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Journal articles on the topic 'Poincaré-Steklov operators'

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Published: 25 May 2024

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1

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

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2

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 (August 2006): 5797–812. http://dx.doi.org/10.1016/j.cma.2005.09.029.

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3

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

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4

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

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5

Xu, Jinchao, and Shuo Zhang. "Norms of Discrete Trace Functions of (Ω) and (Ω)." Computational Methods in Applied Mathematics 12, no. 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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6

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 (November 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 operators; the second one consists in making a nonstandard choice of jump operators at subdomains interfaces. Both ideas are tested numerically.
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7

Natarajan, Ramesh. "Domain Decomposition using Spectral Expansions of Steklov--Poincaré Operators II: A Matrix Formulation." SIAM Journal on Scientific Computing 18, no. 4 (July 1997): 1187–99. http://dx.doi.org/10.1137/s1064827594274309.

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8

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 (August 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 spectral properties of the corresponding parameter depending operator bundles are also given. Furthermore, we derive boundary integral equations for the solution of the transmission problems, which lead finally to "local" pseudo-differential operator equations with corresponding Steklov–Poincaré operators on the interface. We discuss their solvability and uniqueness. The above regularity results are used in order to characterize the regularity of the solutions of these integral equations.
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9

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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10

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 (July 1, 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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11

Xu, Jinchao, and Sheng Zhang. "Preconditioning the Poincaré-Steklov operator by using Green's function." Mathematics of Computation 66, no. 217 (January 1, 1997): 125–39. http://dx.doi.org/10.1090/s0025-5718-97-00799-0.

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12

Kharytonov, A. A. "Solution of elliptic inverse problems using the Poincaré-Steklov operator." International Journal of Applied Electromagnetics and Mechanics 19, no. 1-4 (April 24, 2004): 63–67. http://dx.doi.org/10.3233/jae-2004-537.

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13

Menad, M., and C. Daveau. "Comparison of several discretization methods of the Steklov–Poincaré operator." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 19, no. 3 (2006): 271–87. http://dx.doi.org/10.1002/jnm.611.

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14

Nazarov, S. A. "Finite-Dimensional Approximations of the Steklov–Poincaré Operator in Periodic Elastic Waveguides." Doklady Physics 63, no. 7 (July 2018): 307–11. http://dx.doi.org/10.1134/s1028335818070108.

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15

Demarcke, Pieterjan, and Hendrik Rogier. "The Poincaré–Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations." IEEE Antennas and Wireless Propagation Letters 10 (2011): 503–6. http://dx.doi.org/10.1109/lawp.2011.2157072.

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16

Bobylev, A. A. "On the Positive Definiteness of the Poincaré–Steklov Operator for Elastic Half-Plane." Moscow University Mechanics Bulletin 76, no. 6 (November 2021): 156–62. http://dx.doi.org/10.3103/s0027133021060029.

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17

Arfi, Kevin, and Anna Rozanova-Pierrat. "Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d-sets." Discrete & Continuous Dynamical Systems - S 12, no. 1 (2019): 1–26. http://dx.doi.org/10.3934/dcdss.2019001.

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18

Nazarov, S. A. "Finite-Dimensional Approximations of the Steklov–Poincaré Operator for the Helmholtz Equation in Periodic Waveguides." Journal of Mathematical Sciences 232, no. 4 (June 7, 2018): 461–502. http://dx.doi.org/10.1007/s10958-018-3890-1.

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19

Bobylev, A. A. "Computing a Transfer Function of the Poincaré–Steklov Operator for a Functionally Graded Elastic Strip." Moscow University Mechanics Bulletin 78, no. 5 (October 2023): 134–42. http://dx.doi.org/10.3103/s0027133023050023.

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20

Fokoué, Diane, and Yves Bourgault. "Numerical analysis of finite element methods for the cardiac extracellular-membrane-intracellular model: Steklov–Poincaré operator and spatial error estimates." ESAIM: Mathematical Modelling and Numerical Analysis 57, no. 4 (July 2023): 2595–621. http://dx.doi.org/10.1051/m2an/2023052.

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The extracellular-membrane-intracellular (EMI) model consists in a set of Poisson equations in two adjacent domains, coupled on interfaces with nonlinear transmission conditions involving a system of ODEs. The unusual coupling of PDEs and ODEs on the boundary makes the EMI models challenging to solve numerically. In this paper, we reformulate the problem on the interface using a Steklov–Poincaré operator. We then discretize the model in space using a finite element method (FEM). We prove the existence of a semi-discrete solution using a reformulation as an ODE system on the interface. We derive stability and error estimates for the FEM. Finally, we propose a manufactured solution and use it to perform numerical tests. The order of convergence of the numerical method agrees with what is expected on the basis of the theoretical analysis of the convergence.
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21

Aletti, Matteo, and Damiano Lombardi. "A reduced-order representation of the Poincaré-Steklov operator: an application to coupled multi-physics problems." International Journal for Numerical Methods in Engineering 111, no. 6 (January 20, 2017): 581–600. http://dx.doi.org/10.1002/nme.5490.

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22

Dobbelaere, D., D. De Zutter, J. Van Hese, J. Sercu, T. Boonen, and H. Rogier. "A Calderón multiplicative preconditioner for the electromagnetic Poincaré–Steklov operator of a heterogeneous domain with scattering applications." Journal of Computational Physics 303 (December 2015): 355–71. http://dx.doi.org/10.1016/j.jcp.2015.09.052.

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23

Hardin, Thomas J., and Christopher A. Schuh. "Fast finite element calculation of effective conductivity of random continuum microstructures: The recursive Poincaré–Steklov operator method." Journal of Computational Physics 342 (August 2017): 1–12. http://dx.doi.org/10.1016/j.jcp.2017.04.021.

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24

Boeykens, Freek, Hendrik Rogier, Jan Van Hese, Jeannick Sercu, and Tim Boonen. "Rigorous Analysis of Internal Resonances in 3-D Hybrid FE-BIE Formulations by Means of the Poincaré–Steklov Operator." IEEE Transactions on Microwave Theory and Techniques 61, no. 10 (October 2013): 3503–13. http://dx.doi.org/10.1109/tmtt.2013.2277990.

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25

Vodstrčil, Petr, Dalibor Lukáš, Zdeněk Dostál, Marie Sadowská, David Horák, Oldřich Vlach, Jiří Bouchala, and Jakub Kružík. "On favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D." Computers & Mathematics with Applications 167 (August 2024): 12–20. http://dx.doi.org/10.1016/j.camwa.2024.04.033.

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26

Bobylev, A. A. "Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip." Differential Equations 59, no. 1 (January 2023): 119–34. http://dx.doi.org/10.1134/s0012266123010093.

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27

Nazarov, S. A. "Finite-dimensional approximations to the Poincaré–Steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity." Transactions of the Moscow Mathematical Society 80 (April 1, 2020): 1–51. http://dx.doi.org/10.1090/mosc/290.

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28

BOGATYREV, A. B. "On spectra of pairs of Poincaré-Steklov operators." Russian Journal of Numerical Analysis and Mathematical Modelling 8, no. 3 (1993). http://dx.doi.org/10.1515/rnam.1993.8.3.177.

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29

Laadj, Toufik, and Khaled M’hamed-Messaoud. "Steklov–Poincaré Operator for A System of Coupled Abstract Cauchy Problems." Differential Equations and Dynamical Systems, April 9, 2019. http://dx.doi.org/10.1007/s12591-019-00470-2.

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