Relevant bibliographies by topics / Poisson's equation

Academic literature on the topic 'Poisson's equation'

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Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Poisson's equation"

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Khairi, Fathul, and Malahayati. "Penerapan Fungsi Green dari Persamaan Poisson pada Elektrostatika." Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education 1, no. 1 (April 30, 2021): 56–79. http://dx.doi.org/10.14421/quadratic.2021.011-08.

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The Dirac delta function is a function that mathematically does not meet the criteria as a function, this is because the function has an infinite value at a point. However, in physics the Dirac Delta function is an important construction, one of which is in constructing the Green function. This research constructs the Green function by utilizing the Dirac Delta function and Green identity. Furthermore, the construction is directed at the Green function of the Poisson's equation which is equipped with the Dirichlet boundary condition. After the form of the Green function solution from the Poisson's equation is obtained, the Green function is determined by means of the expansion of the eigen functions in the Poisson's equation. These results are used to analyze the application of the Poisson equation in electrostatic.
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Laugesen, Richard S., Prashant G. Mehta, Sean P. Meyn, and Maxim Raginsky. "Poisson's Equation in Nonlinear Filtering." SIAM Journal on Control and Optimization 53, no. 1 (January 2015): 501–25. http://dx.doi.org/10.1137/13094743x.

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Fox, Bennett L., and Paul Glasserman. "Estimating Derivatives Via Poisson's Equation." Probability in the Engineering and Informational Sciences 5, no. 4 (October 1991): 415–28. http://dx.doi.org/10.1017/s0269964800002205.

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Let x(j) be the expected reward accumulated up to hitting an absorbing set in a Markov chain, starting from state j. Suppose the transition probabilities and the one-step reward function depend on a parameter, and denote by y(j) the derivative of x(j) with respect to that parameter. We estimate y(0) starting from the respective Poisson equations that x = [x(0),x(l),…] and y = [y(0),y(l),…] satisfy. Relative to a likelihood-ratio-method (LRM) estimator, our estimator generally has (much) smaller variance; in a certain sense, it is a conditional expectation of that estimator given x. Unlike LRM, however, we have to estimate certain components of x. Our method has broader scope than LRM: we can estimate sensitivity to opening arcs.
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Chicone, C., and B. Mashhoon. "Nonlocal gravity: Modified Poisson's equation." Journal of Mathematical Physics 53, no. 4 (April 2012): 042501. http://dx.doi.org/10.1063/1.3702449.

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Zhou, Yecheng, and Angus Gray-Weale. "A numerical model for charge transport and energy conversion of perovskite solar cells." Physical Chemistry Chemical Physics 18, no. 6 (2016): 4476–86. http://dx.doi.org/10.1039/c5cp05371d.

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Taufer, Jiří, and Emil Vitásek. "Transfer of boundary conditions for Poisson's equation on a circle." Applications of Mathematics 39, no. 1 (1994): 15–23. http://dx.doi.org/10.21136/am.1994.134240.

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Hanley, Mary. "Existence of Solutions to Poisson's Equation." Canadian Mathematical Bulletin 51, no. 2 (June 1, 2008): 229–35. http://dx.doi.org/10.4153/cmb-2008-024-8.

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AbstractLet Ω be a domain in ℝn (n ≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasure μ on ℝn, there is a function u with specified boundary conditions that satisfies the Poisson equation Δu = μ on Δ in the sense of distributions.
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Berg, M. van den, and D. Bucur. "Sign changing solutions of Poisson's equation." Proceedings of the London Mathematical Society 121, no. 3 (April 29, 2020): 513–36. http://dx.doi.org/10.1112/plms.12334.

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Chalupka, Slavko, Jaroslava Sisákova, and Eva Vargová. "Boundary perturbation formalism for Poisson's equation." Studia Geophysica et Geodaetica 36, no. 4 (December 1992): 325–28. http://dx.doi.org/10.1007/bf01625485.

