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Добірка наукової літератури з теми "Nonlocal Neumann boundary conditions"

Автор: Grafiati
Опубліковано: 10 березня 2023

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Статті в журналах з теми "Nonlocal Neumann boundary conditions"

1

Dipierro, Serena, Xavier Ros-Oton, and Enrico Valdinoci. "Nonlocal problems with Neumann boundary conditions." Revista Matemática Iberoamericana 33, no. 2 (2017): 377–416. http://dx.doi.org/10.4171/rmi/942.

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2

You, Huaiqian, Xin Yang Lu, Nathaniel Trask, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 55 (2021): S811—S851. http://dx.doi.org/10.1051/m2an/2020058.

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Анотація:
In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞(Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.
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3

You, Huaiqian, XinYang Lu, Nathaniel Task, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4 (June 18, 2020): 1373–413. http://dx.doi.org/10.1051/m2an/2019089.

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Анотація:
In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞ (Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.
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4

Turmetov, B. Kh, and V. V. Karachik. "NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 51–58. http://dx.doi.org/10.14529/mmph220205.

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Анотація:
The solvability conditions for a class of boundary value problems for a nonlocal biharmonic equation in the unit ball with the Neumann conditions on the boundary are studied. The nonlocality of the equation is generated by some orthogonal matrix. The presence and uniqueness of a solution to the proposed Neumann boundary condition is examined, and an integral representation of the solution to the Dirichlet problem in terms of the Green's function for the biharmonic equation in the unit ball is obtained. First, some auxiliary statements are established: the Green's function of the Dirichlet problem for the biharmonic equation in the unit ball is given, the representation of the solution to the Dirichlet problem in terms of this Green's function is written, and the values of the integrals of the functions perturbed by the orthogonal matrix are found. Then a theorem for the solution to the auxiliary Dirichlet problem for a nonlocal biharmonic equation in the unit ball is proved. The solution to this problem is written using the Green's function of the Dirichlet problem for the regular biharmonic equation. An example of solving a simple problem for a nonlocal biharmonic equation is given. Next, we formulate a theorem on necessary and sufficient conditions for the solvability of the Neumann boundary condition for a nonlocal biharmonic equation. The main theorem is proved based on two lemmas, with the help of which it is possible to transform the solvability conditions of the Neumann boundary condition to a simpler form. The solution to the Neumann boundary condition is presented through the solution to the auxiliary Dirichlet problem.
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5

Bogoya, Mauricio, and Cesar A. Gómez S. "On a nonlocal diffusion model with Neumann boundary conditions." Nonlinear Analysis: Theory, Methods & Applications 75, no. 6 (April 2012): 3198–209. http://dx.doi.org/10.1016/j.na.2011.12.019.

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6

Aksoylu, Burak, and Fatih Celiker. "Nonlocal problems with local Dirichlet and Neumann boundary conditions." Journal of Mechanics of Materials and Structures 12, no. 4 (May 20, 2017): 425–37. http://dx.doi.org/10.2140/jomms.2017.12.425.

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7

Gomez, C. A., and J. A. Caicedo. "ON A RESCALED NONLOCAL DIFFUSION PROBLEM WITH NEUMANN BOUNDARY CONDITIONS." Advances in Mathematics: Scientific Journal 10, no. 8 (August 7, 2021): 3013–22. http://dx.doi.org/10.37418/amsj.10.8.2.

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Анотація:
In this work, we consider the rescaled nonlocal diffusion problem with Neumann Boundary Conditions \[ \begin{cases} u_t^{\epsilon}(x,t)=\displaystyle\frac{1}{\epsilon^2} \int_{\Omega}J_{\epsilon}(x-y)(u^\epsilon(y,t)-u^\epsilon(x,t))dy\\ \qquad \qquad+\displaystyle\frac{1}{\epsilon}\int_{\partial \Omega}G_\epsilon(x-y)g(y,t)dS_y,\\ u^\epsilon(x,0)=u_0(x), \end{cases} \] where $\Omega\subset\mathbb{R}^{N}$ is a bounded, connected and smooth domain, $g$ a positive continuous function, $J_\epsilon(z)=C_1\frac{1}{\epsilon^N}J(\frac{z}{\epsilon}), G_\epsilon(x)=C_1\frac{1}{\epsilon^N}G(\frac{x}{\epsilon}),$ $J$ and $G$ well defined kernels, $C_1$ a normalization constant. The solutions of this model have been used without prove to approximate the solutions of a family of nonlocal diffusion problems to solutions of the respective analogous local problem. We prove existence and uniqueness of the solutions for this problem by using the Banach Fixed Point Theorem. Finally, some conclusions are given.
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8

