MultiLevel Local Time-Stepping Methods of Runge--Kutta-type for Wave Equations

DOI10.1137/16M1084407zbMath1373.65069OpenAlexW2738905093MaRDI QIDQ5358957

Martin Almquist, Michaela Mehlin

Publication date: 22 September 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1084407

zbMATH Keywords

multilevelstabilityfinite element methodsfinite differencesRunge-Kutta methodsemidiscretizationwave equationshyperbolic problemsnumerical experimentmultirate methodsexplicit time integrationlocal mesh refinementlocal time stepping

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Cites Work

• Unnamed Item
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• High order finite difference methods for the wave equation with non-conforming grid interfaces
• Causal-path local time-stepping in the discontinuous Galerkin method for Maxwell's equations
• Review of summation-by-parts schemes for initial-boundary-value problems
• Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
• Acoustic wave propagation in complicated geometries and heterogeneous media
• Multirate explicit Adams methods for time integration of conservation laws
• Stable boundary treatment for the wave equation on second-order form
• Component splitting for semi-discrete Maxwell equations
• Efficient multiple time-stepping algorithms of higher order
• Multirate linear multistep methods
• Stable and accurate wave-propagation in discontinuous media
• A conservative space-time mesh refinement method for the 1-D wave equation. I: Construction
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Nonuniform-time-step explicit Runge-Kutta scheme for high-order finite difference method
• Newmark local time stepping on high-performance computing architectures
• Multi-level explicit local time-stepping methods for second-order wave equations
• Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
• High-order explicit local time-stepping methods for damped wave equations
• Introduction and study of fourth order theta schemes for linear wave equations
• Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations
• Finite elements with mesh refinement for wave equations in polygons
• Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
• Multirate timestepping methods for hyperbolic conservation laws
• Nonuniform time-step Runge-Kutta discontinuous Galerkin method for computational aeroacoustics
• Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
• Stable Coupling of Nonconforming, High-Order Finite Difference Methods
• Error Analysis of a Second-Order Locally Implicit Method for Linear Maxwell's Equations
• HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION
• Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
• Split Runge-Kutta method for simultaneous equations
• Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
• Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
• A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations
• The Effect of Quadrature Errors on Finite Element Approximations for Second Order Hyperbolic Equations
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes
• Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation
• Discontinuous Galerkin Finite Element Method for the Wave Equation
• Spectral Methods
• Multirate partitioned Runge-Kutta methods