Academic literature on the topic 'Von Neumann stability condition'
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Journal articles on the topic "Von Neumann stability condition"
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Kamel, Aladin H. "A stability checking procedure for finite-difference schemes with boundary conditions in acoustic media." Bulletin of the Seismological Society of America 79, no. 5 (October 1, 1989): 1601–6. http://dx.doi.org/10.1785/bssa0790051601.
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Abstract The manner in which boundary conditions are approximated and introduced into finite-difference schemes has an important influence on the stability and accuracy of the results. The standard von Neumann stability condition applies only for points which are not in the vicinity of the boundaries. This stability condition does not take into consideration the effects caused by introducing the boundary conditions to the scheme. In this paper, we extend the von Neumann condition to include boundary conditions. The method is based on studying the time propagating matrix which governs the space-time behavior of the numerical grid. Examples of applying the procedure on schemes with different boundary conditions are given.
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Li, Yong Heng, and Xia Li. "Extension of Von Neumann Model of National Economic System." Applied Mechanics and Materials 55-57 (May 2011): 101–4. http://dx.doi.org/10.4028/www.scientific.net/amm.55-57.101.
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The Von Neumann Model on national economical system is investigated. A new discrete-time input-output model on national economic system based on the classic Von Neumann Model is provided and the stability of this kind of model is researched. This new system belongs to the singular system. By the new mathematic method, this singular linear system will not be converted into the general linear system. Finally, a sufficient stability condition under which the discrete-time singular Extended Von Neumann Model is admissible is proved.
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Haney, Matthew M. "Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case." GEOPHYSICS 72, no. 5 (September 2007): SM35—SM46. http://dx.doi.org/10.1190/1.2750639.
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Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable.
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Wu, Xiu Mei, Tao Zi Si, and Lei Jiang. "Stable Computer Control Algorithm of Von Neumann Model." Advanced Materials Research 634-638 (January 2013): 4026–29. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.4026.
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The problem of computer control algorithm for the singular Von Neumann input-output model is researched. A kind of new mathematic method is applied to study the singular systems without converting them into general systems. A kind of stability condition under which the singular input-output model is admissible is proved with the form of linear matrix inequality. Based on this, a new state feedback stability criterion is established. Then the formula of a desired state feedback controller is derived.
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WESSELING, P. "von Neumann stability conditions for the convection-diffusion eqation." IMA Journal of Numerical Analysis 16, no. 4 (1996): 583–98. http://dx.doi.org/10.1093/imanum/16.4.583.
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M. Jemimah, M. Alpha, and Abubakar Alkasim. "Exact Solution of Couple Burgers’ Equation using Cubic B-Spline Collocation Method for Fluid Suspension/Colloid under the Influence of Gravity." African Journal of Advances in Science and Technology Research 14, no. 1 (April 30, 2024): 73–85. http://dx.doi.org/10.62154/ymthy538.
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In this research, Cubic B-Spline plane method was used to solve numerically the one-dimensional Burger’s Equation with initial condition , boundary conditions; . The cubic trigonometric B-spline was used for interpolating the solutions at each time and using the Von-Neumann method to check the stability. The obtained numerical result showed that the method was efficient, robust and reliable for solving Burgers’ Equation accurately even involving high Reynolds numbers for which the exact solutions have failed.
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Hafiz, Khandaker Md Eusha Bin, and Laek Sazzad Andallah. "Second Order Scheme For Korteweg-De Vries (KDV) Equation." Journal of Bangladesh Academy of Sciences 43, no. 1 (July 16, 2019): 85–93. http://dx.doi.org/10.3329/jbas.v43i1.42237.
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The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using convex combination method is determined. Von Neumann stability analysis is performed to determine the stability condition for a second order scheme. The well-known qualitative behavior of the KdV equation is verified and error estimation for comparisons is performed.
Journal of Bangladesh Academy of Sciences, Vol. 43, No. 1, 85-93, 2019
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Quintana-Murillo, J., and S. B. Yuste. "An Explicit Numerical Method for the Fractional Cable Equation." International Journal of Differential Equations 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/231920.
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An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann-Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first-order derivative by a forward difference formula, the Riemann-Liouville derivatives by the Grünwald-Letnikov formula, and the spatial derivative by a three-point centered formula. The accuracy, stability, and convergence of the method are considered. The stability analysis is carried out by means of a kind of von Neumann method adapted to fractional equations. The convergence analysis is accomplished with a similar procedure. The von-Neumann stability analysis predicted very accurately the conditions under which the present explicit method is stable. This was thoroughly checked by means of extensive numerical integrations.
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Luiz, Kariston Stevan, Juniormar Organista, Eliandro Rodrigues Cirilo, Neyva Maria Lopes Romeiro, and Paulo Laerte Natti. "Numerical convergence of a Telegraph Predator-Prey system." Semina: Ciências Exatas e Tecnológicas 43, no. 1Esp (November 30, 2022): 51–66. http://dx.doi.org/10.5433/1679-0375.2022v43n1espp51.