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Nicholson, D. M. C., and W. A. Shelton. "Removed sphere method for Poisson's equation." Journal of Physics: Condensed Matter 14, no. 22 (May 24, 2002): 5601–8. http://dx.doi.org/10.1088/0953-8984/14/22/312.

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Dissertations / Theses on the topic "Poisson's equation"

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Xie, Wenzheng. "A sharp inequality for Poisson's equation in arbitrary domains and its applications to Burgers' equation." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/31859.

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Let Ω be an arbitrary open set in IR³. Let || • || denote the L²(Ω) norm, and let [formula omitted] denote the completion of [formula omitted] in the Dirichlet norm || ∇•||. The pointwise bound [forumula omitted] is established for all functions [formula omitted] with Δ u є L² (Ω). The constant [formula omitted] is shown to be the best possible. Previously, inequalities of this type were proven only for bounded smooth domains or convex domains, with constants depending on the regularity of the boundary. A new method is employed to obtain this sharp inequality. The key idea is to estimate the maximum value of the quotient ⃒u(x)⃒/ || ∇u || ½ || Δ u || ½, where the point x is fixed, and the function u varies in the span of a finite number of eigenfunctions of the Laplacian. This method admits generalizations to other elliptic operators and other domains. The inequality is applied to study the initial-boundary value problem for Burgers' equation: [formula omitted] in arbitrary domains, with initial data in [formula omitted]. New a priori estimates are obtained. Adapting and refining known theory for Navier-Stokes equations, the existence and uniqueness of bounded smooth solutions are established. As corollaries of the inequality and its proof, pointwise bounds are given for eigenfunctions of the Laplacian in terms of the corresponding eigenvalues in two- and three-dimensional domains.
Science, Faculty of
Mathematics, Department of
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Nystrand, Thomas. "Summation By Part Methods for Poisson's Equation with Discontinuous Variable Coefficients." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-235418.

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Nowadays there is an ever increasing demand to obtain more accurate numericalsimulation results while at the same time using fewer computations. One area withsuch a demand is oil reservoir simulations, which builds upon Poisson's equation withvariable coefficients (PEWVC). This thesis focuses on applying and testing a high ordernumerical scheme to solve the PEWVC, namely Summation By Parts - SimultaneousApproximation Term (SBP-SAT). The thesis opens with proving that the method isconvergent at arbitrary high orders given sufficiently smooth coefficients. Theconvergence is furthermore verified in practice by test cases on the Poisson'sequation with smoothly variable permeability coefficients. To balance observed lowerboundary flux convergence, the SBP-SAT method was modified with additionalpenalty terms that were subsequently shown to work as expected. Finally theSBP-SAT method was tested on a semi-realistic model of an oil reservoir withdiscontinuous permeability. The correctness of the resulting pressure distributionvaried and it was shown that flux leakage was the probable cause. Hence theproposed SBP-SAT method performs, as expected, very well in continuous settingsbut typically allows undesirable leakage in discontinuous settings. There are possiblefixes, but these are outside the scope of this thesis.
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Moussa, Jonathan Edward. "The Schroedinger-Poisson selfconsistency in layered quantum semiconductor structures." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-1124103-230904/.

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Mayboroda, Svitlana. "The poisson problem on Lipschitz domains." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4133.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2005.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (January 25, 2007) Vita. Includes bibliographical references.
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Garcia, Hilares Nilton Alan. "A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/94618.

