Relevant bibliographies by topics / Poisson's equation Numerical solutions

Academic literature on the topic 'Poisson's equation Numerical solutions'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Poisson's equation Numerical solutions"

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ATKINSON, K. E. "The Numerical Evaluation of Particular Solutions for Poisson's Equation." IMA Journal of Numerical Analysis 5, no. 3 (1985): 319–38. http://dx.doi.org/10.1093/imanum/5.3.319.

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Sauer-Budge, A. M., J. Bonet, A. Huerta, and J. Peraire. "Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson's Equation." SIAM Journal on Numerical Analysis 42, no. 4 (January 2004): 1610–30. http://dx.doi.org/10.1137/s0036142903425045.

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Evans, D. J. "The numerical solution of poisson's equation in a rhombus." International Journal of Computer Mathematics 42, no. 3-4 (January 1992): 193–211. http://dx.doi.org/10.1080/00207169208804062.

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CHEN, C. S., C. S. HUANG, and K. H. LIN. "ON THE CONVERGENCE OF THE MFS–MPS SCHEME FOR 1D POISSON'S EQUATION." International Journal of Computational Methods 10, no. 02 (March 2013): 1341006. http://dx.doi.org/10.1142/s0219876213410065.

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The method of fundamental solutions (MFS) has been an effective meshless method for solving homogeneous partial differential equations. Coupled with radial basis functions (RBFs), the MFS has been extended to solve the inhomogeneous problems through the evaluation of the approximate particular solution and homogeneous solution. In this paper, we prove the the approximate solution of the above numerical process for solving 1D Poisson's equation converges in the sense of Lagrange interpolating polynomial using the result of Driscoll and Fornberg [2002].
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Ma, Zu-Hui, Weng Cho Chew, and Li Jun Jiang. "A Novel Efficient Numerical Solution of Poisson's Equation for Arbitrary Shapes in Two Dimensions." Communications in Computational Physics 20, no. 5 (November 2016): 1381–404. http://dx.doi.org/10.4208/cicp.230813.291113a.

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AbstractEven though there are various fast methods and preconditioning techniques available for the simulation of Poisson problems, little work has been done for solving Poisson's equation by using the Helmholtz decomposition scheme. To bridge this issue, we propose a novel efficient algorithm to solve Poisson's equation in irregular two dimensional domains for electrostatics through a quasi-Helmholtz decomposition technique—the loop-tree basis decomposition. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or inhomogeneous. A novel point of this method is to first find the electric flux efficiently by applying the loop-tree basis functions. Subsequently, the potential is obtained by finding the inverse of the gradient operator. Furthermore, treatments for both Dirichlet and Neumann boundary conditions are addressed. Finally, the validation and efficiency are illustrated by several numerical examples. Through these simulations, it is observed that the computational complexity of our proposed method almost scales as , where N is the triangle patch number of meshes. Consequently, this new algorithm is a feasible fast Poisson solver.
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Matsuura, T., S. Saitoh †, and D. D. Trong ‡. "Numerical solutions of the poisson equation." Applicable Analysis 83, no. 10 (October 2004): 1037–51. http://dx.doi.org/10.1080/00036810410001724616.

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Wu, C., and E. E. Kunhardt. "Numerical solution of Poisson's equation for rapidly varying driving functions." Journal of Computational Physics 84, no. 1 (September 1989): 247–54. http://dx.doi.org/10.1016/0021-9991(89)90190-3.

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Nakamura, Y., and I. Tsukabayashi. "Modified Korteweg—de Vries ion-acoustic solitons in a plasma." Journal of Plasma Physics 34, no. 3 (December 1985): 401–15. http://dx.doi.org/10.1017/s0022377800002968.

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Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.
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Abdallah, S., and C. F. Smith. "Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines." Journal of Turbomachinery 112, no. 3 (July 1, 1990): 391–98. http://dx.doi.org/10.1115/1.2927672.