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Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented.
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Erkurşun Özcan, Nazife. "On ergodic properties of operator nets on the predual of von neumann algebras." Studia Scientiarum Mathematicarum Hungarica 55, no. 4 (December 2018): 479–86. http://dx.doi.org/10.1556/012.2018.55.4.1414.
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In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.
Dissertations / Theses on the topic "Von Neumann stability condition"
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Courtin, Victor. "Extensions of some approximate Riemann Solvers for the computation of mixed incompressible-compressible flows." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM041.
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Dans cette thèse, on s'intéresse à la simulation d'écoulements compressibles à l'aide de méthodes numériques implicites de type solveurs de Riemann, telles que la méthode de Roe ou le schéma HLLC. L'objectif est de développer des extensions faible nombre de Mach afin de préserver la précision des solutions discrètes dans la limite bas Mach. Ce type d'écoulement est souvent rencontré dans la simulation de configurations industrielles, caractérisées par la présence de zones plus ou moins étendues à faible vitesse.On se focalise sur la composante hyperbolique des équations de Navier-Stokes, qui constitue le cœur du problème d'analyse numérique abordé dans cette thèse, les équations d'Euler. On y expose une analyse approfondie et détaillée retraçant un sujet de recherche vieux de plusieurs décennies, qui présente encore d'importants défis, même pour ce modèle académique. La littérature recense un grand nombre d'extensions possibles pour le schéma de Roe, qui sont généralement faciles à implémenter. Ces extensions consistent à modifier certains termes de la dissipation numérique, en amplifiant ou diminuant leur contribution dans la limite faible nombre de Mach (on parle de « rescaling » de la dissipation numérique). Elles permettent par ailleurs d'obtenir une solution discrète compressible approchant la solution analytique issue de la théorie du potentiel pour le problème incompressible, sans pour autant introduire une détérioration des résultats dans le régime compressible. La capture des ondes de choc pour les écoulements transsoniques et supersoniques reste quasiment inchangée. Cependant, il existe plusieurs études suggérant de faire preuve de vigilance quant au choix de la formulation de ce type de correction. Il est connu de la littérature que des pertes de stabilité numérique sont généralement observées, ainsi que des risques d'apparition de problèmes de découplage vitesse-pression, détériorant fortement la précision globale de la solution discrète dans les faibles vitesses.Ces travaux se fondent sur deux corrections très différentes du schéma de Roe, issues de la littérature scientifique, et qui présentent des propriétés discrètes distinctes. La première approche, proposée par C.-C. Rossow, amplifie les sauts de pression en introduisant une vitesse artificielle du son, tandis que la seconde, développée par F. Rieper, vise à uniquement atténuer les sauts de vitesse. Ces deux approches illustrent deux stratégies majeures fréquemment utilisées dans les extensions à faible nombre de Mach. Nous commençons tout d'abord par l'analyse asymptotique discrète de l'approche proposée par C.-C. Rossow non publiée dans la littérature, en abordant également la formulation de la condition de stabilité au sens de von Neumann. On montre que cette correction évite l'écueil du découplage vitesse-pression. Ensuite, nous présentons une méthode numérique, visant à construire des phases implicites exactes nécessaires à l'intégration temporelle, en utilisant la différentiation algorithmique et un solveur direct. Ces techniques nous permettent de contourner la contrainte très stricte de stabilité sur le pas de temps, et d'obtenir des solutions discrètes en quelques centaines d'itérations, et ce même pour des écoulements à très faible nombre de Mach. La généralisation de ces travaux au schéma HLLC se fait ensuite en poursuivant l'analyse de la structure d'onde faite par M. Pelanti. Ces travaux révèlent une profonde similarité entre les dissipations numériques de ces méthodes. En particulier, nous dérivons un formalisme commun entre ces deux schémas, afin de simplifier les analyses, et la transposition d'une correction d'un solveur de Riemann approché à l'autre, au sens d'une relation très claire entre les deux méthodes. Cette analyse nous permet en particulier de dériver le schéma HLLC-Rossow, mais également d'expliciter l'expression de la matrice de viscosité du schéma HLLC, qui exhibe une ressemblance intéressante avec celle du schéma RoeIn this thesis, we focus on the simulation of compressible flows using implicit Godunov-type methods, such as the Roe method or the HLLC scheme. The objective is to develop low Mach number extensions that preserve the accuracy of discrete solutions in the low Mach number limit. This type of flow is frequently encountered in the simulation of industrial configurations, which are often characterized by the presence of more or less extensive low-speed areas.We focus on the hyperbolic component of the Navier-Stokes equations, which form the core of the numerical analysis problem addressed in this thesis, the Euler equations. We present an in-depth and detailed analysis of research topic that has been the subject of investigations for decades, and which continues to present significant challenges, even for this academic model. A review of the literature reveals a large number of possible extensions to the Roe scheme, which are generally easy to implement. These involve modifying specific terms of the numerical dissipation, either by amplifying or by diminishing their contribution in the low Mach number limit (also known as a rescaling of the numerical dissipation). They also enable us to obtain a discrete compressible solution that approaches the analytical solution derived from potential theory for the incompressible problem, without introducing any deterioration in the results in the compressible regime. The capture of shock waves for transonic and supersonic flows remains almost unaltered. However, there are a number of studies suggesting that care should be taken in the choice of formulation for this type of correction. It is well documented in the literature that losses in numerical stability are generally observed, as well as the risk of velocity-pressure decoupling problems appearing, which can significantly deteriorate the overall accuracy of the discrete solution for low-speed flows.This work is based on two very different corrections of the Roe scheme, taken from the scientific literature, and highlighting distinct discrete properties. The first approach, proposed by C.