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As finite element discretizations ever grow in size to address real-world problems, there is an increasing need for fast algorithms. Nowadays there are many GPU/CPU parallel approaches to solve such problems. Multigrid methods can be used to solve large-scale problems, or even better they can be used to precondition the conjugate gradient method, yielding better results in general. Capabilities of multigrid algorithms rely on the effectiveness of the inter-grid transfer operators. In this thesis we focus on the aggregation approach, discussing how different aggregation strategies affect the convergence rate. Based on these discussions, we propose an alternative parallel aggregation algorithm to improve convergence. We also provide numerous experimental results that compare different aggregation approaches, multigrid methods, and conjugate gradient iteration counts, showing that our proposed algorithm performs better in serial and parallel.
Modeling real-world problems incurs a high computational cost because these mathematical models involve large-scale data manipulation. Thus we need fast and efficient algorithms. Nowadays there are many high-performance approaches for these problems. One such method is called the Multigrid algorithm. This approach models a physical domain using a hierarchy of grids, and so the effectiveness of these approaches relies on how well data can be transferred from grid to grid. In this thesis, we focus on the aggregation approach, which clusters a grid’s vertices according to its connections. We also provide an alternative parallel aggregation algorithm to give a faster solution. We show numerous experimental results that compare different aggregation approaches and multigrid methods, showing that our proposed algorithm performs better in serial and parallel than other popular implementations.
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Geng, Weihua. "Interface method and Green's function based Poisson Boltzmann equation solver and interface technique based molecular dynamics." Diss., Connect to online resource - MSU authorized users, 2008.

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Pilorget, Marc. "Development of a dynamic calculation tool forsimulation of ditching." Thesis, KTH, Lättkonstruktioner, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-31695.

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The present document is the final master thesis report written by Marc PILORGET,student at SUPAERO (home institution) and KTH (Royal Institute of Technology,Exchange University). This six months internship was done at DASSAULT AVIATION(Airframe engineering department) based in Saint-Cloud, France. It spanned from the 5thof July to the 23rd of December. The thesis work aims at developing an SPH (SmoothParticle Hydrodynamics) calculation method for ditching and implementing it in the finiteelement software ELFINI® developed by DASSAULT. Ditching corresponds to a phasewhen the aeroplane is touching the water. The problematic of ditching has always beenan area of interest for DASSAULT and the whole aeronautical industry. So far, only testsand simple analytical calculations have been performed. Most of the work was carried bythe NACA (National Advisory Committee for Aeronautics) in the late 70's. However in thepast decade, a new method for fluid-structure coupling problems has been developed. Itis called SPH. The basic principle is the following: the domain is represented by means ofparticles and each particle of fluid is treated separately and submitted to the Navier-Stokes equations. The particle is influenced by the neighbouring particles with a weightfunction depending on the distance between the two particles. Particles are also placed atthe interface solid-fluid: they are called limit particles. The final purpose of this SPHmethod is to access to the structural response of an aircraft when ditching. The crucialinterest of such a method compared to methods used so far is the absence of mesh. Theanalysis of large deformation problems by the finite element method may require thecontinuous remeshing of the domain to avoid the breakdown of the calculation due toexcessive mesh distortion. When considering ditching or other large deformationsproblems, the mesh generation is a far more time-consuming task than the constructionand solution of a discrete set of equations. For DASSAULT-AVIATION, the long termobjective is to get a numerical tool able to model ditching. The SPH method is used tosolve the equations for the fluid and is coupled with a finite element method for thestructure. So far, the compressible solver for 2D geometries has been implemented.Tests are going to be performed to ensure the program’s robustness. Then theincompressible solver for 2D geometries will be studied both theoretically andnumerically.
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Brenčys, Liutauras. "Puasono lygties sprendimas naudojantis šaltinio apibendrintomis hiperbolinės funkcijomis." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110804_100133-71588.

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Sudarytas Puasono lygties sprendimo per „rutuliukų“ potencialus algoritmas. Šiuo metodu Puasono lygties sprendimo uždavinys suvedamas į tiesinių algebrinių lygčių sistemos sprendimą. Sudaryta ir išbandyta matematiniu paketu MATHCAD to sprendimo programa. Palyginti gauti sprendiniai su tais, kurie gaunami analiziškai, įvertintas gautų sprendinių tikslumas. Šį sprendimo būdą galima panaudoti realiems fizikiniams potencialams paskaičiuoti, turint galvoje realų potencialą su kuriuo realūs krūviai.
It consists of Poisson equation solution in the "ball" potential algorithm. In this method the Poisson equation, the decision problem are reduced to linear algebraic equations system solution. Created and tested a mathematical package MATHCAD program for that decision. Compared to solutions with those obtained analytically, estimated to obtain accurate solutions. This solution can be used to calculate the real physical potentials, given the real potential of the real workloads.
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Kåhlman, Niklas. "Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84777.

