A reduced‐order extrapolated natural boundary element method based on POD for the 2D hyperbolic equation in unbounded domain
Copyright policy )A reduced‐order extrapolated natural boundary element method based on POD for the 2D hyperbolic equation in unbounded domain
In this article, we primarily focuses to study the order‐reduction for the classical natural boundary element (NBE) method for the two‐dimensional (2D) hyperbolic equation in unbounded domain. To this end, we first build a semi‐discretized format about time for the hyperbolic equation and discuss the existence, stability, and convergence of the time semi‐discretized solutions. We then establish the classical fully discretized NBE format from the time semi‐discretized one and analyze the existence, stability, and convergence of the classical NBE solutions. Next, using proper orthogonal decomposition method, we build a reduced‐order extrapolated NBE (ROENBE) format containing very few unknowns but having adequately high accuracy, and we also discuss the existence, stability, and convergence of the ROENBE solutions. Finally, we use some numerical examples to show that the ROENBE method is far superior to the classical NBE one. It shows that the ROENBE method is reliable and effective for solving the 2D hyperbolic equation with the unbounded domain.
- North China Electric Power University China (People's Republic of)
convergence, Error bounds for boundary value problems involving PDEs, natural boundary element method, existence, Existence problems for PDEs: global existence, local existence, non-existence, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, stability, proper orthogonal decomposition, two-dimensional hyperbolic equation with a unbounded domain, reduced-order extrapolated natural boundary element format, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
convergence, Error bounds for boundary value problems involving PDEs, natural boundary element method, existence, Existence problems for PDEs: global existence, local existence, non-existence, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, stability, proper orthogonal decomposition, two-dimensional hyperbolic equation with a unbounded domain, reduced-order extrapolated natural boundary element format, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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