-C. Rossow, amplifies pressure jumps by introducing an artificial speed of sound, whereas the second approach, developed by F. Rieper, aims to attenuate velocity jumps exclusively. These two approaches illustrate two major strategies frequently used in low-Mach extensions. We begin with a discrete asymptotic analysis of the approach proposed by C.-C. Rossow, which has not been published in the literature, including the formulation of the von Neumann stability condition. It is demonstrated that this correction avoids the issue of pressure- velocity decoupling. Next, we present a numerical method for constructing the exact implicit phases required for time integration, using algorithmic differentiation and a direct solver. These techniques enable us to bypass the very strict stability constraint on the time step, thereby facilitating the acquisition of discrete solutions within a few hundred iterations, even for very low Mach number flows. The generalization of this work to the HLLC scheme is then made by continuing the wave structure analysis carried out by M. Pelanti. This work demonstrates a significant similarity between the numerical dissipations of these methods. In particular, a common formalism between these two schemes is derived, with the aim of simplifying the analyses, and transposing of a correction from one approximate Riemann solver to the other, in the sense of a very clear relationship between the two methods. In particular, this analysis enables us to derive the HLLC-Rossow scheme, but also to clarify the expression of the viscosity matrix of the HLLC scheme, which exhibits an interesting resemblance to that of the Roe scheme
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Roudaut, Julien. "Algèbres moyennables." Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC016.
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Introduite en 1929 par Von Neumann, la moyennabilité a pris une place importante dans les mathématiques actuelles. Initialement formulée pour les groupes, elle admet des caractérisations dans de nombreux domaines, dont la condition de Folner est l'une des plus classiques. Dans la thèse, on définit, et étudie, une nouvelle notion de moyennabilité pour les algèbres, basée sur cette condition de Folner. La structure des algèbres est riche, et l'on commence par établir de nombreux résultats structurels (de stabilité notamment), que l'on met ensuite en oeuvre au travers l'étude de deux exemples : les algèbres de chemins (sur un graphe orienté), et les algèbres semi-simples. Dans chacun des cas, on obtient des caractérisations élégantes pour la condition de Folner et la moyennabilité, qui permettent d'illustrer les différences entre les deux notions. On revient ensuite au cas des algèbres de groupe, avec la question centrale du lien entre la moyennabilité d'un groupe et celle de son algèbre de groupe, et, si le problème reste ouvert en général, on donne des réponses partielles. En particulier, on s'intéresse à un résultat d'Ornstein-Weiss, concernant des propriétés de pavage dans un groupe moyennable, et l'on obtient, par exemple, que les groupes résolubles ont bien leur algèbre de groupe moyennable. Enfin, dans les annexes, on rappelle plusieurs définitions essentielles (ultrafiltes, décompositions paradoxales), et l'on expose différentes pistes et résultats, en lien avec les algèbres moyennables, mais qui n'ont pas trouvé pleinement leur place dans le corps de la thèseIntroduced by Von Neumann in 1929, amenability has taken an important place in current mathematics. Initially formulated for groups, it admits characterizations in many areas, whose Folner's condition is one of most classic. In the thesis, we define, and study, a new notion of amenability for algebras, based on this Folner's condition. The structure of algebras is rich, and we start with proving many structural results (stability results especially), and we then use these tools through the study of two examples : path algebras (over a directed graph), and semisimple algebras. In each case, we obtain elegant characterizations for Folner's condition and amenability, which illustrate the differences between the two notions. Next, we corne back to group algebras, with the central question of the link between the amenability of a group and that of its group algebra, and, even if this problem is still open in general case, we give some partial answers. Especially, we consider a result of Ornstein-Weiss, concerning paving properties in an amenable group, and we show, for example, that soluble groups are algebraically amenable. Finally, in annexes, we recall some essential definitions (ultrafilter, paradoxical decompositions), and we expose several results, related to amenable algebras, which have not found their place in the main text of the thesis
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Konangi, Santosh. "Stability Analysis of Artificial-Compressibility-type and Pressure-Based Formulations for Various Discretization Schemes for 1-D and 2-D Inviscid Flow, with Verification Using Riemann Problem." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321371661.
