Academic literature on the topic 'Poincaré-Steklov operators'

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Journal articles on the topic "Poincaré-Steklov operators"

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Novikov, R. G., and I. A. Taimanov. "Darboux Moutard Transformations and Poincaré—Steklov Operators." Proceedings of the Steklov Institute of Mathematics 302, no. 1 (2018): 315–24. http://dx.doi.org/10.1134/s0081543818060160.

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Deparis, Simone, Marco Discacciati, Gilles Fourestey, and Alfio Quarteroni. "Fluid–structure algorithms based on Steklov–Poincaré operators." Computer Methods in Applied Mechanics and Engineering 195, no. 41-43 (2006): 5797–812. http://dx.doi.org/10.1016/j.cma.2005.09.029.

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Demidov, A. S., and A. S. Samokhin. "Explicit Numerically Implementable Formulas for Poincaré–Steklov Operators." Computational Mathematics and Mathematical Physics 64, no. 2 (2024): 237–47. http://dx.doi.org/10.1134/s0965542524020040.

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Natarajan, Ramesh. "Domain Decomposition Using Spectral Expansions of Steklov–Poincaré Operators." SIAM Journal on Scientific Computing 16, no. 2 (1995): 470–95. http://dx.doi.org/10.1137/0916029.

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Xu, Jinchao, та Shuo Zhang. "Norms of Discrete Trace Functions of (Ω) and (Ω)". Computational Methods in Applied Mathematics 12, № 4 (2012): 500–512. http://dx.doi.org/10.2478/cmam-2012-0025.

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AbstractThis paper discusses the constructive and computational presentations of several non-local norms of discrete trace functions of H¹(Ω) and H²(Ω) defined on the boundary or interface of an unstructured grid. We transform the nonlocal norms of trace functions to local norms of certain functions defined on the whole domain by constructing isomorphic extension operators. A unified approach is used to explore several typical examples. Additionally, we also discuss exactly invertible Poincaré–Steklov operators and their discretization.
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ACHDOU, YVES, and FREDERIC NATAF. "PRECONDITIONERS FOR THE MORTAR METHOD BASED ON LOCAL APPROXIMATIONS OF THE STEKLOV-POINCARÉ OPERATOR." Mathematical Models and Methods in Applied Sciences 05, no. 07 (1995): 967–97. http://dx.doi.org/10.1142/s0218202595000516.

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Many implicit Navier-Stokes solvers involve the discretization of an elliptic partial differential equation of the type −Δu+ηu=f, where η is a large positive parameter. The discretization studied here is the mortar finite element method, a domain decomposition method allowing nonmatching meshes at subdomains interfaces. Two kinds of improvements are proposed here in order to reduce the condition number of the corresponding linear systems: the first one lies on building preconditioners by approximating Steklov-Poincaré operators on subdomains boundaries by second-order partial differential oper
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Natarajan, Ramesh. "Domain Decomposition using Spectral Expansions of Steklov--Poincaré Operators II: A Matrix Formulation." SIAM Journal on Scientific Computing 18, no. 4 (1997): 1187–99. http://dx.doi.org/10.1137/s1064827594274309.

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NICAISE, SERGE, and ANNA-MARGARETE SÄNDIG. "TRANSMISSION PROBLEMS FOR THE LAPLACE AND ELASTICITY OPERATORS: REGULARITY AND BOUNDARY INTEGRAL FORMULATION." Mathematical Models and Methods in Applied Sciences 09, no. 06 (1999): 855–98. http://dx.doi.org/10.1142/s0218202599000403.

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This paper is devoted to some transmission problems for the Laplace and linear elasticity operators in two- and three-dimensional nonsmooth domains. We investigate the behaviour of harmonic and linear elastic fields near geometrical singularities, especially near corner points or edges where the interface intersects with the boundaries. We give a short overview about the known results for 2-D problems and add new results for 3-D problems. Numerical results for the calculation of the singular exponents in the asymptotic expansion are presented for both two- and three-dimensional problems. Some
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Hao, Sijia, and Per-Gunnar Martinsson. "A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré–Steklov operators." Journal of Computational and Applied Mathematics 308 (December 2016): 419–34. http://dx.doi.org/10.1016/j.cam.2016.05.013.