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A primitive variable formulation is used for the solution of the incompressible Euler equation. In particular, the pressure Poisson equation approach using a nonstaggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a nonstaggered grid. Numerical solutions of the momentum equations are obtained using the second-order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive overrelaxation method. Three turbo-machinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.
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Caspi, S., M. Helm, and L. J. Laslett. "Numerical Solution of Boundary Condition to Poisson's Equation and Its Incorporation into the Program Poisson." IEEE Transactions on Nuclear Science 32, no. 5 (October 1985): 3722–24. http://dx.doi.org/10.1109/tns.1985.4334481.

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

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Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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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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Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-215378.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Different bin resolutions and time steps are investigated. As expected, the results become better with increasing bin resolution. LDM and BSM do not show the anomalous dispersion which is a weakness of DM
Es werden zwei verschiedene Methoden zur numerischen Lösung der \"Gleichung für stochastisches Einsammeln\" (stochastic collection equation, SCE) vorgestellt. Sie werden als Lineare Diskrete Methode (LDM) bzw. Bin Shift Methode (BSM) bezeichnet. Konzeptuell sind beide der bekannten Diskreten Methode (DM) von Kovetz und Olund ähnlich. Für LDM und BSM wird deren Konzept auf zwei prognostische Momente erweitert. Für LDM und BSM werden die\" Aufteil-Faktoren\" (die für DM zeitlich konstant sind) dadurch zeitabhängig. Es werden Simulationsrechnungen für die Koaleszenzfunktion nach Golovin (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach Hall gezeigt. Verschiedene Klassenauflösungen und Zeitschritte werden untersucht. Wie erwartet werden die Ergebnisse mit zunehmender Auflösung besser. LDM und BSM zeigen nicht die anomale Dispersion, die eine Schwäche der DM ist
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Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Wissenschaftliche Mitteilungen des Leipziger Instituts für Meteorologie ; 17 = Meteorologische Arbeiten aus Leipzig ; 5 (2000), S. 61-73, 2000. https://ul.qucosa.de/id/qucosa%3A15149.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Different bin resolutions and time steps are investigated. As expected, the results become better with increasing bin resolution. LDM and BSM do not show the anomalous dispersion which is a weakness of DM.
Es werden zwei verschiedene Methoden zur numerischen Lösung der \"Gleichung für stochastisches Einsammeln\" (stochastic collection equation, SCE) vorgestellt. Sie werden als Lineare Diskrete Methode (LDM) bzw. Bin Shift Methode (BSM) bezeichnet. Konzeptuell sind beide der bekannten Diskreten Methode (DM) von Kovetz und Olund ähnlich. Für LDM und BSM wird deren Konzept auf zwei prognostische Momente erweitert. Für LDM und BSM werden die\" Aufteil-Faktoren\" (die für DM zeitlich konstant sind) dadurch zeitabhängig. Es werden Simulationsrechnungen für die Koaleszenzfunktion nach Golovin (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach Hall gezeigt. Verschiedene Klassenauflösungen und Zeitschritte werden untersucht. Wie erwartet werden die Ergebnisse mit zunehmender Auflösung besser. LDM und BSM zeigen nicht die anomale Dispersion, die eine Schwäche der DM ist.
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Sjölander, Filip. "Numerical solutions to the Boussinesq equation and the Korteweg-de Vries equation." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297544.

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The aim of the report is to numerically construct solutions to two analytically solvable non-linear differential equations: the Korteweg–De Vries equation and the Boussinesq equation. To accomplish this, a range of numerical methods where implemented, including Galerkin methods. To asses the accuracy of the solutions, analytic solutions were derived for reference. Characteristic of both equations is that they support a certain type of wave-solutions called "soliton solutions", which admit an intuitive physical interpretation as solitary traveling waves. Theses solutions are the ones simulated. The solitons are also qualitatively studied in the report.
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Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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Maral, Tugrul. "Spectral (h-p) Element Methods Approach To The Solution Of Poisson And Helmholtz Equations Using Matlab." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607945/index.pdf.