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Kunadian, Illayathambi. "NUMERICAL INVESTIGATION OF THERMAL TRANSPORT MECHANISMS DURING ULTRA-FAST LASER HEATING OF NANO-FILMS USING 3-D DUAL PHASE LAG (DPL) MODEL." UKnowledge, 2004. http://uknowledge.uky.edu/gradschool_theses/324.
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Ultra-fast laser heating of nano-films is investigated using 3-D Dual Phase Lag heat transport equation with laser heating at different locations on the metal film. The energy absorption rate, which is used to model femtosecond laser heating, is modified to accommodate for three-dimensional laser heating. A numerical solution based on an explicit finite-difference method is employed to solve the DPL equation. The stability criterion for selecting a time step size is obtained using von Neumann eigenmode analysis, and grid function convergence tests are performed. DPL results are compared with classical diffusion and hyperbolic heat conduction models and significant differences among these three approaches are demonstrated. We also develop an implicit finite-difference scheme of Crank-Nicolson type for solving 1-D and 3-D DPL equations. The proposed numerical technique solves one equation unlike other techniques available in the literature, which split the DPL equation into a system of two equations and then apply discretization. Stability analysis is performed using a von Neumann stability analysis. In 3-D, the discretized equation is solved using delta-form Douglas and Gunn time splitting. The performance of the proposed numerical technique is compared with the numerical techniques available in the literature.
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Simon, Amélie. "Modélisation des phénomènes de films liquides dans les turbines à vapeur." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC001/document.
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Dans la production d'électricité, un des leviers centraux pour réduire les détériorations et les pertes causées par l'humidité dans les turbines à vapeur est l'étude des films liquides. Ces films minces, sont créés par la déposition de gouttes et sont fortement cisaillés. Des gouttes peuvent ensuite être arrachées du film. A l'heure actuelle, aucun modèle complet et valide n'existe pour décrire ce phénomène. Un modèle 2D à formulation intégrale associé à des lois de fermetures a été dérivé pour représenter ce film. Comparé aux équations classiques de Saint-Venant, le modèle prend en compte davantage d'effets : le transfert de masse, l'impact des gouttes, le cisaillement à la surface libre, la tension de surface, le gradient de pression et la rotation. Une analyse des propriétés du modèle (hyperbolicité, entropie, conservativité, analyse de stabilité linéaire, invariance par translation et par rotation) est réalisée pour juger de la pertinence du modèle. Un nouveau code 2D est implémenté dans un module de développement libre du code EDF Code Saturne et une méthode de volumes finis pour un maillage non-structure a été développée. La vérification du code est ensuite effectuée avec des solutions analytiques dont un problème de Riemann. Le modèle, qui dégénère en modèle classique de Saint-Venant pour le cas d'un film tombant sur un plan inclinée, est validé par l'expérience de Liu and Gollub, 1994, PoF et comparé à des modèles de références (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Un autre cas d'étude met en scène un film cisaillé en condition basse-pression de turbine à vapeur et, est validé par l'expérience de Hammitt et al., 1981, I. Enfin, le code film est couplé aux données 3D du champ de vapeur autour d'un stator d'une turbine basse-pression du parc EDF, issues de Blondel, 2014, PhD thesis. Cette application industrielle montre la faisabilité d'une simulation d'un film en condition réelle du turbine à vapeurIn the electricity production, one central key to reduce damages and losses due to wetness in steam turbines is the study of liquid films. These thin films are created by the deposition of droplets and are highly sheared. This film may then be atomized into coarse water. At the moment, no comprehensive and validated model exists to describe this phenomenon. A 2D model based on a integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effect : mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and the rotation. The model properties (hyperbolicity, entropy, conservativity, linear stability, Galilean invariance and rotational invariance) has been analyzed to judge the pertinence of the model. A new 2D code is implemented in a free module of the code EDF Code Saturne and a finite volume method for unstructured mesh has been developed. The verification of the code is then carried out with analytical solutions including a Riemann problem. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated by the experiment of Liu and Gollub, 1994, PoF and compared to reference models (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Another study depicts a sheared film under low-pressure steam turbine conditions and is validated by the experiment of Hammitt et al., 1981, FiI. Lastly, the code film is coupled to 3D steam data around a fixed blade of a BP100 turbine, from Blondel, 2014, PhD thesis. This industrial application shows the feasibility of liquid film's simulation in real steam turbine condition
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Neumann, Axel [Verfasser]. "Compensating microphonics in SRF cavities to ensure beam stability for future free electron lasers = Mikrophoniekompensation in supraleitenden Hohlraumresonatoren zur Gewährleistung der Strahlstabilität für zukünftige freie Elektronen-Laser / von Axel Neumann." 2008. http://d-nb.info/992024609/34.