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In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.
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Hoyles, Matthew, and Matthew Hoyles@anu edu au. "Computer Simulation of Biological Ion Channels." The Australian National University. Theoretical Physics, 2000. http://thesis.anu.edu.au./public/adt-ANU20010702.135814.

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This thesis describes a project in which algorithms are developed for the rapid and accurate solution of Poisson's equation in the presence of a dielectric boundary and multiple point charges. These algorithms are then used to perform Brownian dynamics simulations on realistic models of biological ion channels. An iterative method of solution, in which the dielectric boundary is tiled with variable sized surface charge sectors, provides the flexibility to deal with arbitrarily shaped boundaries, but is too slow to perform Brownian dynamics. An analytical solution is derived, which is faster and more accurate, but only works for a toroidal boundary. Finally, a method is developed of pre-calculating solutions to Poisson's equation and storing them in tables. The solution for a particular configuration of ions in the channel can then be assembled by interpolation from the tables and application of the principle of superposition. This algorithm combines the flexibility of the iterative method with greater speed even than the analytical method, and is fast enough that channel conductance can be predicted. The results of simulations for a model single-ion channel, based on the acetylcholine receptor channel, show that the narrow pore through the low dielectric strength medium of the protein creates an energy barrier which restricts the permeation of ions. They further show that this barrier can be removed by dipoles in the neck of the channel, but that the barrier is not removed by shielding by counter-ions. The results of simulations for a model multi-ion channel, based on a bacterial potassium channel, show that the model channel has conductance characteristics similar to those of real potassium channels. Ions appear to move through the model multi-ion channel via rapid transitions between a series of semi-stable states. This observation suggests a possible physical basis for the reaction rate theory of channel conductance, and opens up an avenue for future research.
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Books on the topic "Poisson's equation"

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B, Palʹ͡tsev A., ed. Metody resheni͡ia uravneni͡ia Puassona v oblast͡iakh s uzkoĭ shchelʹ͡iu. Moskva: Vychislitelʹnyĭ ͡tsentr RAN, 1992.

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Soh, Woo Y. Direct coupling methods for time-accurate solution of incompressible Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1992.

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United States. National Aeronautics and Space Administration., ed. Direct coupling methods for time-accurate solution of incompressible Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1992.

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Akademi͡ia nauk SSSR. Vychislitelʹnyĭ ͡tsentr, ed. Metody resheni͡ia kraevykh zadach i asimptotiki resheniĭ pri singul͡iarnom deformirovanii oblasti. Moskva: Vychislitelʹnyĭ ͡tsentr AN SSSR, 1988.

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Korotkov, D. ͡IU. Metody priblizhennoĭ faktoriza͡tsii dl͡ia resheni͡ia uravneniĭ ėllipticheskogo tipa. Moskva: Vychislitelʹnyĭ ͡tsentr AN SSSR, 1989.

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Ponce, Augusto C. Elliptic PDEs, measures and capacities: From the Poisson equation to nonlinear Thomas-Fermi problems. Zürich: European Mathematical Society, 2016.

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Sorenson, Reese L. Three-dimensional zonal grids about arbitrary shapes by Poisson's equation. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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Sorenson, Reese L. Three-dimensional zonal grids about arbitrary shapes by Poisson's equation. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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Cooke, J. Robert. MacPoisson: Finite element analysis and Poisson's equation with the Macintosh. Ithaca, NY (P.O. Box 4448, Ithaca 14852): Cooke Publications, 1987.

