A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics. I: Formulation. II: Algorithms and analysis

DOI10.1016/S0045-7825(96)01191-7zbMath0892.73059OpenAlexW1993342384WikidataQ127807457 ScholiaQ127807457MaRDI QIDQ1370762

J. Ning

Publication date: 3 August 1998

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

Full work available at URL: https://doi.org/10.1016/s0045-7825(96)01191-7

zbMATH Keywords

dissipationdispersiontime integration algorithmsspectral characteristicsgeneralized Galerkin methodlower-order algorithmsnumerial stabilityparametrized temporal finite elements

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05)

Related Items

An efficient time-discontinuous Galerkin procedure for nonlinear structural dynamics, An explicit family of time marching procedures with adaptive dissipation control, A general framework for conservative single-step time-integration schemes with higher-order accuracy for a central-force system., A time integration algorithm for linear transient analysis based on the reproducing kernel method, Subcycling first- and second-order generalizations of the trapezoidal rule, Collocation methods with controllable dissipation for linear dynamics, Time discontinuous Galerkin methods with energy decaying correction for non-linear elastodynamics, An implicit family of time marching procedures with adaptive dissipation control, Saddle-point principles and numerical integration methods for second-order hyperbolic equations, The Nørsett time integration methodology for finite element transient analysis, Bi-discontinuous time step integration algorithms. I: First-order equations.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Practical performance of the \(\theta _ 1\)-method and comparison with other dissipative algorithms in structural dynamics
• Canonical Runge-Kutta methods
• Primal and mixed forms of Hamilton's principle for constrained rigid body systems: Numerical studies
• Mixed finite element formulations in the time domain for solution of dynamic problems
• A general framework for interpreting time finite element formulations
• Space-time finite element methods for elastodynamics: Formulations and error estimates
• A unified set of single-step asymptotic annihilation algorithms for structural dynamics
• Variational approaches for dynamics and time-finite-elements: Numerical studies
• High-order integration of smooth dynamical systems: Theory and numerical experiments
• A unified set of single step algorithms. Part 1: General formulation and applications
• Time integration of the equations of motion in mechanism analysis
• Time finite element methods for structural dynamics
• Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum
• The Stability Of The Houbolt Time Marching Scheme In Non-linear Systems
• High‐order hierarchical A‐ and L‐stable integration methods
• Instability, chaos, and growth and decay of energy of time‐stepping schemes for non‐linear dynamic equations
• Dynamic finite element analysis applied to a simple model exhibiting dynamic instability