Full textBooks on the topic "Von Neumann stability condition"
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Shi, Jian. A simplified Von Neumann method for linear stability analysis. Cranfield, Bedford, England: Cranfield Institute of Technology, College of Aeronautics, 1993.
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Edmunds, D. E., and W. D. Evans. Unbounded Linear Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0003.
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This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.
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Tiwari, Sandip. Information mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0001.
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Information is physical, so its manipulation through devices is subject to its own mechanics: the science and engineering of behavioral description, which is intermingled with classical, quantum and statistical mechanics principles. This chapter is a unification of these principles and physical laws with their implications for nanoscale. Ideas of state machines, Church-Turing thesis and its embodiment in various state machines, probabilities, Bayesian principles and entropy in its various forms (Shannon, Boltzmann, von Neumann, algorithmic) with an eye on the principle of maximum entropy as an information manipulation tool. Notions of conservation and non-conservation are applied to example circuit forms folding in adiabatic, isothermal, reversible and irreversible processes. This brings out implications of fluctuation and transitions, the interplay of errors and stability and the energy cost of determinism. It concludes discussing networks as tools to understand information flow and decision making and with an introduction to entanglement in quantum computing.
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Grant, Robert. Neurocutaneous syndromes. Oxford University Press, 2011. http://dx.doi.org/10.1093/med/9780198569381.003.0235.
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This chapter describes several neurocutaneous syndromes, including tuberous sclerosis, neurofibromatosis, Sturge–Weber syndrome, Von-Hippel–Lindau disease and ataxia telangiectasia amongst others.Tuberous sclerosis, also known as Epiloia or Bournville’s Disease, is an autosomal dominant multisystem disease it usually presents in childhood with a characteristic facial rash, adenoma sebaceum, seizures, and sometimes learning difficulties. Central nervous system lesions in tuberous sclerosis are due to a developmental disorder of neurogenesis and neuronal migration. Other organs such as the heart and kidney are less commonly involved. The condition has very variable clinical expression and two-thirds of cases are thought to be new mutations, therefore it is important to examine and screen relatives. Management may involve many specialists and close co-operation between specialists is essential.The neurofibromatoses are autosomal-dominant neurocutaneous disorders that can be divided into ‘peripheral’ and ‘central’ types, although there is significant overlap. The characteristic features of neurofibromatosis type 1 are café au lait spots, neurofibromas, Lisch nodules, osseous lesions, macrocephaly, short stature and mental retardation, axillary freckling, and associations with several different types of tumours.Sturge–Weber syndrome involves a characteristic ‘port-wine’ facial naevus or angioma associated with an underlying leptomeningeal angioma or other vascular anomaly. It affects approximately 1/20 000 people. There can be seizures, low IQ, and underlying cerebral hemisphere atrophy as a result of chronic state of reduced perfusion and increased oxygen extraction. Patients may present with focal seizures which are generally resistant to anticonvulsant medication and can develop glaucoma.Von-Hippel– Lindau disease is one of the most common autosomal-dominant inherited genetic diseases that are associated with familial cancers. Von-Hippel–Lindau disease is characterized by certain types of central nervous system tumours, cerebellar and spinal haemangioblastomas, and retinal angiomas, in conjunction with bilateral renal cysts carcinomas or phaechromocytoma, or pancreatic cysts/islet cell tumours (Neumann and Wiestler 1991).Other neurocutaneous syndromes discussed include Hypomelanosis of Ito, Gorlin syndrome, Sjogren–Larsson syndrome, Proteus syndrome, Hemiatrophy and hemihypertrophy, Menke’s syndrome, Xeroderma pigmentosum and Cockayne’s syndrome.
Book chapters on the topic "Von Neumann stability condition"
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Ashyralyev, Allaberen, Koray Turk, and Deniz Agirseven. "On the Stability of the Time Delay Telegraph Equation with Neumann Condition." In Springer Proceedings in Mathematics & Statistics, 201–11. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69292-6_15.
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Faenza, Yuri, Clifford S. Stein, and Jia Wan. "Von Neumann-Morgenstern Stability and Internal Closedness in Matching Theory." In Integer Programming and Combinatorial Optimization, 168–81. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-59835-7_13.
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Wen, Chih-Yung, Yazhong Jiang, and Lisong Shi. "Numerical Features of CESE Schemes." In Engineering Applications of Computational Methods, 69–76. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0876-9_6.