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Center, Ames Research, ed. Three-dimensional zonal grids about arbitrary shapes by Poisson's equation. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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Book chapters on the topic "Poisson's equation"

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Sleeman, Brian D. "Partial Differential Equations, Poisson Equation." In Encyclopedia of Systems Biology, 1635–38. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_274.

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Selvadurai, A. P. S. "Poisson’s equation." In Partial Differential Equations in Mechanics 2, 503–647. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-09205-7_2.

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Zhu, Yichao. "Poisson’s Equation." In Equations and Analytical Tools in Mathematical Physics, 99–139. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5441-1_3.

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Zhu, Yichao. "Poisson’s Equation." In Equations and Analytical Tools in Mathematical Physics, 99–139. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5441-1_3.

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Parker, David F. "Laplace’s Equation and Poisson’s Equation." In Springer Undergraduate Mathematics Series, 55–76. London: Springer London, 2003. http://dx.doi.org/10.1007/978-1-4471-0019-5_4.

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Hong, Sung-Min, Anh-Tuan Pham, and Christoph Jungemann. "Poisson Equation." In Computational Microelectronics, 175–76. Vienna: Springer Vienna, 2011. http://dx.doi.org/10.1007/978-3-7091-0778-2_10.

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Wartak, Marek S. "Poisson Equation." In Introduction to Simulations of Semiconductor Lasers, 94–121. Boca Raton: CRC Press, 2024. http://dx.doi.org/10.1201/9781003265849-6.

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Hernández-Lerma, Onésimo, and Jean Bernard Lasserre. "Ergodicity and Poisson’s Equation." In Further Topics on Discrete-Time Markov Control Processes, 1–38. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0561-6_1.

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Curry, Joan E. "Poisson-Boltzmann Equation." In Encyclopedia of Earth Sciences Series, 1–2. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39193-9_15-1.

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Curry, Joan E. "Poisson-Boltzmann Equation." In Encyclopedia of Earth Sciences Series, 1240–41. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-39312-4_15.

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Conference papers on the topic "Poisson's equation"

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Laugesen, Richard, Prashant G. Mehta, Sean P. Meyn, and Maxim Raginsky. "Poisson's equation in nonlinear filtering." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7040041.

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Logg, Anders, Carl Lundholm, and Magne Nordaas. "Solving Poisson's equation on the Microsoft HoloLens." In VRST '17: 23rd ACM Symposium on Virtual Reality Software and Technology. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3139131.3141777.

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Quraishi, S. M., and K. Sandeep. "A wavelet based approach for solving Poisson's equation." In 2009 International Conference on Emerging Trends in Electronic and Photonic Devices & Systems (ELECTRO-2009). IEEE, 2009. http://dx.doi.org/10.1109/electro.2009.5441075.

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Alotto, P., and F. Freschi. "A Second order Cell Method for Poisson's equation." In 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2010). IEEE, 2010. http://dx.doi.org/10.1109/cefc.2010.5481645.

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Alsalti-Baldellou, Àdel, Carlo Janna, Xavier Álvarez-Farré, and F. Xavier Trias. "Exploiting symmetries for preconditioning Poisson's equation in CFD simulations." In PASC '23: Platform for Advanced Scientific Computing Conference. New York, NY, USA: ACM, 2023. http://dx.doi.org/10.1145/3592979.3593410.

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Murray, Nathan, Lawrence Ukeiley, and Richard Raspet. "Calculating Surface Pressure Fluctuations from PIV Data Using Poisson's Equation." In 45th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-1306.

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Hélvio de Farias Costa Peixoto and Rodrigo Bird Burgos. "Direct Solution of 2D Poisson's Equation Using Wavelet Scaling Functions." In 23rd ABCM International Congress of Mechanical Engineering. Rio de Janeiro, Brazil: ABCM Brazilian Society of Mechanical Sciences and Engineering, 2015. http://dx.doi.org/10.20906/cps/cob-2015-2160.