Andreu, F., J. M. Mazón, J. D. Rossi, and J. Toledo. "A nonlocal p-Laplacian evolution equation with Neumann boundary conditions." Journal de Mathématiques Pures et Appliquées 90, no. 2 (August 2008): 201–27. http://dx.doi.org/10.1016/j.matpur.2008.04.003.

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9

Agarwal, Praveen, Jochen Merker, and Gregor Schuldt. "Singular Integral Neumann Boundary Conditions for Semilinear Elliptic PDEs." Axioms 10, no. 2 (April 24, 2021): 74. http://dx.doi.org/10.3390/axioms10020074.

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Анотація:
In this article, we discuss semilinear elliptic partial differential equations with singular integral Neumann boundary conditions. Such boundary value problems occur in applications as mathematical models of nonlocal interaction between interior points and boundary points. Particularly, we are interested in the uniqueness of solutions to such problems. For the sublinear and subcritical case, we calculate, on the one hand, illustrative, rather explicit solutions in the one-dimensional case. On the other hand, we prove in the general case the existence and—via the strong solution of an integro-PDE with a kind of fractional divergence as a lower order term—uniqueness up to a constant.
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10

Karachik, Valery, Batirkhan Turmetov, and Hongfen Yuan. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball." Mathematics 10, no. 7 (April 3, 2022): 1158. http://dx.doi.org/10.3390/math10071158.

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Анотація:
Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green’s functions.
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Більше джерел

Дисертації з теми "Nonlocal Neumann boundary conditions"

1

Roman, Svetlana. "Green's functions for boundary-value problems with nonlocal boundary conditions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111227_092148-01085.

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Анотація:
In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introduction the topicality of the problem is defined, the goals and tasks of the research are formulated, the scientific novelty of the dissertation, the methodology of research, the practical value and the significance of the results are presented. m-order differential problem and its Green's function are investigated in the first chapter. The relation between two Green's functions and the existence condition of Green's function are obtained. In the second chapter, the main definitions and results of the first chapter are formulated for the second-order differential equation with additional conditions. In the examples the application of the received results is analyzed for problems with nonlocal boundary conditions in detail. In the third chapter, the second-order difference equation with two additional conditions is considered. The expression of Green's function and its existence... [to full text]
Disertacijoje tiriami antros ir aukštesnės eilės diferencialinis ir diskretusis uždaviniai su įvairiomis, tame tarpe ir nelokaliosiomis, sąlygomis, kurios yra aprašytos tiesiškai nepriklausomais tiesiniais funkcionalais. Pateikiamos šių uždavinių Gryno funkcijų išraiškos ir jų egzistavimo sąlygos, jei žinoma homogeninės lygties fundamentalioji sistema. Gautas dviejų Gryno funkcijų sąryšis uždaviniams su ta pačia lygtimi, bet su papildomomis sąlygomis. Rezultatai pritaikomi uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Įvadiniame skyriuje aprašyta tiriamoji problema ir temos objektas, išanalizuotas temos aktualumas, išdėstyti darbo tikslai, uždaviniai, naudojama tyrimų metodika, mokslinis darbo naujumas ir gautų rezultatų reikšmė, pateikti ginamieji teiginiai ir darbo rezultatų aprobavimas. m-tosios eilės diferencialinis uždavinys ir jo Gryno funkcija nagrinėjami pirmajame skyriuje. Surastas uždavinio sprendinys, išreikštas per Gryno funkciją. Pateikta Gryno funkcijos egzistavimo sąlyga. Antrajame skyriuje pateikti pirmojo skyriaus pagrindiniai apibrėžimai ir rezultatai antros eilės diferencialinei lygčiai. Pavyzdžiuose išsamiai išanalizuotas gautų rezultatų pritaikymas uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Trečiajame skyriuje nagrinėjama antros eilės diskrečioji lygtis su dviem sąlygomis. Surastos diskrečiosios Gryno funkcijos išraiška ir jos egzistavimo sąlyga. Taip pat pateiktas dviejų Gryno funkcijų sąryšis, kuris leidžia surasti diskrečiosios... [toliau žr. visą tekstą]
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2

Mäder-Baumdicker, Elena [Verfasser], and Ernst [Akademischer Betreuer] Kuwert. "The area preserving curve shortening flow with Neumann free boundary conditions = Der flächenerhaltende Curve Shortening Fluss mit einer freien Neumann-Randbedingung." Freiburg : Universität, 2014. http://d-nb.info/1123480648/34.