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AbstractIn this chapter, some remarks are made on the numerical characteristics of the CESE schemes described in foregoing chapters. Due to the special formulation, rigorous analysis of the CESE schemes will take more efforts than that of traditional finite difference schemes. However, it is possible to extend the widely used modified equation analysis, modified wavenumber analysis, and von Neumann stability analysis to the CESE schemes.
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Lacková, Katarína, and Peter Frolkovič. "Von Neumann Stability Analysis of Upwind Numerical Scheme Applied to Level Set Equation with Small Curvature Term." In SEMA SIMAI Springer Series, 133–43. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55264-9_12.
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Wesseling, P. "A Method to Obtain von Neumann Stability Conditions for the Convection-Diffusion Equation." In Numerical Methods for Fluid Dynamics V, 211–24. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198514800.003.0013.
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Abstract For the computation of time-dependent incompressible flows, the pressure-correction method is widely used. For the velocity prediction step something very close to the convection-diffusion equation is solved, and von Neumann stability analysis boils down to von Neumann stability analysis for the convection-diffusion equation, which is the topic of this paper. From now on, by stability we will mean stability in the sense of von Neumann, i.e. non-growth of Fourier components in the frozen coefficients case on an infinite domain.
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Zwillinger, Daniel. "Stability: Von Neumann Test." In Handbook of Differential Equations, 621–22. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-12-784391-9.50164-0.
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"Stability of Products." In Hochschild Cohomology of Von Neumann Algebras, 160–70. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526190.009.
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HIAI, FUMIO, MASANORI OHYA, and MAKOTO TSUKADA. "SUFFICIENCY, KMS CONDITION AND RELATIVE ENTROPY IN VON NEUMANN ALGEBRAS." In Selected Papers of M Ohya, 420–30. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812794208_0030.
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"Expanding the von Neumann Stability Mode for the Discretized Black-Scholes Equation." In The Mathematics of Derivatives, 169–71. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119197034.app3.
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Abe, Sumiyoshi. "Generalized Nonadditive Information Theory and Quantum Entanglement." In Nonextensive Entropy. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195159769.003.0007.
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Nonadditive classical information theory is developed in the axiomatic framework and then translated into quantum theory. The nonadditive conditional entropy associated with the Tsallis entropy indexed by q is given in accordance with the formalism of nonextensive statistical mechanics. The theory is applied to the problems of quantum entanglement and separability of the Werner-Popescu-type mixed state of a multipartite system, in order to examine if it has any points superior to the additive theory with the von Neumann entropy realized in the limit q → 1. It is shown that the nonadditive theory can lead to the necessary and sufficient condition for separability of the Werner-Popescu-type state, whereas the von Neumann theory can give only a much weaker condition…. Tsallis' nonextensive generalization of Boltzmann-Gibbs statistical mechanics [3, 15, 16] and its success in describing behaviors of a large class of complex systems naturally lead to the question of whether information theory can also admit an analogous generalization. If the answer is affirmative, then that will be of particular importance in connection with the problem of quantum entanglement and quantum theory of measurement [6, 8], in which necessities of a nonadditive information measure and an information content are suggested. One should also remember that there exists a conceptual similarity between a complex system and an entangled quantum system. In these systems, a "part" is indivisibly connected with the rest. An external operation on any part drastically influences the whole system, in general. Thus, the traditional reductionistic approach to an understanding of the nature of such a system may not work efficiently. In this chapter, we report a recent development in nonadditive quantum information theory based on the Tsallis entropy indexed by q [15] and its associated nonadditive conditional entropy [1]. This theory includes the ordinary additive theory with the von Neumann entropy in a special limiting case: q → To see if it has points superior to the additive theory, we apply it to the problems of separability and quantum entanglement.
Conference papers on the topic "Von Neumann stability condition"
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Liao, Jun, Renwei Mei, and James F. Klausner. "A Study on Numerical Instability of Inviscid Two-Fluid Model Near Ill-Posedness Condition." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72652.
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The two-fluid model is widely used in studying gas-liquid flow inside pipelines because it can qualitatively predict the flow field at low computational cost. However, the two-fluid model becomes ill-posed when the slip velocity exceeds a critical value, and computations can be quite unstable before flow reaches the unstable condition. In this study computational stability of various convection schemes for the two-fluid model is analyzed. A pressure correction algorithm for inviscid flow is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis for the wave growth rates by using the 1st order upwind, 2nd order upwind, QUICK, and the central difference schemes shows that the central difference scheme is more accurate and more stable than the other schemes. The 2nd order upwind scheme is much more susceptible to instability at long waves than the 1st order upwind and inaccurate for short waves. The instability associated with ill-posedness of the two-fluid model is significantly different from the instability of the discretized two-fluid model. Excellent agreement is obtained between the computed and predicted wave growth rates. The connection between the ill-posedness of the two-fluid model and the numerical stability of the algorithm used to implement the inviscid two-fluid model is elucidated.