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A spectral element solver program using MATLAB is written for the solution of Poisson and Helmholtz equations. The accuracy of spectral methods (p-type high order) and the geometric flexibility of the low-order h-type finite elements are combined in spectral element methods. Rectangular elements are used to solve Poisson and Helmholtz equations with Dirichlet and Neumann boundary conditions which are homogeneous or non homogeneous. Robin (mixed) boundary conditions are also implemented. Poisson equation is also solved by discretising the domain with curvilinear quadrilateral elements so that the accuracy of both isoparametric quadrilateral and rectangular element stiffness matrices and element mass matrices are tested. Quadrilateral elements are used to obtain the stream functions of the inviscid flow around a cylinder problem. Nonhomogeneous Neumann boundary conditions are imposed to the quadrilateral element stiffness matrix to solve the velocity potentials.
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Sundström, Carl. "Numerical solutions to high frequency approximations of the scalar wave equation." Thesis, Uppsala universitet, Tillämpad beräkningsvetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-429072.

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Throughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which indicates an error in myimplementation.
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Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.

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Pusch, Gordon D. "Differential algebraic methods for obtaining approximate numerical solutions to the Hamilton-Jacobi equation." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-07282008-135711/.

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Books on the topic "Poisson's equation Numerical solutions"

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Vorobiev, Leonid G. A symplectic Poisson solver based on fast Fourier transformation: The first trial. Tsukuba-shi, Ibaraki-ken Japan: National Laboratory for High Energy Physics, 1995.

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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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Cooke, J. Robert. Applied finite element analysis: An Apple II implementation. New York: Wiley, 1986.

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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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Imaging, multi-scale, and high-contrast partial differential equations: Seoul ICM 2014 Satellite Conference, August 7-9, 2014, Daejeon, Korea. Providence, Rhode Island: American Mathematical Society, 2016.

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Constanda, Christian, Dale Doty, and William Hamill. Boundary Integral Equation Methods and Numerical Solutions. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26309-0.

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Gear, C. William. Differential-algebraic equation index transformations. Urbana, IL (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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Solving polynomial equation systems. Cambridge, U.K: Cambridge University Press, 2003.

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Solving Kepler's equation over three centuries. Richmond, Va: Willmann-Bell, 1993.

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Book chapters on the topic "Poisson's equation Numerical solutions"

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Bottoni, Maurizio. "Numerical Solution of Poisson Equation." In Mechanical Engineering Series, 257–90. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79717-1_6.

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Chinesta, Francisco, Roland Keunings, and Adrien Leygue. "PGD Solution of the Poisson Equation." In The Proper Generalized Decomposition for Advanced Numerical Simulations, 25–46. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02865-1_2.

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Majda, George. "On Singular Solutions of the Vlasov-Poisson Equations." In Vortex Flows and Related Numerical Methods, 67–75. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8137-0_5.

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Bottoni, Maurizio. "Derivation and Numerical Solutions of Poisson-Like Equations." In Mechanical Engineering Series, 291–342. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79717-1_7.

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Hummel, J. A. "Numerical solutions of the schiffer equation." In Computational Methods and Function Theory, 71–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0087898.

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Constanda, Christian, Dale Doty, and William Hamill. "Existence of Solutions." In Boundary Integral Equation Methods and Numerical Solutions, 25–33. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26309-0_3.

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Kastberg, Anders. "Numerical Solutions of the Atomic Schrödinger Equation." In Structure of Multielectron Atoms, 281–88. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36420-5_14.

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Cole, E. A. B. "Approximate and numerical solutions of the Schrödinger equation." In Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming, 303–37. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-937-4_13.

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Seitz, Florian, and Hansjörg Kutterer. "Numerical Solutions for the Non-Linear Liouville Equation." In International Association of Geodesy Symposia, 463–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04709-5_77.

