Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

DOI10.1016/j.amc.2010.07.079zbMath1342.76019OpenAlexW2163047247MaRDI QIDQ606841

Beny Neta, Joseph M. Lindquist, Francis X. Giraldo

Publication date: 18 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.07.079

zbMATH Keywords

Klein-Gordon equationadvectionspectral elementsRunge-Kuttahigh-ordernon-reflecting boundary conditionHigdonGivoli-Neta

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral methods applied to problems in fluid mechanics (76M22) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (7)

A Legendre spectral element method on a large spatial domain to solve the predator-prey system modeling interacting populations ⋮ A space-time spectral method for solving the nonlinear Klein-Gordon equation ⋮ High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements ⋮ A Higdon-like non-reflecting boundary condition for the Klein-Gordon equation with evanescent waves ⋮ High-order adjustable boundary condition for absorbing evanescent modes of waveguides and its application in coupled fluid-structure analysis ⋮ An energy-preserving Crank-Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation ⋮ An averaged vector field Legendre spectral element method for the nonlinear Schrödinger equation

Cites Work

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• High-order non-reflecting boundary conditions for the linearized 2-D Euler equations: no mean flow case
• A spectral element solution of the Klein-Gordon equation with high-order treatment of time and non-reflecting boundary
• A spectral element method for fluid dynamics: Laminar flow in a channel expansion
• Non-reflecting boundary conditions
• High-order absorbing boundary conditions for anisotropic and convective wave equations
• Absorbing boundary conditions for acoustic and elastic waves in stratified media
• Numerical solution of problems on unbounded domains. A review
• High-order non-reflecting boundary scheme for time-dependent waves
• Finite element formulation with high-order absorbing boundary conditions for time-dependent waves
• High-order non-reflecting boundary conditions for dispersive waves
• High-order local non-reflecting boundary conditions: a review
• A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems
• A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases
• High-order local absorbing conditions for the wave equation: Extensions and improvements
• High-order absorbing boundary conditions incorporated in a spectral element formulation
• High-order Higdon-like boundary conditions for exterior transient wave problems
• Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation
• Numerical Absorbing Boundary Conditions for the Wave Equation
• Radiation boundary conditions for wave-like equations
• High-order Explicit Runge-Kutta Formulae, Their Uses, and Limitations
• Radiation boundary conditions for acoustic and elastic wave calculations
• Radiation Boundary Conditions for Dispersive Waves
• Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatment
• High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection
• Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models
• Radiation Boundary Conditions for Elastic Wave Propagation

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