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The coupling of natural boundary element and finite element method for 2D hyperbolic equations.

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Titel: The coupling of natural boundary element and finite element method for 2D hyperbolic equations.
Autoren: Yu, Dehao, Du, Qikui
Verlagsinformationen: Global Science Press, Hong Kong; Chinese Academy of Sciences, Institute of Computational Mathematics, Beijing
Schlagwörter: numerical examples, hyperbolic equation, convergence, boundary element, finite element, Poisson integral formula, exterior initial boundary value problems, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, artificial boundary, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, natural boundary reduction
Beschreibung: The paper deals with the coupling of natural boundary element and finite element methods for exterior initial boundary value problems of hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary consisting of a circle with a sufficiently large radius is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in a bounded subdomain. Moreover, the natural integral equation and the Poisson integral formula are obtained in the infinite domain outside the circle. The coupled variational formulation is given. The authors discuss the finite element discretization for the variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, one numerical example is presented to illustrate feasibility end efficiency of the method.
Publikationsart: Article
Dateibeschreibung: application/xml
Zugangs-URL: https://zbmath.org/1998921
Dokumentencode: edsair.c2b0b933574d..5f3fd58fc6cbe1b8dacd5718f181ca02
Datenbank: OpenAIRE
Beschreibung
Abstract:The paper deals with the coupling of natural boundary element and finite element methods for exterior initial boundary value problems of hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary consisting of a circle with a sufficiently large radius is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in a bounded subdomain. Moreover, the natural integral equation and the Poisson integral formula are obtained in the infinite domain outside the circle. The coupled variational formulation is given. The authors discuss the finite element discretization for the variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, one numerical example is presented to illustrate feasibility end efficiency of the method.