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Constanda, Christian, Dale Doty, and William Hamill. "The Mathematical Model." In Boundary Integral Equation Methods and Numerical Solutions, 1–8. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26309-0_1.

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Conference papers on the topic "Poisson's equation Numerical solutions"

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Shibata, Daisuke, and Takayuki Utsumi. "Numerical Solutions of Poisson Equation by the CIP-Basis Set Method." In ASME 2009 InterPACK Conference collocated with the ASME 2009 Summer Heat Transfer Conference and the ASME 2009 3rd International Conference on Energy Sustainability. ASMEDC, 2009. http://dx.doi.org/10.1115/interpack2009-89150.

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An accurate and reliable real space method for the ab initio calculation of electronic-structures of materials has been desired. Historically, the most popular method in this field has been the Plane Wave method. However, because the basis functions of the Plane Wave method are not local in real space, it is inefficient to represent the highly localized inner-shell electron state and it generally give rise to a large dense potential matrix which is difficult to deal with. Moreover, it is not suitable for parallel computers, because it requires Fourier transformations. These limitations of the Plane Wave method have led to the development of various real space methods including finite difference method and finite element method, and studies are still in progress. Recently, we have proposed a new numerical method, the CIP-Basis Set (CIP-BS) method [1], by generalizing the concept of the Constrained Interpolation Profile (CIP) method from the viewpoint of the basis set. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the sub-grid scale solution approaches the local real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the sub-grid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The governing equations are unambiguously discretized into matrix form equations requiring the residuals to be orthogonal to the basis functions via the same procedure as the Galerkin method. We have already demonstrated that the method can be applied to calculations of the band structures for crystals with pseudopotentials. It has been certified that the method gives accurate solutions in the very coarse meshes and the errors converge rapidly when meshes are refined. Although, we have dealt with problems in which potentials are represented analytically, in Kohn-Sham equation the potential is obtained by solving Poisson equation, where the charge density is determined by using wave functions. In this paper, we present the CIP-BS method gives accurate solutions for Poisson equation. Therefore, we believe that the method would be a promising method for solving self-consistent eigenvalue problems in real space.
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Abdallah, S., and C. F. Smith. "Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines." In ASME 1989 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/89-gt-140.

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A primitive variable formulation is used for the solution of the incompressible Euler’s equation. In particular, the pressure Poisson equation approach using a non-staggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a non-staggered grid. Numerical solutions of the momentum equations are obtained using the second order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive over-relaxation method. Three turbomachinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.
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Chen, J. H., and S. Abdallah. "Computation of Incompressible Flow in Turbomachines Using the Primitive Variable Formulation." In ASME 1987 International Gas Turbine Conference and Exhibition. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/87-gt-85.

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The primitive variable approach is adapted here for the solution of incompressible flow in turbomachines using non-staggered grids. In this approach, a pressure Poisson equation with Neumann boundary conditions is solved in lieu of the continuity equation. Solutions for the Poisson equation exist only if a compatibility condition is satisfied. This condition is not automatically satisfied on non-staggered grids. Failure to satisfy the compatibility condition results in non-convergent solutions. A consistent finite difference method which satisfies this condition using a non-staggered grid in general curvilinear coordinates is developed. Numerical solutions are obtained for the pressure equation using the successive over-relaxation method. The velocity field is computed from the momentum equations by explicitly marching in time. The computed solutions are compared with the available numerical results for both inviscid and viscous laminar flows in cascades.
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Lu, Fuzhi, Jun Yang, and Daniel Y. Kwok. "Numerical and Experimental Studies on Electrical Potential Distribution of Pressure Driven Flow in Parallel Plate Microchannels." In ASME 2004 2nd International Conference on Microchannels and Minichannels. ASMEDC, 2004. http://dx.doi.org/10.1115/icmm2004-2416.