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Tang, Wei, Tao Shan, Xunwang Dang, Maokun Li, Fan Yang, Shenheng Xu, and Ji Wu. "Study on a Poisson's equation solver based on deep learning technique." In 2017 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS). IEEE, 2017. http://dx.doi.org/10.1109/edaps.2017.8277017.

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Bozkaplan, Buse, Pelin Keskin Şen, and Berra Gültekin Sınır. "The Critical Velocity and Post-Buckling Behavior of Axially Moving Beams with Poisson’s Ratio." In 6th International Students Science Congress. Izmir International Guest Student Association, 2022. http://dx.doi.org/10.52460/issc.2022.017.

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In this study, the critical velocity of axially moving beams is calculated and the post-buckling behaviors of beams are investigated. The governing equation of the axially moving beam problem is obtained by using vector approach. This approach is also known as Newton’s second law method. The obtained equations depend on normal force, shear force and moment. The opposite side of the equation depends on the acceleration since the dynamic analysis is done. Using Hook’s law, the normal forces and the moment are rewritten in displacement form, then the governing equation is obtained in displacement form. The dimensionless form of the resulting equation is as obtained. It is solved to provide simple-simple support conditions. Thus, the critical velocity value and the post-buckling graph are obtained depending on the displacement. As a result of these analyzes; the effects of the Poisson ratio on critical velocity and post-buckling behavior are observed. The effect of Poisson's ratio on critical velocity and post-buckling effect in axial moving beam problems are revealed.
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Zhu, Wenxing, Zhipeng Huang, Jianli Chen, and Yao-Wen Chang. "Analytical solution of Poisson's equation and its application to VLSI global placement." In ICCAD '18: IEEE/ACM INTERNATIONAL CONFERENCE ON COMPUTER-AIDED DESIGN. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3240765.3240779.

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Reports on the topic "Poisson's equation"

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Glynn, Peter W. A Lyapunov Bound for Solutions of Poisson's Equation. Fort Belvoir, VA: Defense Technical Information Center, November 1989. http://dx.doi.org/10.21236/ada220223.

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Batygin, Yuri K. Spectral Method for 3-dimensional Poisson's Equation in Cylindrical Coordinates with Regular Boundaries. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/784945.

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Kavouklis, C. A 6th Order Mehrstellen Finite Volume Discretization of Poisson's Equation in Three Dimensions. Office of Scientific and Technical Information (OSTI), February 2022. http://dx.doi.org/10.2172/1844490.

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Bergmann, D. A comparison of conjugate gradient, SIP, and other iterative methods for the solution of Poisson's equation with irregular boundary conditions. Office of Scientific and Technical Information (OSTI), June 1990. http://dx.doi.org/10.2172/6686014.

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Lasater, M. S., C. T. Kelley, A. G. Salinger, D. L. Woolard, and P. Zhao. Solution of the Wigner-Poisson Equations for RTDs. Fort Belvoir, VA: Defense Technical Information Center, January 2004. http://dx.doi.org/10.21236/ada446723.

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Day, Marcus S., Phillip Colella, Michael J. Lijewski, Charles A. Rendleman, and Daniel L. Marcus. Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains. Office of Scientific and Technical Information (OSTI), May 1998. http://dx.doi.org/10.2172/771633.

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Chao, E. H., S. F. Paul, R. C. Davidson, and K. S. Fine. Direct numerical solution of Poisson`s equation in cylindrical (r, z) coordinates. Office of Scientific and Technical Information (OSTI), July 1997. http://dx.doi.org/10.2172/304205.

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Johansen, H., and P. Colella. A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains. Office of Scientific and Technical Information (OSTI), January 1997. http://dx.doi.org/10.2172/459443.

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W.W. Lee and R.A. Kolesnikov. On Higher-order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit. Office of Scientific and Technical Information (OSTI), February 2009. http://dx.doi.org/10.2172/950698.

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Babuska, I., T. Strouboulis, C. S. Upadhyay, and S. K. Gangaraj. Study of Superconvergence by a Computer-Based Approach. Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada277537.

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