Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string

DOI10.1016/j.cma.2010.04.013zbMath1231.74146OpenAlexW2072626556MaRDI QIDQ658902

Patrick Joly, Juliette Chabassier

Publication date: 8 February 2012

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

Full work available at URL: https://doi.org/10.1016/j.cma.2010.04.013

zbMATH Keywords

energy preservationfinite elements numerical schemesnonlinear Hamiltonian systems of wave equationspiano string

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Strings (74K05)

Related Items (14)

Efficient energy-preserving methods for general nonlinear oscillatory Hamiltonian system ⋮ Energy-preserving finite element methods for a class of nonlinear wave equations ⋮ Numerical analysis and simulation for a nonlinear wave equation ⋮ Energy Conserving Galerkin Finite Element Methods for the Maxwell--Klein--Gordon System ⋮ An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions ⋮ Time-explicit hybrid high-order method for the nonlinear acoustic wave equation ⋮ Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string ⋮ An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics ⋮ Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term ⋮ Stability and dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string ⋮ New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions ⋮ Time domain simulation of a piano. Part 2: numerical aspects ⋮ Explicit exactly energy-conserving methods for Hamiltonian systems ⋮ Well-posedness and the energy and charge conservation for nonlinear wave equations in discrete space-time

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