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A number of papers have been published on the computational approaches to electrokinetic flows. Nearly all of these decoupled approaches rely on the assumption of the Poisson-Boltzmann equation and do not consider the effect of velocity field on the electric double layers. By means of a charge continuity equation, we present here a numerical model for the simulation of pressure driven flow with electrokinetic effects in parallel-plate microchannels. Our approach is similar to that given by van Theemsche et al. [Anal. Chem., 74, 4919 (2002)] except that we assumed liquid conductivity to be constant and allows simulation to be performed in experimental dimension. The numerical simulation requires the solution of the Poisson equation, charge continuity equation and the incompressible Navier-Stokes equations. The simulation is implemented in a finite-volume based Matlab code. To validate the model, we measured the electrical potential downstream along the channel surface. The simulated results were also compared with known analytical solutions and experimental data. Results indicate that the linear potential distribution assumption in the streaming direction is in general not valid, especially when the flow rate is large for the specific channel geometry. The good agreement between numerical simulation and experimental data suggests that the present model can be employed to predict pressure-driven flow in microchannels.
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da Silva, Joao Rogerio, Jose Geraldo Peixoto de Faria, Marcio Matias Afonso, and Giancarlo Queiroz Pellegrino. "Effect of local support configuration on the precision of numerical solutions of Poisson equation obtained with differential quadrature method." In 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). IEEE, 2016. http://dx.doi.org/10.1109/cefc.2016.7816366.

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Venkataraman, P. "Approximate Analytical Solutions to Nonlinear Inverse Boundary Value Problems." 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/detc2016-59306.

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A nontraditional approach to the nonlinear inverse boundary value problem is illustrated using multiple examples of the Poisson equation. The solutions belong to a class of analytical solutions defined through Bézier functions. The solution represents a smooth function of high order over the domain. The same procedure can be applied to both the forward and the inverse problem. The solution is obtained as a local minimum of the residuals of the differential equations over many points in the domain. The Dirichlet and Neumann boundary conditions can be incorporated directly into the function definition. The primary disadvantage of the process is that it generates continuous solution even if continuity and smoothness are not expected for the solution. In this case they will generate an approximate analytical solution to either the forward or the inverse problem. On the other hand, the method does not need transformation or regularization, and is simple to apply. The solution is also good at damping the perturbations in measured data driving the inverse problem. In this paper we show that the method is quite robust for linear and nonlinear inverse boundary value problem. We compare the results with a solution to a nonlinear inverse boundary value problem obtained using a traditional approach. The application involves a mixture of symbolic and numeric computations and uses a standard unconstrained numerical optimizer.
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Tijsseling, A. S. "Exact Solution of the Linear Hyperbolic Four-Equation System in Axial Liquid-Pipe Vibration." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32209.

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The so-called “FSI four-equation model” describes the axial vibration of liquid-filled pipes. Two equations for the liquid are coupled to two equations for the pipe, through terms proportional to the Poisson contraction ratio, and through mutual boundary conditions. Skalak (1955/1956ab) defined this basic model, which disregards friction and damping effects. The four equations can be solved with the method of characteristics (MOC). The standard approach is to cover the distance-time plane with equidistantly spaced grid-points and to time-march from a given initial state. This approach introduces error, because either numerical interpolations or wave speed adjustments are necessary. This paper presents a method of exact calculation in terms of a simple recursion. The method is valid for transient events only, because the calculation time grows exponentially with the duration of the event. The calculation time is proportional to the temporal and spatial resolution. The exact solutions are used to investigate the error due to numerical interpolations and wave speed adjustments, with emphasis on the latter.
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Tamayol, A., and M. Bahrami. "Parallel Flow in Ordered Fibrous Structures: An Analytical Approach." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78166.