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Zhang, Yi, Varun Jain, Artur Palha, and Marc Gerritsma. "The Discrete Steklov–Poincaré Operator Using Algebraic Dual Polynomials." Computational Methods in Applied Mathematics 19, no. 3 (2019): 645–61. http://dx.doi.org/10.1515/cmam-2018-0208.

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AbstractIn this paper, we will use algebraic dual polynomials to set up a discrete Steklov–Poincaré operator for the mixed formulation of the Poisson problem. The method will be applied in curvilinear coordinates and to a test problem which contains a singularity. Exponential convergence of the trace variable in {H^{1/2}}-norm will be shown.
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Dissertations / Theses on the topic "Poincaré-Steklov operators"

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Zreik, Mahdi. "Spectral properties of Dirac operators on certain domains." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0085.

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Cette thèse se focalise sur l'étude spectrale des modèles de perturbations de l'opérateur de Dirac libre en dimensions 2 et 3.Le premier chapitre de cette thèse étudie la perturbation de l'opérateur de Dirac par une grande masse M, supportée sur un domaine. Notre objectif principal est d'établir, sous la condition d'une masse M suffisamment grande, la convergence de l'opérateur perturbé vers l'opérateur de Dirac avec la condition au bord MIT bag, au sens de la norme de la résolvante. Pour se faire, nous introduisons ce que nous appelons les opérateurs Poincaré-Steklov (PS) (comme un analogue d
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Hilal, Mohammed Azeez. "Domain decomposition like methods for solving an electrocardiography inverse problem." Thesis, Nantes, 2016. http://www.theses.fr/2016NANT4060.

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L’objectif de cette thèse est d’étudier un problème électrocardiographique (ECG), modélisant l’activité électrique cardiaque en utilisant un modèle bidomaine stationnaire. Deux types de modélisation sont considérées : la modélisation basée sur un modèle mathématique directe et la modélisation basée sur un problème inverse de Cauchy. Dans le premier cas, le problème directe est résolu en utilisant la méthode de décomposition de domaine et l’approximation par la méthode des éléments finis. Dans le deuxième cas le problème inverse de Cauchy de l’ECG a été reformulé en un problème de point fixe. P
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Perlich, Lars. "Holomorphic Semiflows and Poincaré-Steklov Semigroups." Doctoral thesis, 2019. https://tud.qucosa.de/id/qucosa%3A36097.

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Die Arbeit untersucht einen überraschenden Zusammenhang zwischen Halbflüssen von holomorphen Selbstabbildungen auf einfach zusammenhängenden Gebieten und Halbgruppen, die von Poincaré-Steklov Operatoren erzeugt werden. Mithilfe von Erzeuger von Kompositionshalbgruppen auf Banachräumen von analytischen Funktionen werden insbesondere Dirichlet-zu-Neumann und Dirichlet-zu-Robin Operatoren konstruiert. Dieser Zugang eröffnet einen neuen Ansatz für das Studium partiellen Differentialgleichungen, die mit solchen Operatoren assoziiert sind.<br>We study a surprising connection between semiflows of ho
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Held, Joachim. "Ein Gebietszerlegungsverfahren für parabolische Probleme im Zusammenhang mit Finite-Volumen-Diskretisierung." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B39E-E.

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Book chapters on the topic "Poincaré-Steklov operators"

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Khoromskij, Boris N., and Gabriel Wittum. "Elliptic Poincaré-Steklov Operators." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18777-3_2.

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Quarteroni, A., and A. Valli. "Theory and Application of Steklov-Poincaré Operators for Boundary-Value Problems." In Applied and Industrial Mathematics. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-009-1908-2_14.

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Hu, Qiya. "A New Kind of Multilevel Solver for Second Order Steklov-Poincaré Operators." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75199-1_49.

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Novotny, Antonio André, Jan Sokołowski, and Antoni Żochowski. "Steklov–Poincaré Operator for Helmholtz Equation." In Applications of the Topological Derivative Method. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05432-8_3.

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Gosse, Laurent. "Viscous Equations Treated with $$\mathcal{L}$$ -Splines and Steklov-Poincaré Operator in Two Dimensions." In Innovative Algorithms and Analysis. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49262-9_6.

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