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Zhang, Yuxuan, and Dingxi Wang. "Numerical stability analysis of solution methods for steady and harmonic balance equations." In GPPS Hong Kong24. GPPS, 2023. http://dx.doi.org/10.33737/gpps23-tc-112.
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This study presents an investigation into the stability and convergence properties of solution methods for the steady and unsteady Euler equations. A central scheme with artificial dissipation is used for the spatial discretization, and a Runge- Kutta scheme with or without implicit residual smoothing, such as LU-SGS for a steady solution and LU-SGS/BJ for an unsteady solution, is used for time integration. Both the von Neumann and matrix methods are used to analyze the stability of the involved solution methods. The stability of these schemes obtained by the two stability analysis methods is identical for periodic boundary conditions as expected. However, with inlet, outlet and slip wall boundary conditions, the stability can be analyzed using the matrix method only. It is found that these boundary conditions enhance stability of solution methods. Additionally, the matrix method can also allow for the analysis of the impacts of non-uniformity in grids and flow fields, as well as second-order artificial dissipation. For the unsteady Euler equations solved using the harmonic balance method, the stability analysis demonstrates that the time spectral source term must be handled implicitly to avoid instability for analysis with high grid-reduced frequency. The conclusions can be readily extended to the RANS equations and verified in a nozzle and the NASA rotor 37.
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Zhu, Yuze, Yuxuan Zhang, Sen Zhang, and Dingxi Wang. "Investigation of the Sigma Approximation Technique for the Solution of the Time Spectral Equation System." In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/gt2024-125788.
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Abstract The time spectral method is commonly utilized to analyze periodic unsteady flows within turbomachines. However, the time spectral solutions in regions with large temporal and spatial gradients, such as wakes, shocks, and boundary layers, can be plagued with unphysical oscillations, known as the Gibbs phenomenon. This paper presents an investigation into the sigma approximation technique, which is capable of significantly attenuating the Gibbs phenomenon by dampening high-frequency nonlinear components in the time spectral solutions. Central to this technique are three sigma factors: the exponent, the cut-off number, and the number of harmonics, which collectively determine the damping effects for each frequency. However, the optimal combination of them remains to be ascertained considering the trade-off between the accuracy of solutions and the reduction of unphysical oscillations. In this study, numerical simulations are performed to evaluate the efficacy of this technique based on a two-row compressor configuration. It is found that the Gibbs-type unphysical oscillations can be effectively mitigated without notably compromising the solution accuracy through an optimal combination scheme of sigma factors. The NASA Stage 35 case study further verifies the effectiveness of the proposed optimal sigma factor combination in preserving the accuracy of time spectral solutions. Moreover, the von Neumann analysis reveals that the sigma approximation technique can enhance the numerical stability of the time spectral equation system, thereby allowing the use of aggressive numerical parameters to accelerate convergence. The stability analysis results are verified by a two-dimension bump under two different flow conditions and further assessed using a two-row compressor.
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Rajasekar, M., and R. Anbu. "Periodic boundary condition for Von Neumann CA with radius 2." In RECENT TRENDS IN PURE AND APPLIED MATHEMATICS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135251.
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Jagadeesh Anmala. "Time-step Criteria and Fourier (von Neumann) Stability Analysis of Two-Dimensional Finite Element Schemes for Shallow Water Equations." In 2005 Tampa, FL July 17-20, 2005. St. Joseph, MI: American Society of Agricultural and Biological Engineers, 2005. http://dx.doi.org/10.13031/2013.19081.
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Volders, K. "Stability of central finite difference schemes on non-uniform grids for the Black–Scholes PDE with Neumann boundary condition." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756624.
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Schussnig, Richard, Douglas R. Q. Pacheco, Manfred Kaltenbacher, and Thomas-Peter Fries. "Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12217.