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In this study, fully-developed flow parallel to ordered fibrous structures is investigated analytically. The considered fibrous media are made up of inline (square), staggered, and hexagonal arrays of cylinders. Starting from the general solution of Poisson’s equation, compact analytical solutions are proposed for both velocity distribution and permeability of the considered structures. In addition, independent numerical simulations are performed for the considered patterns over the entire range of porosity and the results are compared with the proposed solutions. The developed models are successfully verified through comparison with existing experimental data, collected by others, and the present numerical results over a wide range of porosity. The results show that for the ordered arrangements with high porosity, the parallel permeability is independent of the microstructure geometry; on the other hand, for lower porosities the hexagonal arrays results in lower pressure drop, as expected.
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Zhang, Yunxing, Wenyang Duan, Kangping Liao, Shan Ma, and Guihua Xia. "Numerical Simulation of Solitary Wave Breaking With Adaptive Mesh Refinement." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95224.

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Abstract The numerical simulation of wave breaking problem is still a tough challenge, partly due to the large grid number and CPU time requirement for capturing the multi-scale structures embedded in it. In this paper, a two-dimensional two-phase flow model with Adaptive Mesh Refinement (AMR) is proposed for simulating solitary wave breaking problems. Fractional step method is employed for the velocity-pressure decoupling. The free surface flow is captured with the Volume-of-Fluid (VOF) method combined with Piecewise Linear Interface Calculation (PLIC) for the reconstruction of the interface. Immersed boundary (IB) method is utilized to account for the existence of solid bodies. A geometric multigrid method is adopted for the solution of Pressure Poisson Equation (PPE). Benchmark case of advection test is considered first to test the VOF method. Then the solitary wave propagation problem is utilized to validate the model on AMR grid as well as analyze the efficiency of AMR. Furthermore, the solitary wave past a submerged stationary stage problem is simulated to validate the combined IB-VOF-AMR model. All the numerical results are compared with analytic solutions, experimental data or other published numerical results, and good agreements are obtained. Finally, the influence of stage height on the occurrence of wave breaking is analyzed. The locations of wave breaking are summarized for different stage heights.
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Gallandat, Noris, and J. Rhett Mayor. "Enhanced Passive Thermal Management of Grid-Scale Power Routers Utilizing Ionic Wind." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38713.

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This paper presents a numerical model assessing the potential of ionic wind as a heat transfer enhancement method for the cooling of grid distribution assets. Distribution scale power routers (13–37 kV, 1–10 MW) have stringent requirements regarding lifetime and reliability, so that any cooling technique involving moving parts such as fans or pumps are not viable. Increasing the air flow — and thereby enhancing heat transfer — through Corona discharge could be an attractive solution to the thermal design of such devices. In this work, the geometry of a rectangular, vertical channel with a corona electrode at the entrance is considered. The multiphysics problem is characterized by a set of four differential equations: the Poisson equation for the electric field and conservation equations for electric charges, momentum and energy. The electrodynamics part of the problem is solved using a finite difference approximation (FDA). Solutions for the potential, electric field and free charge density are presented for a rectangular control volume with mixed boundary conditions.
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Reports on the topic "Poisson's equation Numerical solutions"

1

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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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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Chang, B. Analytical Solutions for Testing Ray-Effect Errors in Numerical Solutions of the Transport Equation. Office of Scientific and Technical Information (OSTI), May 2003. http://dx.doi.org/10.2172/15004539.

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Hart, Carl, and Gregory Lyons. A tutorial on the rapid distortion theory model for unidirectional, plane shearing of homogeneous turbulence. Engineer Research and Development Center (U.S.), July 2022. http://dx.doi.org/10.21079/11681/44766.

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The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is assumed that the time-varying velocity spectral tensor can be made stationary by substituting an eddy-lifetime parameter in place of time. General and particular RDT evolution equations for stochastic increments are derived in detail. Analytical solutions for the RDT evolution equation, with and without an effective eddy viscosity, are given. An alternative expression for the eddy-lifetime parameter is shown. The turbulence kinetic energy budget is examined for RDT. Predictions by RDT are shown for velocity (co)variances, one-dimensional streamwise spectra, length scales, and the second invariant of the anisotropy tensor of the moments of velocity. The RDT prediction of the second invariant for the velocity anisotropy tensor is shown to agree better with direct numerical simulations than previously reported.
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