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3

Benincasa, Tommaso <1981&gt. "Analysis and optimal control for the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3066/1/benincasa_tommaso_tesi.pdf.

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4

Benincasa, Tommaso <1981&gt. "Analysis and optimal control for the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3066/.

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5

PERROTTA, Antea. "Differential Formulation coupled to the Dirichlet-to-Neumann operator for scattering problems." Doctoral thesis, Università degli studi di Cassino, 2020. http://hdl.handle.net/11580/75845.

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Анотація:
This Thesis proposes the use of the Dirichlet-to-Neumann (DtN) operator to improve the accuracy and the efficiency of the numerical solution of an electromagnetic scattering problem, described in terms of a differential formulation. From a general perspective, the DtN operator provides the “connection” (the mapping) between the Dirichlet and the Neumann data onto a proper closed surface. This allows truncation of the computational domain when treating a scattering problem in an unbounded media. Moreover, the DtN operator provides an exact boundary condition, in contrast to other methods such as Perfectly Matching Layer (PML) or Absorbing Boundary Conditions (ABC). In addition, when the surface where the DtN is introduced has a canonical shape, as in the present contribution, the DtN operator can be computed analytically. This thesis is focused on a 2D geometry under TM illumination. The numerical model combines a differential formulation with the DtN operator defined onto a canonical surface where it can be computed analytically. Test cases demonstrate the accuracy and the computational advantage of the proposed technique.
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6

Coco, Armando. "Finite-Difference Ghost-Cell Multigrid Methods for Elliptic problems with Mixed Boundary Conditions and Discontinuous Coefficients." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1107.

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Анотація:
The work of this thesis is devoted to the development of an original and general numerical method for solving the elliptic equation in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, ...) using Cartesian grids. It can be then considered an immersed boundary method, and the scheme we use is based on a finite-difference ghost-cell technique. The entire problem is solved by an effective multigrid solver, whose components have been suitably constructed in order to be applied to the scheme. The method is extended to the more challenging case of discontinuous coefficients, and the multigrid is suitable modified in order to attain the optimal convergence factor of the whole iteration procedure. The development of the multigrid is an important feature of this thesis, since multigrid solvers for discontinuous coefficients maintaining the optimal convergence factor without depending on the jump in the coefficient and on the problem size is recently studied in literature. The method is second order accurate in the solution and its gradient. A convergence proof for the first order scheme is provided, while second order is confirmed by several numerical tests.
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7

Cao, Shunxiang. "Numerical Methods for Fluid-Solid Coupled Simulations: Robin Interface Conditions and Shock-Dominated Applications." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/93514.

