltonian Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-01777-3_6.

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Liao, Shijun. "Relationship to Euler Transform." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_5.

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Ta'asan, S. "Canonical-variables multigrid method for Euler equations." In Lecture Notes in Physics. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-59280-6_117.

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Ragnisco, O. "A Simple Method to Generate Integrable Symplectic Maps." In Solitons and Chaos. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84570-3_28.

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Oñate, Eugenio. "Slender Plane Beams. Euler-Bernoulli Theory." In Structural Analysis with the Finite Element Method Linear Statics. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-1-4020-8743-1_1.

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Farooq, M. Asif, and B. Müller. "Cartesian Grid Method for the Compressible Euler Equations." In Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_47.

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Haunschmied, Josef L., Alain Pietrus, and Vladimir M. Veliov. "The Euler Method for Linear Control Systems Revisited." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43880-0_9.

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Malagi, Keshav S., P. S. Kulkarni, and S. M. Deshpande. "A Multidimensional Kinetic Upwind Method for Euler Equations." In Computational Fluid Dynamics 2006. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-92779-2_28.

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Rajarajeswari, P., A. Ramamohanreddy, and D. Vasumathi. "Problem Solving Process for Euler Method by Using Object Oriented Design Method." In Advances in Intelligent Systems and Computing. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2731-1_20.

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Conference papers on the topic "The symplectic Euler method"

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ZHANG, Jing-Hua, and Xing-Xing ZHAO. "Dynamic Buckling of a FGM Euler-Bernoulli Beam under Thermal Shock via Symplectic Method." In 2014 International Conference on Mechanics and Civil Engineering (icmce-14). Atlantis Press, 2014. http://dx.doi.org/10.2991/icmce-14.2014.46.

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Hewlett, Joe, Laszlo Kovacs, Alfonso Callejo, Paul G. Kry, József Kövecses, and Jorge Angeles. "Adaptive Semi-Implicit Integrator for Articulated Rigid-Body Systems." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60370.

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This paper concerns the dynamic simulation of constrained rigid-body systems in the context of real-time applications and stable integrators. The goal is to adaptively find a balance between the stability of an over-damped implicit scheme and the energetic consistency of the symplectic, semi-implicit Euler scheme. As a starting point, we investigate in detail the properties of a new time stepping scheme proposed by Tournier et al., “Stable constrained dynamics”, ACM transactions on Graphics, 2015, which approximates a full non-linear implicit solution with a single linear system without compromising stability. This introduces a geometric stiffness term that improves numerical stability up to a certain time step size, at the cost of large mechanical dissipation compared to the traditional formulation. Dissipation is sometimes undesirable from a mechanical point of view, especially if the dissipation is not quantified. In this paper, we propose to use an additional control parameter to regulate how “implicit” the Jacobian matrix is, and change the degree to which the geometric stiffness term contributes. For the selection of this parameter, adaptive schemes will be proposed based on the monitoring of energy drift. The proposed adaptive method is verified through the simulation of chain-like systems.
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GUO, HAN-YING, JIANZHONG PAN, KE WU, and BIN ZHOU. "THE EULER-LAGRANGE COHOMOLOGY ON SYMPLECTIC MANIFOLDS." In Proceedings of a Satellite Conference to the International Congress of Mathematicians in Beijing 2002. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702500_0012.

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Wang, Yushun, Bin Wang, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Applications of the Multi-Symplectic Euler-box Scheme." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241629.

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Guo, Han-Ying. "Discrete variation, Euler-Lagrange cohomology and symplectic, multisymplectic structures." In NONEQUILIBRIUM AND NONLINEAR DYNAMICS IN NUCLEAR AND OTHER FINITE SYSTEMS:International Conference. AIP, 2001. http://dx.doi.org/10.1063/1.1427487.

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Vucheva, V., and N. Kolkovska. "A symplectic numerical method for Boussinesq equation." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’18. Author(s), 2018. http://dx.doi.org/10.1063/1.5064941.

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Gao, Q., H. W. Zhang, W. X. Zhong, et al. "Symplectic Method Based on Dual Variable Principle." In PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL MECHANICS AND THE 12TH INTERNATIONAL CONFERENCE ON THE ENHANCEMENT AND PROMOTION OF COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE. AIP, 2010. http://dx.doi.org/10.1063/1.3452292.

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Bian, Wenfenga, Baoxian Jia, and Biao Wang. "The symplectic method of electric and elastic problems." In International Conference on Smart Materials and Nanotechnology in Engineering. SPIE, 2007. http://dx.doi.org/10.1117/12.780279.

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Monovasilis, Th, Z. Kalogiratou, T. E. Simos, et al. "A Trigonometrically Fitted Symplectic Runge-Kutta-Nyström Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637002.

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Khoshnoud, Farbod, Houman Owhadi, and Clarence W. de Silva. "Stochastic Simulation of a Casimir Oscillator." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39746.

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Stochastic simulation of a Casimir Oscillator is presented in this paper. This oscillator is composed of a flat boundary of semiconducting oscillator parallel to a fixed plate separated by vacuum. In this system the oscillating surface is attracted to the fixed plate by the Casimir effect, due to quantum fluctuations in the zero point electromagnetic field. Motion of the oscillating boundary is opposed by a spring. The stored potential energy in the spring is converted into kinetic energy when the spring force exceeds the Casimir force, which generates an oscillatory motion of the moving plate. Casimir Oscillators are used as micro-mechanical switches, sensors and actuators. In the present paper, a stochastic simulation of a Casimir oscillator is presented for the first time. In this simulation, Stochastic Variational Integrators using a Langevin equation, which describes Brownian motion, is considered. Formulations for Symplectic Euler, Constrained Symplectic Euler, Stormer-Verlet and RATTLE integrators are obtained and the Symplectic Euler case is solved numerically. When the moving parts in a micro/nano system travel in the vicinity of 10 nanometers to 1 micrometer range relative to other parts of the system, the Casimir phenomenon is in effect and should be considered in analysis and design of such system. The simulation in this paper considers modeling such uncertainties as friction, effect of surface roughness on the Casimir force, and change in environmental conditions such as ambient temperature. In this manner the paper explores a realistic model of the Casimir Oscillator. Furthermore, the presented study of this system provides a deeper understanding of the nature of the Casimir force.
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Reports on the topic "The symplectic Euler method"

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Friedman, A. Partially-Corrected Euler Method for Solution of ODE's. Office of Scientific and Technical Information (OSTI), 2007. http://dx.doi.org/10.2172/922092.

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Yan, Yiton T. A General Method for Symplectic Particle Tracking in a Three-dimensional Magnetic Field. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/763836.

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Srinivasan, Ganapathi R. A Free-Wake Euler and Navier-Stokes CFD Method and its Application to Helicopter Rotors Including Dynamic Stall. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada278000.

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