Multi-level explicit local time-stepping methods for second-order wave equations

DOI10.1016/j.cma.2015.03.027zbMath1425.65109OpenAlexW2089494256MaRDI QIDQ1734500

Marcus J. Grote, Julien Diaz

Publication date: 27 March 2019

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-01184090/file/Preprint-1410.pdf

zbMATH Keywords

wave propagationfinite element methodsadaptivityexplicit time integrationlocal time-steppingleap-frog method

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) 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)

Related Items (15)

Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation ⋮ Construction and convergence analysis of conservative second order local time discretisation for linear wave equations ⋮ Relaxing the CFL condition for the wave equation on adaptive meshes ⋮ Newmark local time stepping on high-performance computing architectures ⋮ Dahlquist's barriers and much beyond ⋮ MultiLevel Local Time-Stepping Methods of Runge--Kutta-type for Wave Equations ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022 ⋮ A new flux splitting scheme for the Euler equations. II: E-AUSMPWAS for all speeds ⋮ Upwind discontinuous Galerkin space discretization and locally implicit time integration for linear Maxwell’s equations ⋮ Local time-stepping for adaptive multiresolution using natural extension of Runge-Kutta methods ⋮ Arbitrary high order accurate space-time discontinuous Galerkin finite element schemes on staggered unstructured meshes for linear elasticity ⋮ Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation ⋮ Stabilized leapfrog based local time-stepping method for the wave equation ⋮ Asymptotic behavior of acoustic waves scattered by very small obstacles ⋮ Explicit time stepping of PDEs with local refinement in space-time

Uses Software

• ParaView
• Triangle
• AMRCLAW

Cites Work

• Unnamed Item
• Unnamed Item
• ADER-WENO finite volume schemes with space-time adaptive mesh refinement
• An efficient local time-stepping scheme for solution of nonlinear conservation laws
• Component splitting for semi-discrete Maxwell equations
• Exponential multistep methods of Adams-type
• Multirate linear multistep methods
• Adaptive mesh refinement for hyperbolic partial differential equations
• Explicit local time-stepping methods for Maxwell's equations
• Local adaptive mesh refinement for shock hydrodynamics
• A conservative space-time mesh refinement method for the 1-D wave equation. I: Construction
• A conservative space-time mesh refinement method for the 1-D wave equation. II: Analysis
• Space-time mesh refinement for elastodynamics. Numerical results
• High-order explicit local time-stepping methods for damped wave equations
• Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations
• Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
• A discontinuous Galerkin scheme based on a space-time expansion. I: Inviscid compressible flow in one space dimension
• Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations
• Locally implicit discontinuous Galerkin method for time domain electromagnetics
• Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
• HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION
• Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations
• 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
• Numerical Approximations to Nonlinear Conservation Laws with Locally Varying Time and Space Grids
• A Modified Equation Approach to Constructing Fourth Order Methods for Acoustic Wave Propagation
• The Effect of Quadrature Errors on Finite Element Approximations for Second Order Hyperbolic Equations
• Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation
• Discontinuous Galerkin Finite Element Method for the Wave Equation
• Spectral Methods
• An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the One-Dimensional Wave Equation

This page was built for publication: Multi-level explicit local time-stepping methods for second-order wave equations