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Анотація:
This dissertation investigates the development of numerical algorithms for coupling computational fluid dynamics (CFD) and computational solid dynamics (CSD) solvers, and the use of these solvers for simulating fluid-solid interaction (FSI) problems involving large deformation, shock waves, and multiphase flow. The dissertation consists of two parts. The first part investigates the use of Robin interface conditions to resolve the well-known numerical added-mass instability, which affects partitioned coupling procedures for solving problems with incompressible flow and strong added-mass effect. First, a one-parameter Robin interface condition is developed by linearly combining the conventional Dirichlet and Neumann interface conditions. Next, a numerical algorithm is developed to implement the Robin interface condition in an embedded boundary method for coupling a parallel, projection-based incompressible viscous flow solver with a nonlinear finite element solid solver. Both an analytical study and a numerical study reveal that the new algorithm can clearly outperform conventional Dirichlet-Neumann procedures in terms of both stability and accuracy, when the parameter value is carefully selected. Moreover, the studies also indicate that the optimal parameter value depends on the materials and geometry of the problem. Therefore, to efficiently solve FSI problems involving non-uniform structures, a generalized Robin interface condition is presented, in which the constant parameter is replaced by a spatially varying function that depends on the local material and geometric properties of the structure. Numerical experiments using two benchmark problems show that the spatially varying Robin interface condition can clearly improve numerical accuracy compared to the constant- parameter version with the same computational cost. The second part of this dissertation focuses on simulating complex FSI problems featuring shock waves, multiphase flow (e.g., bubbles), and shock-induced material damage and fracture. A recently developed three-dimensional computational framework is employed, which couples a multiphase, compressible CFD solver and a nonlinear finite element CSD solver using an embedded boundary method and a partitioned procedure. In particular, the CFD solver applies a level-set method to capture the evolution of the bubble surface, and the CSD solver utilizes a continuum damage mechanics model and an element erosion method to simulate the dynamic fracture of the material. Two computational studies are presented. The first one investigates the dynamic response and failure of a brittle material exposed to a prescribed shock wave. The predictive capability of the computational framework is first demonstrated by simulating a series of laboratory experiments in the context of shock wave lithotripsy. Then, a parametric study is conducted to elucidate the significant effects of the shock wave's profile on material damage. In the second study, the computational framework is applied to simulate shock-induced bubble collapse near various solid and soft materials. The reciprocal effect of the material's properties (e.g., acoustic impedance, Young's modulus) on bubble dynamics is discussed in detail.
Doctor of Philosophy
Numerical simulations that couple computational fluid dynamics (CFD) solvers and computational solid dynamics (CSD) solvers have been widely used in the solution of nonlinear fluid-solid interaction (FSI) problems underlying many engineering applications. This is primarily because they are based on partitioned solutions of fluid and solid subsystems, which facilitates the use of existing numerical methods and computational codes developed for each subsystem. The first part of this dissertation focuses on developing advanced numerical algorithms for coupling the two subsystems. The aim is to resolve a major numerical instability issue that occurs when solving problems involving incompressible, heavy fluids and thin, lightweight structures. Specifically, this work first presents a new coupling algorithm based on a one-parameter Robin interface condition. An embedded boundary method is developed to enforce the Robin interface condition, which can be advantageous in solving problems involving complex geometry and large deformation. The new coupling algorithm has been shown to significantly improve numerical stability when the constant parameter is carefully selected. Next, the constant parameter is generalized into a spatially varying function whose local value is determined by the local material and geometric properties of the structure. Numerical studies show that when solving FSI problems involving non-uniform structures, using this spatially varying Robin interface condition can outperform the constant-parameter version in both stability and accuracy under the same computational cost. In the second part of this dissertation, a recently developed three-dimensional multiphase CFD - CSD coupled solver is extended to simulate complex FSI problems featuring shock wave, bubbles, and material damage and fracture. The aim is to understand the material’s response to loading induced by a shock wave and the collapse of nearby bubbles, which is important for advancing the beneficial use of shock wave and bubble collapse for material modification. Two computational studies are presented. The first one investigates the dynamic response and failure of a brittle material exposed to a prescribed shock wave. The causal relationship between shock loading and material failure, and the effects of the shock wave’s profile on material damage are discussed. The second study investigates the shock-induced bubble collapse near various solid and soft materials. The two-way interaction between bubble dynamics and materials response, and the reciprocal effects of the material’s properties are discussed in detail.
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8

Roman, Svetlana. "Gryno funkcijos uždaviniams su nelokaliosiomis kraštinėmis sąlygomis." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111227_092259-85107.