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In various practically relevant incompressible flow problems, such as polymer flow or biomedicalengineering applications, the dependence of fluid viscosity on the local shear rate plays an impor-tant role. Standard techniques using inf-sup stable finite elements lead to saddle-point systemsposing a challenge even for state-of-the-art solvers and preconditioners.For efficiency, projection schemes or time-splitting methods decouple the governing equations forvelocity and pressure, resulting in more, but easier to solve linear systems. Doing so, boundaryconditions and correction terms at intermediate steps have to be carefully considered in order toprohibit spoiling accuracy. In the case of Newtonian incompressible fluids, pressure and velocitycorrection schemes of high-order accuracy have been devised (see, e.g. [1, 2]). However, the exten-sion to generalised Newtonian fluids is a non-trivial task and considered an open question. Deteixet al. [3] successfully adapted the popular rotational correction scheme to consider for shear-ratedependent viscosity, but this resulted in substantial numerical overhead caused by necessarily pro-jecting viscous stress components.In this contribution we address this shortcoming and present a split-step scheme, extending pre-vious work by Liu [4]. The new method is based on an explicit-implicit treatment of pressure,convection and viscous terms combined with a Pressure-Poisson equation equipped with fully con-sistent Neumann and Dirichlet boundary conditions. Through proper reformulation, the use ofstandard continuous finite element spaces is enabled due to low regularity requirements. Addition-ally, equal-order velocity-pressure pairs are applicable as in the original scheme.The stability, accuracy and efficiency of the higher-order splitting scheme is showcased in challeng-ing numerical examples of practical interest.[1] Karniadakis, G. E., Israeli, M. and Orszag, S. A. High-order splitting methods for the incom-pressible Navier-Stokes equations. J. Comput. Phys., (1991).[2] Timmermans, L.J.P., Minev, P.D. and Van de Vosse, F. N. An approximate projection schemefor incompressible flow using spectral elements. Internat. J. Numer. Methods Fluids, Vol.22(7), pp. 673–688, (1996).[3] Deteix, J. and Yakoubi, D. Shear rate projection schemes for non-Newtonian fluids, Comput.Methods Appl. Mech. Engrg., Vol. 354, pp. 620–636, (2019).[4] Liu, J. Open and traction boundary conditions for the incompressible NavierStokesequations.J. Comput. Phys., Vol. 228(19), pp. 7250..7267, (2009).
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Quintana Murillo, Joaqui´n, and Santos Bravo Yuste. "On an Explicit Difference Method for Fractional Diffusion and Diffusion-Wave Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86625.
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An explicit difference scheme for solving fractional diffusion and fractional diffusion-wave equations, in which the fractional derivative is in the Caputo form, is considered. The two equations are studied separately: for the fractional diffusion equation, the L1 discretization formula is employed, whereas the L2 discretization formula is used for the fractional diffusion-wave equation. Its accuracy is similar to other well-known explicit difference schemes, but its region of stability is larger. The stability analysis is carried out by means of a procedure similar to the standard von Neumann method. The stability bound, which is given in terms of the the Riemann Zeta function, is checked numerically.
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Zhang, Yuxuan, Dingxi Wang, Sen Zhang, and Yuze Zhu. "Numerical Stability Analysis of Implicit Solution Methods for Harmonic Balance Equations." In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/gt2024-125758.
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Abstract This paper presents an investigation into the numerical stability of various implicit solution methods for an efficient solution of harmonic balance equations for turbomachinery unsteady flows. Those implicit solution methods were proposed to enhance stability and accelerate the convergence of harmonic balance solutions by implicitly integrating the time spectral source term of a harmonic balance equation. They include the block Jacobi method (BJ), the Jacobi iteration method (JI), and their variants, i.e. the modified block Jacobi method (MBJ) and the modified Jacobi iteration method (MJI). These implicit treatments are typically combined with the lower upper symmetric Gauss-Seidel method (LU-SGS) as a preconditioner of a Runge-Kutta scheme. In this study, the von Neumann analysis is applied to evaluate the stability and damping properties of all these methods. The findings reveal that the LU-SGS/BJ and LU-SGS/MJI schemes can allow larger Courant numbers, in the order of hundreds, leading to a significant convergence speedup, while the LU-SGS/MBJ and LU-SGS/JI schemes fail to stabilize the solution, resulting in a Courant number below 10 as the grid-reduced frequency increases. The stabilization effect of the number of Jacobi iterations is also investigated. It is found that the minimum allowable relaxation factor does not change monotonically with the number of Jacobi iterations. Typically 2–4 Jacobi iterations are suggested for the stability and computational efficiency consideration, while any value larger than 4 is not recommended. The stability analysis results are numerically verified by solving the harmonic balance equation system for two cases. One is the inviscid flow over a two-dimensional bump with a pressure disturbance at the outlet. The other is the turbulent flow in a three-dimensional transonic compressor stage.
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Kunadian, Illayathambi, J. M. McDonough, and K. A. Tagavi. "Numerical Simulation of Heat Transfer Mechanisms During Femtosecond Laser Heating of Nano-Films Using 3-D Dual Phase Lag Model." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56823.
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In the present work we investigate femtosecond laser heating of nanoscale metal films irradiated by a pulsating laser in three dimensions using the Dual Phase Lag (DPL) model and consider laser heating at different locations on the metal film. A numerical solution based on an explicit finite-difference method has been employed to solve the DPL heat conduction equation. The stability criterion for selecting a time step size is obtained using von Neumann eigenmode analysis, and grid function convergence tests have been performed. The energy absorption rate, which is used to model femtosecond laser heating, has been modified to accommodate for the three-dimensional laser heating. We compare our results with classical diffusion and hyperbolic heat conduction models and demonstrate significant differences among these three approaches. The present research enables us to study ultrafast laser heating mechanisms of nano-films in 3D.