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Анотація:
Disertacijoje tiriami antros ir aukštesnės eilės diferencialinis ir diskretusis uždaviniai su įvairiomis, tame tarpe ir nelokaliosiomis, sąlygomis, kurios yra aprašytos tiesiškai nepriklausomais tiesiniais funkcionalais. Pateikiamos šių uždavinių Gryno funkcijų išraiškos ir jų egzistavimo sąlygos, jei žinoma homogeninės lygties fundamentalioji sistema. Gautas dviejų Gryno funkcijų sąryšis uždaviniams su ta pačia lygtimi, bet su papildomomis sąlygomis. Rezultatai pritaikomi uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Įvadiniame skyriuje aprašyta tiriamoji problema ir temos objektas, išanalizuotas temos aktualumas, išdėstyti darbo tikslai, uždaviniai, naudojama tyrimų metodika, mokslinis darbo naujumas ir gautų rezultatų reikšmė, pateikti ginamieji teiginiai ir darbo rezultatų aprobavimas. m-tosios eilės diferencialinis uždavinys ir jo Gryno funkcija nagrinėjami pirmajame skyriuje. Surastas uždavinio sprendinys, išreikštas per Gryno funkciją. Pateikta Gryno funkcijos egzistavimo sąlyga. Antrajame skyriuje pateikti pirmojo skyriaus pagrindiniai apibrėžimai ir rezultatai antros eilės diferencialinei lygčiai. Pavyzdžiuose išsamiai išanalizuotas gautų rezultatų pritaikymas uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Trečiajame skyriuje nagrinėjama antros eilės diskrečioji lygtis su dviem sąlygomis. Surastos diskrečiosios Gryno funkcijos išraiška ir jos egzistavimo sąlyga. Taip pat pateiktas dviejų Gryno funkcijų sąryšis, kuris leidžia surasti diskrečiosios... [toliau žr. visą tekstą]
In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introduction the topicality of the problem is defined, the goals and tasks of the research are formulated, the scientific novelty of the dissertation, the methodology of research, the practical value and the significance of the results are presented. m-order differential problem and its Green's function are investigated in the first chapter. The relation between two Green's functions and the existence condition of Green's function are obtained. In the second chapter, the main definitions and results of the first chapter are formulated for the second-order differential equation with additional conditions. In the examples the application of the received results is analyzed for problems with nonlocal boundary conditions in detail. In the third chapter, the second-order difference equation with two additional conditions is considered. The expression of Green's function and its existence... [to full text]
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9

Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation with inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions for a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149965.

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Анотація:
The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.
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10

Bensiali, Bouchra. "Approximations numériques en situations complexes : applications aux plasmas de tokamak." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4332/document.

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Анотація:
Motivée par deux problématiques liées aux plasmas de tokamak, cette thèse propose deux méthodes d'approximation numérique pour deux problèmes mathématiques s'y rattachant. D'une part, pour l'étude du transport turbulent de particules, une méthode numérique basée sur les schémas de subdivision est présentée pour la simulation de trajectoires de particules dans un champ de vitesse fortement variable. D'autre part, dans le cadre de la modélisation de l'interaction plasma-paroi, une méthode de pénalisation est proposée pour la prise en compte de conditions aux limites de type Neumann ou Robin. Analysées sur des problèmes modèles de complexité croissante, ces méthodes sont enfin appliquées dans des situations plus réalistes d'intérêt pratique dans l'étude du plasma de bord
Motivated by two issues related to tokamak plasmas, this thesis proposes two numerical approximation methods for two mathematical problems associated with them. On the one hand, in order to study the turbulent transport of particles, a numerical method based on subdivision schemes is presented for the simulation of particle trajectories in a strongly varying velocity field. On the other hand, in the context of modeling the plasma-wall interaction, a penalization method is proposed to take into account Neumann or Robin boundary conditions. Analyzed on model problems of increasing complexity, these methods are finally applied in more realistic situations of practical interest in the study of the edge plasma
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Книги з теми "Nonlocal Neumann boundary conditions"

1

E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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E, Zorumski William, and Langley Research Center, eds. Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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4

E, Zorumski W., Watson Willie R, and Langley Research Center, eds. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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E, Zorumski W., Watson Willie R, and Langley Research Center, eds. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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6

Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for Helmholtz equations with Neumann boundary conditions. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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10

Periodic time-domain nonlocal nonreflecting boundary conditions for duct acoustics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Частини книг з теми "Nonlocal Neumann boundary conditions"

1

Sayas, Francisco-Javier, Thomas S. Brown, and Matthew E. Hassell. "Neumann boundary conditions." In Variational Techniques for Elliptic Partial Differential Equations, 3–26. Boca Raton, Florida : CRC Press, [2019]: CRC Press, 2019. http://dx.doi.org/10.1201/9780429507069-6.

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2

Arendt, Wolfgang, and Karsten Urban. "Neumann and Robin boundary conditions." In Partial Differential Equations, 241–68. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13379-4_7.

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3

Droniou, Jérôme, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin. "Neumann, Fourier and Mixed Boundary Conditions." In Mathématiques et Applications, 67–97. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-79042-8_3.

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4

Adomian, George. "Decomposition Solutions for Neumann Boundary Conditions." In Solving Frontier Problems of Physics: The Decomposition Method, 190–95. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8289-6_7.

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5

Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Nonlinear Elliptic Equations with Neumann Boundary Conditions." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 387–436. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_12.

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6

Leung, Anthony W. "Large Systems under Neumann Boundary Conditions, Bifurcations." In Systems of Nonlinear Partial Differential Equations, 325–73. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-015-3937-1_7.

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7

Feltrin, Guglielmo. "Neumann and Periodic Boundary Conditions: Existence Results." In Positive Solutions to Indefinite Problems, 69–99. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_3.

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Feltrin, Guglielmo. "Neumann and Periodic Boundary Conditions: Multiplicity Results." In Positive Solutions to Indefinite Problems, 101–30. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_4.

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Aksoylu, Burak, Fatih Celiker, and Orsan Kilicer. "Nonlocal Operators with Local Boundary Conditions: An Overview." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1–38. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-22977-5_34-1.

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Aksoylu, Burak, Fatih Celiker, and Orsan Kilicer. "Nonlocal Operators with Local Boundary Conditions: An Overview." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1293–330. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-58729-5_34.

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Тези доповідей конференцій з теми "Nonlocal Neumann boundary conditions"

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Parks, Michael. "On Neumann-type Boundary Conditions for Nonlocal Models." In Proposed for presentation at the Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology held September 27-29, 2021 in San Diego, CA. US DOE, 2021. http://dx.doi.org/10.2172/1889347.

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Li, Fan, and Lingling Zhang. "Blow-up phenomenon of parabolic equations with nonlocal terms under Neumann boundary conditions." In 2021 3rd International Conference on Industrial Artificial Intelligence (IAI). IEEE, 2021. http://dx.doi.org/10.1109/iai53119.2021.9619348.

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D'Elia, Marta. "Challenges in nonlocal modeling: nonlocal boundary conditions and nonlocal interfaces." In Proposed for presentation at the WCCM 2020 held January 11-15, 2021 in Virtual. US DOE, 2020. http://dx.doi.org/10.2172/1833494.

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LOMBARDO, M. C., and M. SAMMARTINO. "NONLOCAL BOUNDARY CONDITIONS FOR THE NAVIER–STOKES EQUATIONS." In Proceedings of the 13th Conference on WASCOM 2005. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773616_0047.

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Arda, Mustafa, and Metin Aydogdu. "Nonlocal effect on boundary conditions of cantilever nanobeam." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026430.

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Gámez, José L. "Local bifurcation for elliptic problems: Neumann versus Dirichlet boundary conditions." In The First 60 Years of Nonlinear Analysis of Jean Mawhin. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702906_0006.

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Kuryliak, D. B., and Z. T. Nazarchuk. "Wave scattering by wedge with Dirichlet and Neumann boundary conditions." In Proceedings of III International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. DIPED-98. IEEE, 1998. http://dx.doi.org/10.1109/diped.1998.730938.

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Piasecki, Tomasz. "Steady compressible Oseen flow with slip boundary conditions." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-16.

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Nalbant, Nese, and Yasar Sozen. "The positivity of differential operator with nonlocal boundary conditions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756198.

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Ge, Zanyu, Huaibao Xiao, Guizhen Lu, and Dongdong Zeng. "Horizontal diffraction based on parabolic equation with nonlocal boundary conditions." In 2017 IEEE 5th International Symposium on Electromagnetic Compatibility (EMC-Beijing). IEEE, 2017. http://dx.doi.org/10.1109/emc-b.2017.8260444.

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Звіти організацій з теми "Nonlocal Neumann boundary conditions"

1

D'Elia, Marta, and Yue Yu. On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models. Office of Scientific and Technical Information (OSTI), June 2021. http://dx.doi.org/10.2172/1817978.

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D'Elia, Marta, Pavel Bochev, Mauro Perego, Jeremy Trageser, and David Littlewood. An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions. Office of Scientific and Technical Information (OSTI), October 2021. http://dx.doi.org/10.2172/1825041.

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